Shell and Spatial Structures

This paper introduces a novel structural concept for freeform shells, in which the shape is decomposed into flat tiles to be assembled sequentially with the help of falseworks. Once the structure is completed, the tiles are post-tensioned to minimize the tension forces and avoid detachment. The entire design process, from an input shape to fabrication, is managed by an automatic pipeline. The input shape is segmented into a field-aligned quad mesh, computed from the principal stress of the thin shell. The flat tiles are obtained by extruding each face along the normal of the best-fitting plane per face. The contact between adjacent tiles is ensured only at their edge midpoints so the forces can mainly flow along the cross directions. The best configuration of cable paths and pre-loads is found by solving a constrained optimization problem exploiting a reduced beam model of the shell. All tiles can be prefabricated in the shop with an adaptable and reusable molding system. Once the structure is completed, the top surface is finally completed with an in situ cast that fills the gaps and activates the entire shell behavior. In contrast, the bottom surface maintains its jagged aesthetics.

The classical funicularity concept for shell structures has been extended defining the Relaxed Funicularity (R-Funicularity). A parameter called generalized eccentricity has been used for this purpose, following that a shell is R-Funicular when the generalized eccentricity doesn’t exceed an admissibility limit. A shells’ shape optimization process aiming at finding R-Funicular analytical shells is here modified at the geometry definition level by describing the shells’ shape with spline surfaces and using the position of the control polygon vertices as optimization variables. An isogeometric (IG) refinement is applied in order to improve the local control of the shape in the optimization process. An advantage of this approach is that, since it introduces new vertices in the control polygon, the number of optimization variables becomes tunable. Namely, starting with the lowest number used to generate the initial geometry, the additional vertices can possibly be entered as new variables whenever a more accurate local control of the surface is needed. We present significant numerical examples.

Progressive snap through-buckling is a catastrophic collapse that is observed in slender and shallow structures such as reticulated roofs or gridshells [1]. It is usually triggered by a local instability and it spreads up to a portion or to the entire structure causing the static failure. To predict the extent of a local snap to the surrounding nodes, the mechanical consequences of local instabilities have to be investigated: apart from static force rearrangement, the impulse of the dynamic rebound can force a domino effect. In this work, each dynamic rebound has been tuned to an input frequency note to compose a simple music sequence with progressive collapses of Von Mises Truss ensembles. Local instabilities have been based on the interaction formulation [2] and fully elastic material and perfect connections have been considered for the whole deformation process. Finally, a comparison between perfect and imperfect systems is presented to translate imperfection sensitivity to musical performance.

The performances of gridshells depend on the topology of the grid but also on the geometry of the underlying surface. Topology and geometry are linked: the shape of a hanging chain model depends on the pattern of the suspended fabric. In this paper, a method is proposed that generates topologies by varying continuous parameters. The obtained grids are adapted to the support conditions of the considered surface: elements converge towards the supports and arrive perpendicular to the edges otherwise. Grids are then lifted: the spatial mesh is the result of an optimisation to have a funicular surface and flat panels. The spatial mesh is then mechanically evaluated and its performance according to different criteria is represented in a Pareto front. A non-intuitive result shows that a large number of different topologies are situated on the Pareto front. These results show the strength of the method to explore different topologies.

A numerical form-finding procedure, based on Isogeometric Analysis (IgA), is proposed to determine the elevation of a shell having a prescribed covered area so as to carry applied loads in a pure membrane state of stress. The boundary-value problem of a membrane shell is described by Pucher’s equation in terms of external load, Airy potential and shell mid-surface height. Membrane stress components at a point are computed via second derivatives of the Airy potential. Within the IgA framework, the equivalent weak form of the problem is derived and the resulting integral equation is discretized by approximating the relevant fields as a linear combination of control point values and B-Spline basis functions. Once the external load is prescribed, control point values of the Airy potential are computed via a nonlinear optimization routine aimed at minimizing thrusts at edge supports while ensuring a no-traction principal stress state fulfilling boundary conditions. The resulting shell form is then computed in terms of control point heights. Two numerical examples show the effectiveness of the proposed approach.

In 1949 the construction company Nervi & Bartoli patented in Italy a construction system for two-dimensional structures with ribs bent in accordance with isostatic lines of bending moments or normal stresses, invented by an engineer from its staff: Aldo Arcangeli. In the years to come “isostatic lines” ribbed slab would become one of the main and distinctive archetypes used by Pier Luigi Nervi throughout the world. This is a cast-in-place reinforced concrete ribbed slab combining static efficiency with aesthetic and spatial qualities. The paper will present different case-studies, demonstrating (with a trans-disciplinary approach) how and when aesthetic, static and constructive issues overcome a rigorous mathematical morphogenesis. Case studies will show how the different patterns of the ribs are influenced both by structural instances (e.g. geometry, loads and constraints) and by the specificities imposed by each design and building site (e.g. use, craftmanship, economy, and replicability).

Grid-shell structures are popular in roofing for their aesthetic appeal and structural advantages, enabling the construction of lightweight, large roofs using slender elements. However, their widespread use is limited by the complexities involved in their construction. This paper presents an innovative solution to address the challenges associated with grid-shell construction. The proposed approach combines the enhanced Multibody Rope Approach (i-MRA) form-finding method with metaheuristic optimization algorithms to identify optimal design solutions from both structural and constructional perspectives. To facilitate practical implementation, a parametric code was developed using MATLAB, which was later converted to C# for integration with the parametric design software “Grasshopper”. A multi-objective optimization problem was formulated to minimize the use of different structural elements, reduce material consumption, account for production waste, and ensure compliance with structural verification requirements. The optimization process yielded a Pareto front solution that enables the conceptual design of grid-shell structures. This approach provides an efficient and innovative solution to the complex construction of grid-shell structures, which could potentially pave the way for their widespread use in the future.

In 2015–2023, Parametric Building Systems LLC developed and erected free-form aluminum grid shells using only bolted assemblies. The materials used for all core and node elements are high—strength aluminum EN AW-6063 T5/6, EN AW-6082 T5/6. Beam elements and nodes are connected by high-strength bolts with a special coating without welding. The core elements of the grid shell frame are manufactured at the factory, the nodal elements are individually manufactured on 5-axis CNC machines.The design is carried out using parametric and BIM design tools Rhino3D/Grasshopper/Kangaroo/Karamba3D, which ensures the design of mesh shells at the LOD 500 level of detail. One of the advantages of using aluminum is its low volumetric weight, less than three times that of steel, which makes it possible to install without the use of heavy cranes and other lifting equipment.One example of such projects is the curved aluminum grid shell of the Avenue Mall shopping center. It is a shell of arbitrary shape and has dimensions of 55 m × 50 m, the maximum mark of the roof top from ground level is +25 m. The area of the coating, consisting of a metal frame and glass triangles, is 2750 m2. The average length of the core elements is 2.5 m; the angles between them are as close as possible to the value of 60°.

In the present work, the Cohesive/Overlapping Crack Model is extended to the study of masonry or plain concrete structures, which are subjected to off-center compression. Multi-cracking and multi-crushing damage phenomena are simulated by means of the Crack Length Control Scheme, in order to obtain a complete load history of the vaulted structure. This Nonlinear Fracture Mechanics model reveals a high capability in predicting the elastic-plastic-softening behaviour of arches and vaults as well as the local mechanical instabilities, such as snap-back and snap-through, occurring during the post-cracking regime.In the first part of this paper, the Cohesive/Overlapping Crack Model and a description of the adopted multi-crack numerical procedures is provided. In the second part, some parametric analyses on scale effects in masonry arches are reported together with the results obtained for a real case-study. Finally, some future developments and applications of the model are presented.

The construction of the suspension bridge over the Strait of Messina has been stopped due to political and economic problems and it seems also that the final approved project may have problems about his “serviceability” with respect to the wind action on the structure.From since 2006 we have enterprises an intensive study of about an innovative solution for a design of an alternative solution for Messina based on a new type of suspended structure. In 2022 we have also performed a simpler solution applied on the design tender project based on the solution of the Italian engineer Sergio Musmeci.

Architecture is going through major changes as automation in construction is radically transforming standard processing technologies and could lead, in the long-term, to disruptive technologies such as 3D-printing and robotics being applied to improve construction processes. This paper describes the adoption of a parametric approach in the design, fabrication, and assembly of dry-constructed, lightweight, wooden shell structures.The design of the structure in a parametric environment simplifies the process of running multiple kinematic simulations of the construction sequence. These simulations are used to determine the feasibility of each simulated sequence and detect collisions and errors in the robotic arm path. The instructions from the simulation stage are passed through a series of steps to a single collaborative robotic arm that assembles the structure with minimum human intervention. The simulated tests are carried out using a single KUKA lbr iiwa R800 robotic arm equipped with a 2-finger parallel jaw gripper.The complexity of the design requires a multi-disciplinary effort in the development of suitable systems. This research aims to show the potential that robotics and 3D printing could offer in terms of enabling the adoption of more complex and efficient free-form shell structures with decreased need for formwork and temporary supports.

Nowadays, it is crucial to develop analysis methodologies to confidently simulate the structural behaviour of historical masonry constructions. From this perspective, the possibility of using reality-based models as starting data is becoming increasingly attractive. This methodology allows considering some aspects that are usually neglected in the analysis of masonry structures, e.g., the as-built geometry and the block arrangement. This study investigates the implications of applying this approach to a case study: the Palazzata di Vicoforte in Piedmont, Italy. Starting from dense point clouds obtained through LiDAR acquisitions and photogrammetric surveys, a very accurate NURBS modelling has been performed to develop Finite Element micro-Models of two cross vaults characterized by very similar macro-geometry, but different brick pattern. The models are numerically analysed under differential abutment settlements. Comparison of the results obtained from vaults of ideal geometry shows the importance of accurately modelling both macro and micro geometry.

There are 4 fundamental 2nd order tensors in shell theory, firstly the stress and internal moment tensors which are in equilibrium with the applied loads and loading couples, and secondly the rate of membrane strain and the rate of bending tensors which are compatible with the velocity of the shell as it deforms.Shell theory is completed by the constitutive relationships which give the stress and moment in terms of the membrane strain and bending deformation.The fundamental tensors are associated with a number of vectors including the applied loads, loading couples, velocity and angular velocity. We show that the 4 fundamental tensors can all be linearly assembled from vectors using the gradient and also a 3rd order tensor containing the surface permutation tensor and the unit normal.Since a vector describes a surface in 3D space, all these quantities have a graphic significance which can be described using images and models - 3D graphic statics which is the application of differential geometry to statics.We demonstrate that if the moment is described in an appropriate way, using 2 vectors, then internal moments are in equilibrium with zero imposed loads and loading couples, although boundary moments and forces are required. Thus internal moments in shells are ‘redundant’ in the nomenclature of structural theory. For flat plates, one of the redundant moments has to be replaced by a non-redundant moment.

Structural optimization is an active research branch in engineering, especially dealing with complex and concomitant aspects likewise in seismic design. Capacity design criteria for seismic design and detailing must be respected, e.g. according to the “strong-column weak-beam” principle. In steel structures, the choice of a specific beam-column joint typology may strongly affect its behavior under horizontal actions. In this study, the authors investigated the role of beam-column joint stiffness within an optimization paradigm related to steel structure frames. Specifically, the authors adopted simplified modeling assumptions for analysis under lateral loads in the Python environment and Computer and Structures inc. SAP2000 finite element software. Indeed, the main focus hitherto is oriented toward the problem definition accounting for geometric constraints and beam-column rotational stiffness capacity. Future investigations will adopt more realistic modeling procedures accounting for the typical non-linearities involved during strong dynamic actions.

In the present work, a refined theory with three-dimensional capabilities is proposed for the structural analysis of shell structures made of smart materials for advanced engineering applications. Principal curvilinear coordinates are used for the geometry definition of the structure. The kinematic description of the configuration variables is performed according to the Equivalent Single Layer (ESL) approach with higher order theories. A constitutive relation for elastic anisotropic laminates is considered. The fundamental equations, written in the strong form, are derived from the Hamilton principle together with the boundary conditions, and they are numerically solved by means of the Generalized Differential Quadrature (GDQ) method. The accuracy and the computational efficiency of the present theory is shown by means of different applicative examples. The numerical predictions of the present ESL model are compared to refined solutions coming from three-dimensional Finite-Element-based simulations. Furthermore, some parametric investigations are performed on a doubly-curved panel made of Variable Angle Tow (VAT) anisotropic materials in order to show the sensitivity of the VAT distribution on the dynamic response of the shell under consideration. The present formulation is very accurate if compared to refined models, despite its reduced computational demand, and it can be useful for design purposes of doubly-curved elements made of advanced materials.

In this research, equilibrium analysis of curved structures is carried out via a computational approach based on the constrained force density method, with the aim of taking into account both the effects of a finite compressive strength of the material and any possible stereotomy of the voussoirs composing the structures. The procedure relies on independent sets of branches for networks with fixed plan projection. At each joint, a suitable set of local constraints is formulated to take into account the moment capacity. Then, a multi-constrained minimization problem is stated. In order to validate this approach, a benchmark case study is examined, i.e., a dome with arbitrary stereotomy. To this purpose, a classical semi-analytical graphical method, originally devised by the French scholar Durand-Claye is adopted. A re-visited version of this method, formulated in terms of the static theorem of Limit Analysis, is exploited in order to determine the complete set of admissible solutions with respect to both the equilibrium conditions and the strength requirements of the material.

Aldo Favini, an exponent of the Italian structural school, was entrusted with the design of a fuel station in Sesto S. Giovanni for Aquila s.p.a. company. He envisaged a peculiar structure: a thin cylindrical vault made of reinforced concrete, whose external shape was sinuously corrugated with a thickness within the value of 60 mm. The corrugated roof is supported by a stiff hollow transverse beam, which rests on a V-shaped pillar and a slender column. Unfortunately, this structure has been demolished. The proposed corrugation shows an interesting enhancement “by shape” in structural behaviour since the shape increases the stiffness and the bearing capacity with respect to a plane surface, allowing for such a reduced thickness. Corrugated shells are also known for the iconic dome of the “Palazzetto dello Sport” in the Flaminio district of Rome, whose rim is gently corrugated and provides structural enhancements. This paper aims to give a new gaze to the tradition of shell construction in Italy, where the shape is wisely adapted to improve structural performances efficiently. The development of analytical and numerical methods to analyse such structures is crucial, especially when a safety assessment is required before a refurbishment to avoid disgraceful decisions like the demolition of the “Aquila” fuel station. Furthermore, although nowadays the building of corrugated concrete shells is decreasing, new construction techniques of 3d concrete printing make readily available the realization of sophisticated shapes, where corrugation should be fully included because of their natural predisposition to improve the mechanical behaviour of shape-resistant structures.

Masonry vaults are common elements in heritage buildings and, due to their age, may accumulate damages and deformations due to various actions like overloads, support movements, earthquakes, etc. The use of terrestrial laser scanners and structure from motion photogrammetry survey to study these deformations can offer valuable information for structural assessment and conservation, especially when limited knowledge of buildings history is available. The analysis of the deviation between the surveyed point cloud and a reference geometry can reveal deformation patterns and aid the damage detection and action evaluation on the structure. This paper aims to explore the role of the reference geometry to provide a reliable and more accurate identification and quantification of deformations. Deviation analyses will be performed on the vaults of the main nave of two different churches with different reference geometries (i.e. geometries derived from the survey and geometrical primitives fitted on point-cloud) and the results are discussed comparing the deviation maps obtained and the already known deformation and caused.

Several families of lines can be generated on a curved surface by plotting different properties. These lines can be classified as either geometrical, or strictly mechanical if the surface becomes a shell structure. Here, we plot these lines on shells and discuss the connection between them, as a preparatory investigation of the structural behaviour of curved surfaces. This analysis is performed by primarily using Rhinoceros [1], Grasshopper [2] and Karamba3D [3]. We also introduce a new typology of mechanical lines: the principal eccentricity lines. Finally, we propose a parametric analysis of different structural surfaces, in order to highlight the most relevant lines for the mechanical behaviour of shell structures and their possible use. Central to the premise of this work is the idea to explore the language of structural form, to the advantage of a structurally inspired design that can ensure the coexistence of structural and architectural design goals.

The Thrust Line Analysis (TLA) is a methodology that can be employed to identify the position and shape of the thrust line in a masonry arch, providing information on the minimum and maximum thrust solutions that can exist within the arch. This paper presents an enhancement to the TLA that considers the influence of the Fiber-Reinforced Cementitious Matrix (FRCM) composite system. The numerical examples presented in this paper show that the proposed extension to the TLA can accurately forecast the behaviour of reinforced masonry arches and can offer valuable perspectives into the design and evaluation of such structures.

The paper deals with design and construction stages of N’Albero, a temporary spatial steel structure built to be the main 2016 Christmas touristic attraction on Naples seafront. Opened to the public for three months, it was visited by more than 250.000 people, estimating the simultaneous presence of 750 visitors. N’Albero main structure consisted of 20.000 prefab steel pipe elements, adopting Allround System by LAYHER, a fast-assembly, safe and economic solution. The whole spatial system was about 45 m-high, with a squared base (30 m × 30 m), tapering gradually to the top through three sky terraces. Using light multidirectional scaffoldings, the main design aspects to consider were: stability, uplift or sliding of the structure; strength of components sufficient to withstand loads without failing; serviceability of a light structure under large deflections. Estimating a dead load of about 200 tons, a ballasting load of 130 tons was used to ensure global stability against wind force. For this deformable system, loading tests were performed during construction to check design, applying inclined (45°) concentrate forces at each terrace level: the effect of these forces, assigned at +13,00 m (F = 5t), +19,00 m (F = 5t) and +31,00 m (F = 2t), was obtained using steel tendons, connected to the structure through an additional steel truss, while the acting hoist was anchored to a crane as counterweight. During tests, all the applied forces were registered by a dynamometric cell. No visual damages or elements instabilities occurred in situ, validating design calculations. Furthermore, these tests revealed a high deformability of the structure, not readable from FEM model, requiring precautionary changes to the original solution. This makes loading tests a reliable way to check and improve structural design in the case of framework with high deformability.

In this study, a novel optimization method has been applied to a geodesic dome inspired by real-world similar structures in which the environmental and cost impact has been minimized by reducing raw materials at the production stage. To achieve this goal, the Cutting Stock Problem (CSP) has been embedded inside the global optimization procedure of the entire structure. The CSP is one of the most famous combinatorial optimisation problems in the (one-dimensional) bin packing problems (BPP) class. The main objective is to produce $$d_j$$ d j copies of each item type j (i.e. elements of the structures with the same cross-sectional Area) by employing the minimum number of bins such that the total weight in any bin does not exceed the capacity. In the civil engineering field, the traditional approach to structural optimization aims to improve the load-bearing capacity and the global performance of the structure itself. This includes, for instance, the maximization of the performance ratio through the minimization of the structure weight. However, this goal doesn’t guarantee maximum efficiency in reusing structural elements and minimising waste during the industrial production phase. To overcome these limits, authors propose a stock-constrained structural optimization in which a heuristic search technique is adopted in order to find the best spatial arrangement of elements composing the structure whit the lowest cut-off waste. Finally, considerations have been discussed by comparing the solution obtained by the traditional weight-minimization approach and the stock-constrained one.

Ferrocement is a thin reinforced cementitious composites of hydraulic cement mortar with layers of wire steel mesh, which has been widely used in the roofing systems in major 20th-century architectures. However, few studies have analyzed its durability for preservation purposes and stiffens time-dependency evolution. In the present paper the results of a recent testing campaign on ferrocement specimens subjected to a corrosive environment are presented. The experimental campaign in monitored by 3D-Digital Image Correlation (DIC) signal processing. In particular, the external evidence obtained by the reconstruction of the strain field may be directly correlated with the 3-D localization of the micro-raking formation in the tested specimen obtained by AE detection. The aim was to assess the behavior of historical ferrocement (used by Pier Luigi Nervi in his constructions) and its durability for identifying the best procedures to protect and preserve it.

Due to their ability to provide broad, lightweight roofs with slim main structural elements, grid-shell roofing systems are becoming more and more common in contemporary engineering and design. However, their widespread and extensive use outside of high-end projects or super architecture has been constrained by their complex and expensive fabrication. In order to solve this, it has been demonstrated that the Multi-body Rope Approach (MRA) is successful in calculating structurally efficient geometries that can decrease internal stresses, which are closely related to the structural shape of gridshells. Different MRA-improving strategies are put forth in this paper: The number of various structural components needed to build a gridshell can be significantly reduced thanks to Multiple Order MRA (MO-MRA) and Repulsive Nodes MRA (RN-MRA) strategy. Due to mass production, the suggested methodology offers lower manufacturing costs as well as improved building stage management. Finally, by a Matlab code and the new approaches were tested in various case-study structures.

Due to their age, elevation, and prolonged exposure to both static and dynamic loading conditions, historical constructions and old masonry structures such as medieval and Gothic cathedrals, bell towers, and other similar structures, are particularly vulnerable. The central nave vault of the Turin cathedral was subjected to an acoustic emission (AE) monitoring technique for structural integrity assessment. These findings are correlated with the evidence from the Thrust Network Analysis (TNA) performed on the cathedral’s central nave vault, taking into account the additional elements added at the start of the XXth century to lessen horizontal forces. In this situation, the analysis’s findings are strictly correlated to the vault’s 3D AE localization, which was obtained by the triangulation method.

A new type of habitation vehicle for future Mars colonization and exploration missions is proposed. The habitat vehicle is characterized by the movement of the habitat cell of varying sizes: from medium-small, for temporary colonization of near settlement, to larger with a greater autonomy, for the exploration purpose of unknown area. The vehicle consists of a pair of compass-shaped structures that support the habitat cell which, once the settlement position is defined, can be laid on the ground.The mechanical and structural configuration allow the module to be raised from the surface, lowered, and transported to a constant altitude with horizontal layout. The module is kept at a constant altitude and horizontal trim during the motion of the vehicle. Furthermore, the function of being able to lower to the ground surface to allow access is ensured. The height and the constant trim during the motion and the lowering and ascent are achieved with a system of ropes wound on pulleys moved by the motion of the vehicle itself, with suitable transmission. The structural components it is previewing to exploits the principle of tensairity strucutres, with the aim of making maximum use of the material and reducing the mass of the structure facilitation the transportation from Earth to Mars.

The proposed method for the definition of the form is based on a multi-body rope approach (MRA) with masses connected by inextensible ropes characterized by a certain slack coefficient and by different constraint conditions. These parameters played a fundamental role in the definition of the shallowness ratio of the grid (rope), and therefore in the effect of the instability of the reversed shape under loading. In this paper, different MRA enhancing strategies were proposed and discussed. These approaches were used to determine the final shape of a funicular prototype for a pavilion inspired by Guarino Guarini’s architecture. The prototype project is based on the principle of Gaudi’s inverted catenary arch. It is composed of a series of arches, each one obtained hanging a metallic chain - which assumed the shape of a catenary curve - and then welding all the rings in order to fix its form. Different possible configurations will be described in this paper.

In the present paper, a form-finding of shallow grid shells was introduced based on the multi-body rope approach (MRA) for the definitions of vaults with optimized shapes and different hole percentages. In order to obtain experimental validation, a physical model was reproduced at the laboratory scale performing ad hoc measurements to compare the observed respect to the simulated behaviour. A 3D printing procedure based on the Fuse Deposition Modeling (FDM) technique in polylactide (PLA) material was used to realize formworks of the cement-based blocks of the scaled prototype. Several static and dynamic load configurations are investigated, collecting the parameters into a sensitivity analysis, which mainly affects the structural behaviour. To compare the natural frequency obtained by experimental tests with those evaluated with a numerical model, an impulse test has been performed. Results show that an improvement in the modelling strategies adopted for the numerical model is necessary for the identification of the real structural dynamic response of the vault.

The construction industry has a massive impact on climate change, and reducing its environmental impact is a critical challenge that requires innovative solutions. Shape and topology optimization methods can play a crucial role in addressing this issue by optimizing the structural geometry and material distribution. In this paper, we present a novel design approach for optimizing shape, topology, global warming potential and buildability. The proposed approach optimizes the shape and layout of structural elements to minimize the overall embodied energy and carbon emissions of the structure while ensuring that the structure is constructible. The methodology is demonstrated through case studies, the optimized design is evaluated based on the performance criteria and constraints that resulting in significant reduction of design cycle time as well as environmental impact while improving buildability. The research presented in this paper provides valuable insights for designers and engineers seeking to create environmentally sustainable yet elegant spatial structures with optimal buildability.

A geodesic dome is a hemispherical thin-shell structure based on a geodesic polyhedron. The triangular elements of the hemisphere are structurally rigid and distribute the structural stress throughout the structure, making geodesic domes able to withstand heavy loads considering their size. After the first geodesic dome was built in Jena (Germany, 1922) on top of the Zeiss optics company as a projection surface for their planetarium projector, thanks to R. Buckminster Fuller, the geodesic domes have been explored far more thoroughly. As a result of their properties, these structures are used for many purposes: as residential modules, greenhouses, water reservoirs and as expositive pavilions. The present paper focuses on geodesic domes optimization, minimizing the overall volume of the frame structure and its connections. In the optimization phase, the base radius of the dome is considered constant, representing a shape constraint. The frequency variability allows for modification of the frame’s number, thus varying the structural topology while acting on the shape of the sections (shape optimization). In the case study, self-weight and asymmetric load actions are considered while including the construction aspects for the assembly of a geodesic dome. The optimization phase involves evolutionary genetic algorithms (EAs) exploiting the results of a Finite Element Analysis (FEA).

The contribution focuses on the patents (1958–64) for modular thin vaults in reinforced concrete filed by the German engineer Wilhelm Johannes Silberkuhl (1912–1984). The thin modular vaults – shaped on narrow hyperbolic paraboloid (HP) sectors – are mainly applied for the roof of industrial buildings and were widely used in Germany and abroad in the 1960s and 1970s. Mainly known as Silberkuhl System, the vaults are entirely prefabricated and prestressed on-site. The study explores the relation between form, construction process, and structural conception of the Silberkuhl modular HP-shells, with the aid of a powered visualization framework based on parametric 3D modeling. The use of a computational modeling environment provides insight into the geometry and the structural behavior of the vaults. The application of the vaults for the Magazzino Merci Rinascente in Rome (1962), still existing, is presented as a paradigmatic case study for the spreading of the system in Italy.

Nowadays, some innovative spatial structural typologies among others rely on timber-concrete hybrid solutions for designing modern buildings. However, the dynamic identification analysis may be more elaborate, and sometimes troublesome, due to the coupling effects of the different dynamic nature of cross-laminated timber and reinforced concrete members. In the current manuscript, the authors explore some preliminary results of the dynamic analysis of a hybrid timber concrete building case study. The operational modal analysis (OMA) based on output-only techniques has been employed, referring specifically to enhanced frequency-domain decomposition (EFDD) and the stochastic subspace identification (SSI) methods. The authors compared several ambient vibration OMA results with forced shaker-induced vibration responses highlighting the absence of nonlinearities during in-service operational conditions in two different moments.

Thin-wall shells (steel plates, steel cylindrical shells, steel spherical shells, etc.) are widely used in many engineering fields such as construction, machinery, chemical industry, navigation, and aviation because of their light weight and high strength. Their failure modes under static pressure or impact dynamic load are mostly buckling instability, and the failure is very sudden, often causing structural failure or even catastrophic accidents without obvious symptoms. In this framework, the significance of this paper is that it considers the influence of external environment corrosion on steel shells’ bearing capacity using plate and shell classical stability theory, and investigates the stable bearing capacity of thin-wall steel shells in view of corrosion impact. By this approach, a theoretical method for the time-varying stable bearing capacity of plate and shell thin-walled steel members under the simultaneous action of corrosion and temperature changes is obtained, providing a useful theory for complex engineering practices such as corrosion and temperature changes, including fire actions.

The undeniable fame achieved by thin concrete shells during the XX century is a well-known story. Their shapes represent the apex of the intersection between science and technology as well as a cultural distinctive character of modernity. The reasons for this enduring attraction on engineers and architects lay in the fact that the design of these geometry-based structures has a parametric nature. The identification of key parameters to control the pre-design phase has supported their design firstly in the realm of membrane theory and then, through the finite element calculation, in the bending theory, determining the extraordinary possibility of optimization that these structures still testify today. This paper illustrates the opportunity offered by the application of current parametric modeling and structural analysis tools to achieve a time-efficient structural evaluation of the influence of the morpho-typological choices make in the pre-design phase on the overall structural performance of hyperbolic paraboloid structures. Retracing the logic and processes of the past with new tools, the proposed analysis opens up new paths for future thin shell design applications.

Tensegrity systems are structures in equilibrium under a self-stress state prior to the application of external loads. Such self-stress state is the result of the superposition of self-stress basis vectors. Tensegrities have complex nonlinear behavior when subjected to external actions (loads or imposed displacements). In this work, the robustness of this particular structural typology is evaluated by numerical simulations. Robustness is the ability of a locally damaged structural system not to behave in a manner disproportionate to the original failure, i.e., the insensitivity to local damage. This concept and its insights have been thoroughly analyzed for several structural systems, as in the case of frame structures. To date, limited studies have been performed on the robustness of tensegrity systems to unexpected conditions. Among the potential damages, one can consider the settlement of one of the supports, the reduction of prestress and the failure of one of the cables. The present study reports the results of a set of damage simulations on a simple T-3 prismatic tensegrity structure. Several risk factors are considered to study the response of the structure to unexpected damage. In particular, the tensegrity configuration is subjected to different stress loss in the constituent elements. The results are obtained through simulations performed in MSC.visualNastran 4D (vN4D), which run dynamic simulations by merging CAD, motion, FEA, and controls technologies into a single functional modeling system. The models were established to obtain different equilibrium configurations and conditions of loss of equilibrium, with the corresponding large displacements measured for the most significant points of the structure, assumed as markers for the resulting effects on the structure.

The premises for Law and Political Science faculties are an important milestone in the building programme of the University of Turin. Not far from the historical seat of the University, the Luigi Einaudi Campus has transformed an abandoned industrial area into a new cultural forum for the city. The geometric complexity of the layout, which originates from the free volumes designed by Foster + Partners, has led to a sophisticated internal spatial differentiation and to innovative solutions developed to give formal unity due to the roof solution. The system of the light-weight tent structures of the roof is characterized by fifty-two reticulated arches anchored at the reinforced concrete slabs on the top of each architectural volumes. The arches are topped by waterproof teflon-coated fiberglass membrane with high mechanical strength and stability against weathering. In this paper, a study of some most representative portions of the structure is proposed considering the influence of connection stiffness reductions. In particular, the robustness under conditions of reduced bracing and various stiffness configurations of the steel nodes of the interconnected arches is an evident problem to be assessed in these kinds of buildings.

We introduce a new class of quadrilateral gridshell structures in axial force equilibrium where beams run symmetrically to the principal stress directions of their limit membrane shell. This kind of structures have the property that, at each node, the axial forces in the four connected beams are approximately equal. This allows for a more homogeneous distribution of forces in the structure, particularly in shapes where stresses are significantly anisotropic, in which case a conventional gridshell typically results in numerous beams remaining nearly unloaded. In this work, we first discuss the properties of principal symmetric structures and evaluate their advantages relative to other types of gridshells. We introduce then a computational pipeline for the design of such structures based on a quadrilateral remeshing and a subsequent optimization, and show some results.

We present a numerical and experimental investigation on the nonlinear equilibrium paths and elastic stability of pinned shallow arches realized by buckling a straight strut and then subjected to a transverse central point load. Finite element analyses were run to compare the behavior of arches with and without initial pre-stress condition. The effects of initial shallowness ratio, axial-to-bending stiffness ratio, and initial geometric imperfections on the equilibrium path and bifurcation points were investigated. As an experimental verification, laboratory tests were conducted on a pinned-pinned shallow arch obtained by buckling a thin, slender steel bar. Static and dynamic measurements were carried out to determine the load-displacement curve, the subsequent static deformed configurations, the frequency-load curves, and the buckling load. The acquired data were used for buckling load predictions and to obtain stability domains in terms of form factors and imperfection-sensitivity parameters.

The collapse of a structure serves as a profound testament to its design quality. Forensic studies in structural engineering have revealed that collapses are intricate events with various interconnected metrics. The introduction of resilience and robustness concepts has revolutionized structural engineering, surpassing the conventional approach of designing for maximum load. This paradigm shift is especially crucial for shells and membranes. Postbuckling investigation emerged as a significant area of study since 1970, offering insights into shell design and stability. This paper focuses on the effect of the improved Multibody Rope Approach (i-MRA) for form finding on the postbuckling behaviour of gridshell structures. The i-MRA exhibits superior postbuckling behaviour, which directly relates to the method’s underlying mechanics. The investigation centres around the mosque roofing in Dakar, Senegal. A comprehensive analysis was conducted, encompassing linear buckling analysis and geometrically nonlinear analysis with imperfections (GNIA) under incremental loading. The study successfully captured crucial insights into the behaviour of the structure throughout both the buckling and postbuckling phases. Additionally, a standard square-plan gridshell was analyzed to validate the findings and evaluate their generality. The research findings demonstrate the efficacy of the i-MRA and provide valuable insights for the design and stability assessment of gridshell structures.

We recently extended the definition of funicularity for continuous shells, introducing the concept of Relaxed Funicularity (R-Funicularity or RF). Funicular shells are defined as shells whose static behavior is given by only local membrane actions. Extension to RF is needed as funicular shells [1] can only attain pure membrane behavior for very specific boundary conditions (bcs). The RF born also for quantifying the quality of the shape of a shell, for given load and bcs, including ’small’ moments effects. Quantification of RF is made by defining a generalized eccentricity (GE) measure and verifying that the GE fall inside some eccentricity limits. Aim of this work is to discuss the nature of the GE and its associated eigenvalue problem, that allows to calculate principal eccentricities (PEs) and their directions. It is also shown how the directions of PEs are related to the relative angle between the principal directions of membrane and bending internal actions.

Bonding lithitic blocks using a pneumatic vacuum is a born by fortune research that started in 2006 at the exhibition Città di Pietra curated by prof. Claudio D’Amato Guerrieri at the X International Architecture Exhibition in Venice. In this occasion, professors D’Amato and Fallacara presented the Alexandros Obelisk. During its deconstruction, it was not possible to proceed with the separation of the ashlars due to the particular conformation of the aforementioned joints whose shapes had created a bonding through pneumatic vacuum. This situation inspired the idea of an innovative construction process of vaulted spaces without the use of centrings. A first attempt has been done by Giuseppe Fallacara in 2019 with a lithic oblique obelisk. This paper aims to illustrate the further research that is being carried on in order to apply the vacuum for structures made with innovative materials and technologies as 3D printing.

Parametric structures in composite material, such as fiber glass and carbon fiber with bicomponent epoxy resin, are usually constructed through the “robotic coreless filament winding” technique, which consist of weaving each fiber element according to a specific numerical parametric definition.This paper illustrates various designs of pavilions in composite materials and discusses architectural implications of using this technology in terms of tectonics and space generated.The topic of research for this paper is the analysis and the description of fiber pavilion designed using the methods of computational design and digital fabrication of spaces and structures.The aim of this research project is to blend textile technology with the stereotomic knowledge of stone construction to parametric design and digital fabrication in order to prototype shell-like structure.One of these is a tree-shaped structure with the stem and the crown which are joined together; or a fiber arch made by triangular blocks. They are a starter point of new structural projects for covered spaces.New construction technology and typology to design new structural shapes are the two goals to demonstrate in lithic and stereotomic field, to transform them into complex but light structures.The next stop of the research will be building a fiber tripod pavilion.

Stereotomy – also known as “the art of cutting solids” – is a discipline that exploits rules of descriptive geometry to optimize the ashlars of a vaulted space, considering aesthetic, static and functional matters. Stereotomy and its innovation through the use of CNC machines have been investigated at the Polytechnic of Bari for twenty years. Even if this discipline is historically associated to the use of stone, the advent of 3D printing is stimulating research towards new possibilities and new directions.This paper aims to present two case studies, consisting of two different prototypes of 3D printed stereotomy. The first one is a portion of a barrel vault composed of osteomorphic hollow blocks, printed using clay. The design process was inspired both by the ancient constructive system of fictile caroselli and by the shape of the Truchet’s ashlars.The second case study deals with the construction of a real scale tripod, composed of hollow ashlars printed using PLA.

Shape optimization is one of the most important types of structural optimization for spatial coatings (shells), in which the boundaries, shapes and contours of the object under study are changed while maintaining its original structure-topology without creating any holes in the model itself. Correct adjustment of the components of the optimization process in the program allows to get a truly optimal result, both from a constructive point of view and from an aesthetic point of view. The article is devoted to the configuration and interaction of two important parameters, which are situated in Shape optimization settings in the Comsol Multiphysics program: maximum displacement (dmax) and filter radius (Rmin) when optimizing the shape of two shells using the gradient method IPOPT (Interior Point OPTimizer). The purpose of the study is to select the most appropriate value of dmax and Rmin for two shells for finding the effective shape optimization decision.

The temple of Diana in Baiae represents one of the most important examples of masonry dome built in ancient times; presenting a very peculiar ogival shape, partially collapsed, is built in Opus Caementitium. In order to assess its structural vulnerability, the paper aims to investigate the performance of different analysis strategies: the Trust Network Analysis (TNA) and classical Finite Elements (FEM). While TNA proved to be very efficient for masonry structures presenting well-defined structural elements (rock blocks), the continuous nature of the roman concrete cast does not permit an univocal and effective discretization of the network. On the other hand, while FEM are generally very efficient in analyzing continuous elements, their solution is strongly influenced by external boundary conditions that, because of ground settlements, represent a critical action for the present case study. A numerical comparison between the outcomes of both strategies in presence of different external actions will present an insight on the limitations and the benefits of these analytical methodologies.

The case study concerns the structural project of the “Palazzo dell’Edilizia of Alessandria”, a multi-functional building that will host the activities of a public company managing building industry and construction workers issues. The early architectural concept design has been carried out by the well-known Architect Daniel Libeskind. LGA Engineering team by means of BIM approach developed the structural design in a Level Of Detail corresponding to a Definitive Project.The building is organized into four above ground stories that house classrooms, offices, conference halls and multi-purpose spaces. Under structural point of view the main body is made of a central rigid concrete core and surrounding steel frames. The most iconic component of whole complex is the 50 m high tower made of steel frames interconnected each other and with the other main elements of the building.During project development, the main structural challenges to deal with has been the design of long span beams, cantilever slabs and beams, out of plane structural elements and their mutual connection, and above all the managing of the complex geometry and the height of the tower steel frame.

Designers propose using high-performance materials or cellular and bio-inspired structures in components with high strength-to-weight ratios, high heat transfer capacity, and energy absorption. An example is fractal geometries, which show highly complex 3D geometries that are unfeasible using conventional manufacturing processes. The work investigates the energy absorption performances of a 3D cross-based fractal structure (3D-CFS). The geometry is inspired by the mathematical 3D Greek cross geometry and designed for production using Additive Manufacturing (AM) powder bed fusion processes for polymers (PBF). The mechanical properties of Polyamide (PA12) and Thermoplastic Polyurethane (TPU) 3D-CFS structures designed with different volume fractions are evaluated using quasi-static and dynamic compression tests. The results show that the 3D-CFS structure is a good candidate for shock absorption applications such as personal protective equipment (PPE) applications.

The flexibility and adaptability provided by technical textiles make them suitable for the aerospace field.Specific requirements for space structures such as resilience, payload constraints, and economic costs can be tackled through a smart use of the newest technologies in material sciences. The future of space exploration has in store the building of human settlements beyond Earth; therefore, it is crucial to improve and perfect the technologies we use to go to space and sustain human life there.For this reason, this paper focuses on studying textiles applied to a Martian habitat named E.L.L.E., an Extreme Livable Lightweight Environment, by proposing a new combination of materials for an inflatable system that allows to decrease the total weight of at least 30% than current space modules.Experimenting with technical textiles in space will enable a deeper understanding of these technologies to encourage their application in extreme environments on Earth for a sustainable architecture.

Timber structure design can reduce embodied carbon for large span systems, by reducing material usage. The work in this paper presents the assessment of wood panel shell structures, focusing on the use of traditional joinery styles to produce self-supported structures. Key design criteria are to minimise external scaffolding to reduce falsework waste, to allow dry stacking without adhesive between panels for de-construction, and to be manufactured and assembled using digital processes. Focusing on a particular shell geometry, selected for its theoretical performance, a procedure is outlined for the definition of integral joints between planar panels. By modelling deflection using the coupled rigid-block analysis (CRA), different joint styles are assessed during and post-assembly, to compare their suitability and demonstrate the mitigation of falsework. Panels are both 3D printed and built as stacked plywood, validating the utility of CRA and finding the effect of scale to demonstrate its use as a structural design tool for intermediate assembly stages.

The Swiss engineer Heinz Isler (1926–2009) is among the most prominent figures in shell design. Thanks to a form-finding approach based on the use of physical models, he designed and built many shell projects in reinforced concrete. His unconventional structures still represent an important source of inspiration for today’s structural engineers. The paper reconstructs Isler’s experimental method by looking at the multiple physical form-finding models he developed for his tennis hall shells. Designed for the first time in 1977, they became one of Isler’s most successful shell typologies, promoted as “HIB” shells in Switzerland. Despite their apparently simple shape, Isler produced the largest number of physical form-finding models for this specific shell type. Their double symmetry challenged his design method: the highest precision was needed to avoid any irregularities in finding the appropriate geometry. By studying the original materials stored at the Heinz Isler Archive (gta Archives, ETH Zurich), details about Isler’s experimental approach to the conceptual design of his shell structures will be revealed for the first time.

Archeological sites are places of big importance for preserving history and culture (Iuorio 2016). However, because of their dimensions, their preservation is a challenging task. This paper aims to give a short overview of current requirements and how they are solved and identify the design points which can be improved further. One of them, which is in the focus of this paper is the issue of the foundations for lightweight structures in archeological use. The problem emerges because at the same time foundations need to be massive and able to resist uplift forces occurring in the lightweight structure while being limited by the archeological site importance which requires the least possible invasiveness to the soil (Zanelli 2013). Presented requirements are similar to the general requirements used in the design of lightweight structures: minimizing the size and the weight of the elements by isolating principal forces and loads and shaping the elements to respond to them. In this case, the observed forces and loads are at the foundation of the structure (Fig. 1). The new foundations’ system is initially developed through virtual simulation that allows understanding the load directions and transfer of forces and also guides the design process. In the successive step, a series of form optimizations then leads to the improved design. Thanks to the virtual data collected through the simulations, it is possible to perform this data driven approach. In the end, these are tested and verified in the Politecnico di Milano wind tunnel, so the real-world data is collected and compared to the virtual one.

Reinforcement Learning (RL) has emerged as a promising approach to solve complex problems in many different domains, including the Architecture, Engineering, Construction and Operation (AECO) industry. RL is a type of machine learning that focuses on training an agent to interact with an environment in order to maximize a reward signal.In the AECO industry, RL has been used to optimize building design, construction planning and scheduling, and building energy management. This contribution presents an application of RL for the generation of an InfraBIM model of a tunnel built by mechanised excavation using a Tunnel Boring Machine (TBM). In particular, the present application was developed to minimise the distance between the theoretical layout and the operational one to be executed by the TBM, considering the geometry of the ring and the structural joints required for the solidity of the structure.RL has the potential to improve efficiency, sustainability, and safety in the AECO industry by enabling intelligent decision-making and optimization across different phases of the construction process.

Heinz Isler, known as the most famous contemporary shell designer, has employed physical modelling techniques for studying and constructing concrete shell structures. The Swiss engineer's work has spread over 50 years of continuous activity (1954 to 2008/9). The innovation in Isler's work stands by the pioneering form-finding methods based on physical structural models (expansion, inflation and hanging) of thin membranes. The strategy was adopted for many of his experimental structures, like (i) the Wyss Garden Centre in Solothurn (1962); (ii) COOP Warehouse Wangen in Olten (1960) and (iii) Deitingen Slid Service Station (1968).In this document, the study focuses on the assessment of Isler’s Shells employing new technologies and strategies based on Algorithm - Aided Design. The design steps comprehend the reparameterization of Isler’s shells samples using Parametric Design techniques (geometry development in Rhinceros3D © + Grasshopper© add-on); the generative approach (parametric design + simulation) is conducted and achieved thanks to Alpaca4D©. The structural analysis relies on a Finite Element Analysis (FEA) carried on through the plug-in for Grasshopper© in Rhinoceros3D©. The results are retrieved to develop and validate the achieved results employing Alpaca4D© with a comparative model developed with the Karamba 3D© add-on and FEM-Design©, an advanced and intuitive structural analysis software.

Vaults assembled from regolith-based components offer a compelling solution to the need for protective infrastructure in future off-Earth settlements. We have studied the stability and seismic performance of a novel pitched-brick vault geometry, which could shield various assets from radiation or other Space hazards. The dry stone scaffoldless vault was modeled as an assembly of mechanically interlocking components using geometric constraint solving. A novel methodology was developed to produce distinct element models with complex, non-convex rigid block geometries. The stability of these models was assessed in 3DEC, a distinct element modeling program, using quasi-static and dynamic time history analyses representative of expected loading in the Lunar context. For quasi-static pushover-type analysis, the proposed vault geometry was stable under its self-weight and exhibited favorable resistance to lateral acceleration. The vault’s dynamic response to an artificial ground motion time history suggests that the structure effectively dissipated energy, and that progressive collapse is unlikely in this type of structure.

Owing to the challenging definition of an appropriate specimen design, the mechanical properties of lattice structures under tensile loads have rarely been investigated. Finite element analysis (FEA) may be used to analyze the deformation mechanisms and optimize the specimen design. In this work, a FEA is carried out on an ad-hoc designed specimen so that the fracture of the lattice specimen under tensile load is localized within the gauge length. The specimen is designed according to EN ISO 527 standard, in which the gauge length is replaced with a strut-based lattice structure. In addition, the lattice density is graded to control the stress distribution. The numerical analysis is experimentally validated using polymeric specimens produced by additive manufacturing (AM). The numerical result shows a deviation due to the geometrical specimen deviation produced by the AM process that, if compensated, enhanced the model's capability to forecast the lattice structure's mechanical behavior.

The purpose of this paper is to contextualize and introduce the academic potential of Augmented Reality (AR) models based on computer-generated holograms for the experimental exploration of spatial structures in architectural (interactive and immersive) design and education by multiple users. This work is driven by the potential impact of concurrently sharing and interacting with mixed reality (MR) scenes via holographic interfaces. With an interfaceable, scalable, and modular computational architecture, this platform is a powerful resource for multiple users, multiple formats (digital and physical), and multiple physical locations to design as well as assess structural and physical properties. The underlying didactic hypothesis is that holograph and MR offer an unparallel sense of immersion while enabling rapid virtual prototyping and project-driven synergy in combination with physical models. We present results on Augmented/Mixed reality as well as Virtual reality (VR) using devices such as the HoloLens and Vive head-mounted devices (HMD) and hand-held devices (HHD) such as the iOS iPad and iPhones and Android tablets all seeing the same time the same architectural holographic scene and interacting with it.

In free-form architecture, computational design tools have made it easy to create geometric models. However, obtaining good structural performance is difficult and requires further steps, such as shape optimization, to enhance system efficiency and material savings. This paper provides a user interface for form-finding and shape optimization of triangular grid shells. Users can minimize structural compliance, while ensuring small changes in their original design. A graph neural network learns to update the nodal coordinates of the grid shell to reduce a loss function based on strain energy. The interface can manage complex shapes and irregular tessellations. A variety of examples prove the effectiveness of the tool.

The aim of the research is to identify new implementation strategies for earth constructions using additive manufacturing techniques. The preliminary part of the study was about the analysis of traditional earth constructions in Abruzzo (Chieti province) with a reflection about coverage systems weaknesses. To provide a coverage issue solution, Nubian vault construction principles were rediscovered by the author. As a result, a massive organism completely made of earth has been designed: it is a 3D printed rural lamione and the application of it in widespread rural areas represents a museal complex itself. The study concludes with reflections about digital fabrication opportunities in the COVID and post-COVID era.

Grid shell structures are optimal when considering their aesthetics and lightness, but their efficiency is highly reduced when their shape deviates from a pure membrane. Many contemporary architectures possess a freeform shape, conceived mostly on aesthetics and functional criteria. In these cases, finding an efficient grid shell often requires substantial shape modifications. This work addresses a new kind of double-layer structure that aims to preserve the desired shape design. The structural system comprises a quad-meshed grid shell aligned to the target shape and enriched with an additional reinforcement layer that adds bending stiffness. This additional layer, going inward and outward of the main surface, presents variable height and discontinuous elements based on the required bending strength. The obtained structural system differs from both grid shells, as these latter may be very deformable in this setup, and from classic double-layer structures (space frames), which are heavier and redundant. In this paper, we show how the presented system compares with grid shell and double-layer competitors in terms of statics and stability. We highlight the pros and cons based on a systematic comparative analysis run on selected freeform shapes.

The establishment of sustainable human settlements in space requires the development of living and operational spaces capable to withstand the harsh environment of extra-terrestrial locations. To reduce the dependence from Earth resources, we should get used to introducing in-situ production of structural elements. This can include the construction of structural elements with a focus on the highest degree of recycling of materials and resources. Regolith, the loose soil found on the surfaces of Mars and other celestial bodies, presents a potential material for building structures due to its abundance and low cost.This paper explores the use of a regolith simulant-based material with the addition of hemp fibres applied to a simple structure. We analyse the performance of a structure under various loading conditions and propose solutions that can improve its strength and durability. Our results demonstrate that the addition of hemp fibres in the regolith mixture enhances the thermo-mechanical properties of the material, making it a promising choice in structures where building efficiency is paramount. This research contributes to advancing sustainable and innovative solutions for space architecture and supports the goal of establishing a permanent human presence in space.

Fiber-reinforced polymer composites have garnered considerable interest in the field of structural engineering due to their promising mechanical properties. However, their application at the building scale still requires further efficiency. Current design approaches often rely on traditional methods used for conventional structural elements; in contrast, this paper focuses on the concept of fibrous tectonics. While thermoset matrices are commonly employed in this composite, our study focuses on developing a comprehensive computational workflow encompassing design, structural analysis, and optimization specifically tailored for fiber-reinforced thermoplastic polymer composite roving in facade applications. The primary objective is to minimize the length of the fiber roving used while ensuring acceptable levels of utilization and deflection, in addition to proposing possible architectural functions for using FRP at building scale, e.g., shading façades.

The proposed case study is the control tower of Swiss Railways in Pollegio - the railway sector with the 50 km long Gotthardtunnel through the Alps. The structure is the result of a competition held in 2006, the construction has been completed in 2014 and it is until now under deformation control.The control tower’s periscope shape, with an asymmetrical upper box and a solid lower shaft, is the direct result of the load-bearing structure being made of prestressed reinforced concrete plates. The shape resulted from specific choices made in the early design stages together with the architects.The structure is a complex spatial system that works three-dimensionally and required many different and detailed studies.In this paper, we will present the overall design process. That process began with the traditional analysis methods based on graphic statics and tension fields refined with finite element analysis that confirmed the important interactions between the multiple structural elements. Those interactions were ultimately validated by the results obtained from continuously monitoring the structure from the construction phase to the present day.

Bridges are complex structures in several aspects, from design to construction, mainly due to their complicated and constrained geometry, high design loads and unique boundary conditions. Moreover, the narrow schedules and the demand for efficiency in the civil engineering industry require a new approach. The Parametric BIM approach removes repetitive time-consuming tasks by introducing parameters and numerical relationships between them. This enhances the design process, increasing efficiency and reducing time and effort. This paper presents a methodology for the development of the geometrical model of different bridge typologies through the modification of input parameters. The approach is applied to composite and concrete box girders bridges, enabling efficient analysis of different structural configurations to explore a range of innovative cost-effective solutions. Thus, the workflow is proposed as a supportive tool for decision-making in the design of new complex structures.

Auxetic metamaterials are gaining popularity as deployable architectural design systems due to their inherent flexibility, adaptability and programmable nature. The efficiency and constructability of these systems – which comprise of rigid panels and hinges - is interlinked to their geometry and corresponding kinematic behaviour. As such they can be considered as structural design systems in which the structural performance directly defines their architectural conceptual design.This research paper presents a purely geometrical methodology for developing Auxetic metamaterials based on graphic statics. Specifically, it is shown how by employing reciprocal convex Airy Stress Functions (ASF) and Minkowski sums it is possible to derive in a direct (and noniterative) way non-standard 2D Auxetic patterns with negative Poisson’s ratio. Furthermore, this methodology can be applied to cases of convex 3D polyhedral surfaces by combining said reciprocal ASFs into cantellated polyhedral objects. Lastly, it is discussed how this construction relates to origami flagstone tessellations.

While the exploration of new configurations of tensegrity structures is expected to contribute to the potential application of the tensegrity concept in building design, their real world implementation poses significant challenges. In this paper, double layer tensegrity networks the two layers of which are minimal surfaces, are considered. Algorithms that address minimal surfaces were developed and were applied and tested during the design and construction of two minimal surface tensegrity structures of ‘helical’ and ‘enneper’ geometry. These two structures were displayed as installations in the context of international exhibitions. For the real world implementation of the algorithms, a method that permits the construction of double layer tensegrity structures from the assembly of collapsible tensegrity units was employed. Spatial constraints, structural considerations, and constructability challenges had also to be addressed. The materialization of these structures has proven the validity of the algorithms, while the challenges encountered, can be used to improve both the design algorithms and the construction and assembly method.

This work explores the potential of parameterisation in the design of ribbed domes, specifically focusing on lowered domes. Drawing inspiration from the cross-herringbone pattern employed during the Renaissance, the study compares various configuration of rib patterns. To achieve this, parametric models were constructed, incorporating a limited set of geometrical parameters, allowing for the generation of multiple geometrical configurations. Each ribbed lowered dome configuration was analysed to comprehend its behavior in terms of displacements and stresses. By conducting numerous simulations and comparing the results, the impact of ribs was estimated, considering two different load conditions. This research sheds light on the influence of various parameters on the structural performance of ribbed domes, contributing to advancements in dome design and engineering.

The ability to work with both form and forces in the structural design process is crucial, particularly during the early design phase, as these are key parameters that impact the static behavior of a structure. Graphic statics offers a powerful geometric framework for the conceptual design of structures in static equilibrium, owing to the interdependence between form and force diagrams. When the form diagram of a self-stressed spatial pin-jointed framework has an underlying planar graph, its corresponding force diagram is reciprocal. It can itself be viewed as a self-stressed framework whose force diagram is the original form diagram. These configurations generally possess inherent architectural elegance and structural performance, making them particularly suitable for lightweight roof structures. This contribution outlines a graphic statics workflow for generating such structures using vector- and polyhedron-based approaches.

Large-span structures are essential for various applications, including commercial buildings, train stations, ferry-boat stations, and airports. However, constructing such structures in seismic areas requires the use of a considerable amount of structural materials, resulting in high resource consumption and CO2 emissions. To overcome this problem, a sustainable design strategy for large-span structures in seismic areas using form finding and structural optimization tools is here proposed, starting from a previous work by some of the authors. This strategy is employed for designing an optimized innovative hybrid structural system comprising of a concrete shell coupled with suspended steel multi-floor frame system. The shape of the shell is initially determined by a form finding procedure for different plan forms; a linear finite element analysis under static and dynamic loads allows to select the most performing shell shape in terms of stress and deformation levels. The framed system is then suspended from the selected shell, and the structural layout is optimized by a shell thickness optimization conducted for gravitational loads. The whole structural system, optimized for gravitational loads, reveals efficient performance also under significant seismic actions, indicating a beneficial interaction between the shell and the frame structure. Therefore, the innovative hybrid structural system and the design approach here proposed helps reduce the quantity of structural material usage, minimizing environmental impact and enhancing structural efficiency.

In this paper, a novel concept of a lightweight deployable vault structure, consisting of a curved folded plate surface, paired with a retractable frame mechanism is proposed. The retractable frame, in its deployed and constrained configuration, will function as a structural and load-bearing system, whereas the rigid origami folded plate structure will serve as a covering surface. A miura-ori first-level derivative crease pattern, such as the Arc Pattern, will be used for this purpose. The retractable frame consists of scissor bars of different lengths combined with four-bar linkages with specific sliding joints. This frame acts as a motion actuator, as well as a supporting and locking mechanism for the folded plate surface. For the study of the form and kinematic behavior of the proposed vault structure, a parametric model has been developed in the Rhino Grasshopper programming environment and small-scale physical models have been constructed.

This paper outlines a general mechanical formulation to computationally handle cable–rib structures by a consistent Complementarity Problem modellisation, so far considering potential material non–linearity within the ribs, localised at plastic joints, as per a classical plastic hinge hypothesis in the Limit Analysis of frames. The formulation is also outlined in a prototype self–made implementation, allowing to achieve and display first consistent results on sample test structures, for necessary understanding and control. This shows that the present modellisation concept, and implementation, shall constitute a liable mechanical tool for promising utilisation and end use adoption in different related application scenarios.

This note concerns a general issue, in the mechanics of masonry arches, with reference to symmetric circular geometries, with variable opening, and possible stereotomy with radial joints (to be potentially formed, at failure, within the ideal continuous arch), in a least-thickness condition, under self-weight, namely the role that a finite inherent friction, among the theoretical joints, may play in ruling out the self-standing conditions and the mechanical features at incipient collapse, setting a change from purely-rotational modes to mechanisms that may include sliding. The issue is systematically investigated, by a full analytical derivation, and validated through an original Complementarity Problem/Mathematical Programming formulation, and numerical implementation, reconstructing the complete underlying map of thickness-to-radius ratio versus friction coefficient of all arch states, and corresponding collapse mechanisms. This investigation shall clear the issue, of the theoretical influence of finite friction, in the above-stated setting, and contribute to provide a full understanding of basic aspects in the methodological description, and physical interpretation, of the mechanics of masonry arches, with implications that may come up to appear also in practical terms, once dealing with this traditional and remarkable structures, in real cases, possibly endowed of historical character and architectural value, to be preserved and renewed.

We investigate a design concept for thin tiled plates having exactly one degree of freedom. A tiled plate is realized as a tessellation composed by rigid tiles hinged to each other along the sides. The plate can deform in just one way, that is, into a predetermined surface. The family of tilings we consider, the monohedral hexagonal one, with either convex or concave tiles, is rich enough to include many noteworthy tessellations. Corresponding plates can approximate surfaces with positive, negative, and null Gaussian curvature, and may exhibit an auxetic behavior. The proposed architecture is highly scalable and easily manufacturable, and it can find applications not only for civil and aerospace engineering purposes, but also for biomechanical scaffolds, energy harvesters, and wearable devices.

The study investigates the use of aluminum gyroid lattices for structural purposes, with a particular focus on feasibility, dimensional accuracy, and compressive load performance. Gyroid lattice samples were built using laser powder bed fusion technology with AlSi10Mg, utilizing cell sizes of 6, 8, and 12 mm and a wall thickness of 0.5 mm. The compression performance of the samples was tested. The study revealed differences in dimensional accuracy in different directions, which was attributed to the fabrication process. All samples were heavier than expected, with additional materials being proportional to cell size. However, the samples exhibited high compressive strength and stiffness, indicating their potential use in load-bearing applications.

Masonry arches and vaults are widespread in historical buildings and infrastructures. The shape of these structures is a crucial aspect for their equilibrium condition and is responsible for their safety. Their current shape can be different from the design one, because it may have been affected by deformations caused by various phenomena over time, such as load changes, earthquakes, foundation settlements and temperature raising/lowering. It follows that the current safety verification must be done by comparing the load thrust line with the current deformed shape of the arch.The paper investigates the effect of thermal distortions on the original shape of the arch and the safety condition, through a rigid-block and lumped deformability model. Thermal distortions are assigned at the joints.The effect of thermal distortions on masonry arches is investigated by assessing the increase or decrease of the load bearing capacity. To this aim, the behavior of an arch case study is investigated by applying an increasing point load and ranging the thermal gradient. A parametric analysis is also performed to assess the effect of the tensile strength of joints.

The use of BIM for historical heritage structures has started to be widely diffused and referred as H-BIM. These models are usually aimed at the management and conservation of monuments; however, these can also contain the information necessary for the characterisation of a numerical structural model. This paper is focused on the interoperability between H-BIM and numerical models applied to masonry vaults, structures that typically require local safety assessments. Different degree of geometry subdivision for structural analysis of masonry vaults, has been identified and related to various numerical modelling approaches and HBIM classification. Based on this, an automatic parametric procedure specific for lunette vaults has been developed. This allows to obtain automatic three-dimensional geometric models that can be efficiently implemented in the H-BIM environment and to obtain and manage the geometric characteristics as input to the numerical modeling. Finally, the application of the methodology to the National Palace of Sintra is presented.

This paper presents a geometry-driven approach to form-finding with reused stock elements. Our proposed workflow uses a K-mean algorithm to cluster stock elements and incorporate their geometrical values early in the form-finding process. A feedback loop improves the reuse rate over multiple iterations, and a best-fit heuristic algorithm is used to examine the reuse states. A detailed example and a case study demonstrate the efficacy of the method. This results in a form-finding method with reused stock elements; hence, promoting sustainable design and reducing environmental impact in the built environment.

Preservation and retrofitting of masonry arches and vaults belonging to the architectural heritage is a difficult task. Currently, the most widespread technique consists of applying fiber-reinforced composite materials to the intrados of these structures. The result is an increase in load-bearing capacity and a reduction in the width of cracks in the joints between blocks, although large deformations are experienced. The effectiveness of this technique relies on the bond between the reinforcement and the masonry substrate. To account for it, in this paper a delamination model is proposed. The arch is modelled by rigid blocks assembled with elastic-cracking interfaces and the reinforcement by means of deformable links connecting, in series, the intrados’ midpoints of adjacent blocks. A nonlinear numerical procedure to investigate the bond behavior is proposed. The delamination process is checked, step by step, searching for both the tensile forces in the mortar joints that cause the occurrence of cracks and the shearing and peeling forces at the intrados’ midpoint of each block that cause delamination. The deformed and cracked shape of the arch with the delaminated reinforcement is provided.

The current study presents the methodology of the wind turbine foundation optimization. Initially the forces applied on the system wind turbine – foundation are being analyzed. It is presented which phenomena need to be faced due to the applied forces and after implementing the sensitivity analysis, the critical check of the system is identified and proved to be the check against overturn. After following a repetitive procedure, the optimum dimensions and reinforcement of the foundation are being calculated while Eurocodes restrictions are met. At a next phase the foundation is being calculated as beam slab leading to the optimum design and the cost calculation through removal of concrete quantity and insert of rock materials either from deposit areas or by reusing the excavation products. The proposed method is implemented on actual wind turbine showing in numbers the saving in time, cost and environmental footprint. The algorithm can be used for any kind of soil, wind turbine and foundation.

More advanced testing methodologies and measurement techniques to identify complex deformation and failure at high strain rates have drawn increasing attention in recent years. This study presents a novel combined tension-torsion split Hopkinson bar (TTHB) system that is conceived to generate a combination of tensile and torsional waves in a single loading case and to measure material data representative of real case impact scenarios. Energy-release mechanism is employed to generate both longitudinal and shear waves practically via the quick release of a bespoke clamp assembly.The synchronisation of the longitudinal and torsional waves, and the wave rise time, were experimentally assessed. Thin-walled tube specimens made of two metallic materials were utilised to examine the capability of the developed TTHB system. Four-ligament tension-torsion specimens were also used and the results compared to those obtained using the thin-walled tubular specimens.The capability of the apparatus is demonstrated by the measurement of the failure envelope of standard and additively manufactured materials at high strain rates..

Concrete spatial architecture was mainly built using techniques that at the time were still experimental and based on design criteria that did not consider seismic actions. The validity of accurate models accounting for such complex structural schemes can be demonstrated, but the latter still would not support a clear comparison with the original predictions.Different from other Morandi’s balanced beam schemes, in the underground Pavilion V of Turin Exhibition Center the main post-tensioned ribs are not parallel beams but are diagonally directed and multiply reciprocally interconnected in order to obtain a spatial structure offering a high overall rigidity and lateral stability, and to contrast the instability of the very thin webs of the main ribs.The paper focuses on how information from the experimental campaign can help to formulate virtual models for prognostic and diagnostic assessments under different scenarios, such as for example the design of structural health monitoring activities and systems.

Space architecture involves the integration of multiple research disciplines to establish a framework for planning secure human settlements in Low Earth Orbit (LEO), on the Moon, or on Mars. Designing sustainable and safe habitats for space exploration requires a diverse range of skills and knowledge. As humanity enters an era of venturing towards neighboring celestial bodies, NASA's Artemis program envisions establishing permanent settlements at the South Pole of the Moon. These settlements aim to serve as testing grounds for future generations, fostering collaboration in the creation of joint infrastructures akin to the International Space Station's cooperative model—a new paradigm of an “ideal city” in a unique environment. The challenge of designing in extreme space environments is being addressed through innovative approaches such as computational design tools, topology optimization processes, and circular design methodologies.

Since the Apollo missions, there have been significant technological advancements and scientific discoveries in robotic exploration of deep space. Currently, NASA's Artemis Program aims to establish human habitation on the Moon, which remains a considerable challenge. To address this, Alta Scuola Politecnica, Thales Alenia Space and MIT have collaborated to design an innovative and adaptable mobile habitat using a holistic multidisciplinary approach for crewed surface exploration missions. The outcome of the Lunar Architecture Design Exploration (LADE) project is a mobile space architecture system that enables human presence on the Moon, supporting medium to long-term missions. This mobile module serves as a crucial component within a more extensive system of hybrid class II and class III shelters, intended for the development of a lunar village. The primary objective is to facilitate the extended stay of four astronauts near the Shackleton crater, strategically located at the South Pole of the Moon, which offers favorable conditions for surface exploration and potential future permanent settlement. The paper presents an in-depth study of the form-finding process and structural analysis adopted for the LADE mobile habitat.

The text explores the fundamental question raised by Edoardo Persico nearly a century ago: Is architecture solely an engineering solution for building problems? It emphasizes the need to combine intuition and demonstration in architecture, drawing inspiration from Dante's works. The study emphasizes the importance of understanding the history and origins of architecture and how seemingly obsolete ideas can become modern again. The research focuses on the Tholos of Athena Pronaia in Delphi, analyzing its structural and architectural form using 3D elaboration. It highlights the interdisciplinary dialogue between contemporary research and classical Greek cosmological vision. The text raises questions about the collapse of ancient Greek temples and proposes innovative solutions. The Tholos of Delphi serves as a timeless icon for studying rational roots and design devices. The research utilizes advanced technologies like 3D printing to create a detailed prototype and evaluate the distribution of elements for balance and structural functionality.

Large-span roof implementation has long been a challenge for designers, who have had to overcome traditional structural engineering limits by introducing creative and innovative solutions. Pier Luigi Nervi revolutionized architecture and engineering with his prefabrication and construction techniques, inspiring professionals globally to explore new materials and solutions. His unique use of reinforced concrete in large-span roofs construction involved prefabricating structural elements and assembling them on-site, leading to faster and more efficient construction. The present research aims to analyse the construction procedures employed for the realisation of the Hangar designed by Nervi in 1939 in Pontecagnano, Italy. By examining original drawings and technical specifications, this research seeks to examine the structural solutions employed in this masterpiece of 20th-century architecture, showcasing Nervi’s pioneering work in structural prefabrication and large vaulted structures.

The dome designed by P. L. Nervi in 1956 for the roof of the “Palazzetto Dello Sport” in Flaminio district, Rome, has a remarkable feature: the wavy shape of its edge provides relevant enhancements of its structural behaviour. Even though such structure is well-known abroad for its aesthetics, from a Structural Mechanics point of view such shape sparks interest in the optimization of shell structures. Primarily, corrugation enhances the bending stiffness at the edge providing a significant reduction of the dome thickness.Taking inspiration from Nervi’s work, this contribution deals with the mechanical analysis of edge-corrugated shells. Attention is paid to the definition of their mathematical and geometrical descriptions and to the realization of a mesh suitable to perform FE analysis. Then some insights are given about the static and dynamic behaviour of these structures. Therefore, the enhancement provided by the corrugated shape is highlighted by comparison with a non-corrugated shape. It is well known that on the shell edge the effect of bending effects must not be neglected. As a consequence, attention is given to stresses and bending moments.The other main issue that will be considered is the behaviour in the non-linear field (especially concerning instability aspects such as snap-through phenomena, the effect of imperfections, etc.). Some numerical simulations of the improvement produced by the new shape are shown with different methods.

Strengthening interventions are significant actions to pass on heritage buildings to future generations. The study of historic strengthening interventions is worthy of understanding the historical past of the monument and gaining insight into how the building structure and structural damage have been interpreted. This paper aims to analyze historical interventions made on masonry vaults, focusing on the relationships between the deformed geometry of the original structure and the geometry of the intervention. In particular, reinforced concrete interventions made from the late 19th to the mid-20th century will be analyzed, considering the mutual effects of earthquakes, seismic codes, conservation theories and engineering practices. While in the field of conservation, the use of concrete was admitted and encouraged in consolidating monuments to avoid the dangers of dismantling and reinstating the parts to be preserved, in the engineering field, its usage seemed everlasting, given structural design and safety assessment. In this understanding, according to the vault’s damage, geometry, and materials, the interventions were with different techniques and in various shapes. Although these interventions do not date back to the first construction of the monuments, they merged into the original structure. Today, the interventions can be defined as the layers showing the evolution of monuments through time.In this paper, by analyzing the cases from Turkey, an overview of consolidation works of the superstructure through comparing of two cases and an understanding of the concept of the interventions over time and putting forward the current situations to guide the subsequent restorations are presented.

In this work, two formulations, and computational implementations, of Limit Analysis (LA), for large-scale 3D truss-frame structures are employed to efficiently investigate the limit elastoplastic response of the fascinating and well-known Palazzetto dello Sport (1957), located in the Flaminio district of Rome (Italy), designed by Pier Luigi Nervi. To this end, a spatial FEM modeling was first generated, whereby the characteristic inclined trestles and supporting skeleton of the above concrete shell dome were modelled according to the corresponding geometric characteristics and mechanical properties acquired by inspecting original design drawings and relevant bibliographic sources. In performing the structural Limit Analysis, the first algorithm step-by-step traces a fully exact evolutive piece-wise linear elastoplastic response of the structure, up to plastic collapse, by reconstructing the sequence of activation of localised plastic joints. The second algorithm, relying on a kinematic iterative direct approach, determines just the collapse mechanism and associated collapse load multiplier, but in a much shorter computational time, showing a rather impressive performance, in truly precipitating from above on the collapse load multiplier, by rapidly adjusting possible mechanisms to the sought collapse mode, in very few iterations. The performed investigation reveals the ingenuity of Nervi’s work, not only with respect to ordinary structural bearing tasks, within the elastic range of regular-service structural response, but also to post-yield performance and ultimate limit load capacity, up to possible ductile failure.

The use of innovative high-performance cementitious materials enables the development of advanced structural systems characterized by enhanced lightness, durability, sustainability, and mechanical performance. In this paper, we propose a partially precast unidirectional ribbed floor system consisting of very high-performance fiber-reinforced concrete (VHPFRC) I-beams, textile reinforced concrete (TRC) stay-in-place formworks, and ordinary fiber-reinforced concrete (FRC) finishes. A description of the conceptual design underlying the proposed building system is followed by a depiction of the materials and construction procedures used. Special emphasis is placed on the mechanical behavior of the TRC, both at the material and structural scales. Within this context, the membrane and flexural responses of thin beam specimens are discussed and followed by the experimental analysis of the movable prefabricated shells inspired by Pier Luigi Nervi’s ferrocement constructions, subject to transient actions associated with typical construction stages.

This study introduces an integrated approach that merges the design of structure and control to study the deployment strategies for tensegrity structures, particularly in the context of space antennas. First, we establish a nonlinear shape control law for clustered tensegrity structures, the solution turns out to solve a constraint linear algebra equation. Leveraging the symmetric nature of the antenna structure, we designate active actuators for the top and bottom cables of the space antenna while considering the remaining cables as passive. To further reduce the number of actuators required, we employ various clustering strategies for the active actuating cables. Results show that the deployment from the initial state to the predetermined targets is successfully guided by the proposed control law through clustering active cables using different actuation strategies. It is significant to note, however, that the energy cost escalates as more cables are clustered into the deployable antenna structures. In the context of space applications, this scenario emphasizes structure design and control are not independent problems. These insights also offer extensive relevance and can be extrapolated to different deployable tensegrity structures and robotic systems.

Geometry has always been a means of proportioning and sizing architectural constructions and has permeated the ways of conceiving buildings from the classical, modern, and contemporary ages, ensuring aesthetic and technical values and thrilling architects and treatise writers. The structural behavior of masonry structures is consequently often aimed at highlighting the close relationship between the geometry and the safety level of structures based on primitive geometries of the architectural heritage, in particular, the arches, the vaulted systems, and the domes.Reality-based 3D surveys and modeling that use laser scanning and photogrammetric methods have important implications for the study of generative geometries, as they are able to allow a direct comparison between the real surfaces surveyed and those designed according to strict geometric principles.The research will highlight the contribution of methods such as point cloud co-registration, deviation analysis, shape recognition and algorithms such as ICP-based (Iterative Closest Points), RANSAC-based to achieve these objectives.

The research focused on the design of a curved shell-supported footbridge using a form-finding algorithm and genetic optimization. The bridge was shaped through a parametric design code, which also allows optimization based on finite element structural analysis. The constrained optimization involved a mono-objective approach aided by penalty functions to control the maximum tension utilization of the concrete material. The objective was to find the optimal bridge shape in terms of minimizing displacement under vertical and horizontal loads, with both the topological optimization of the positions of the bridge supports and the optimization of the control points of the Bezier curve describing the form of the curved deck as key parameters. The results provide insights into effective techniques for optimizing the design of curved shell-supported footbridges subjected to earthquake loads.

This study explores parametric design and optimization to improve a reciprocal frame bridge’s structural efficiency while preserving its historical and architectural significance. The research aims to identify an optimal configuration that minimizes steel requirements for a self-supported bridge while satisfying structural requirements. This objective was achieved by modifying the bridge’s geometrical parameters using a genetic algorithm for mono-objective optimization. A finite element structural analysis was conducted to evaluate the maximum stress in the material, with a penalty function used to ensure structural safety. The parametric design software allowed for efficient and precise optimization of the bridge design. The results demonstrate that the proposed optimization method reduces material usage while maintaining the bridge’s original structural concept of traditional wooden Chinese bridge, validating the approach’s effectiveness for future design of reciprocal frame bridges.

Mimosa Pudica (MP) possess a hierarchical leaf-folding behavior in response to external disturbances [1]. As observed in other plants [2], such fast movements are mechanically achieved by osmotic regulation of tissue pressure in specific apparatus, pulvini in the case of the MP. Depending on the intensity and location of the stimuli, the triggered kinematics can involve a pair of leaves up to the collapse of the entire branch. Because of this progressive on-off behavior, we modeled the folding system as the linear buckling of a concentrated linear elasticity system, realized by rotational springs and considering a simple time function for the electrochemical signaling. We then described the leaves stimuli adaptive functioning by a modal tuning of the spring stiffnesses. Finally, we proposed a tuned buckling loads to train a neural network to describe a learning model [3] for the equilibrium related MP intelligence and morphological features.

Forces geometric visualization and representation in one of the key aspects in Structural Mechanics and its advancement went along with the progress of the subject itself. From graphic statics to modern Computer Vision (CV) systems, there is a constant and significant component of the visual factor when compared to other disciplines in the STEM panorama. In this work, I present the experience carried on in the MSCA FORSEES to try to frame and quantify this visual factor. I will then suggest a new perspective to the problem of forces identification (and related stress and strain) in solids based on some recent discoveries in Neuroscience. The analogy that represents the first step of this exploration is between the Free Energy Principle (FEP) [1] and the Elastic Potential Energy, by defining a structure behavior as the inner agent to sustain structural integrity. Limiting the FEP to the visual sense only [2], we will look through the indissoluble link that lies within the relation of a form and its structural behavior, circling back to the base of the Theory of Elasticity. Final step will be the application to common methods in engineering practice and teaching of AI-based visual tools for structural analysis.