Computational Mechanics and Applied Mathematics: Perspectives from Young Scholars

A cylindrical structure composed of helicoidal transversely isotropic thick layers is considered. It models the behavior of structural elements with helically wound fibers. Such configuration is seen in yarns and cords, typically used as reinforcements in composite materials. Elasticity equations are derived for such a cylinder under axially symmetric loading. To account for the different behavior in tension and compression of the fibers, a bimodular elastic material is considered. The analytical results are compared with the finite element prediction.

Carbonation induced corrosion represents a significant challenge in the durability and structural integrity of reinforced concrete elements. This process occurs when carbon dioxide from the atmosphere penetrates the concrete cover and reacts with the alkaline components of the cement paste, resulting in a decrease in pH and the depassivation of steel reinforcement. Eventually, corrosion residues are formed over the metal surface leading to cracking and spalling of the concrete cover. Concrete carbonation is modelled via a system of coupled transport-diffusion-reaction equations that describe the environmental carbon dioxide diffusion-reaction, pore water saturation and rebar corrosion. Changes in concrete composition and mechanical properties are also considered. As rust deposits increase in volume, cracking and spalling of concrete cover is observed and modelled using the phase field approach for fracture.

Incremental Hole Drilling is a well-established technique for measuring residual stresses; it involves relaxing residual stresses by incrementally drilling into the material and simultaneously measuring strains using strain gauge rosettes. The measured strains and residual stresses are related by an integral formulation, so an elastic inverse solution is required to calculate the stress field. Typically, strains are measured at different depths than those at which the residual stress calculation is performed. Therefore, it is common practice to fit the strain measurements at depth using polynomials or splines. However, the choice of fitting parameters can critically affect the final measurement output. This study evaluates the uncertainty associated with the deformation fitting procedure using Gaussian Process Regression, a probabilistic machine learning algorithm capable of producing uncertainties associated with the fit itself. These fit uncertainties were then propagated to the residual stresses through a Monte Carlo simulation. The developed methodology was applied to AA 7050-T7451 aluminum samples surface treated by laser shock peening.

The objective of this study is to propose a differential geometry-based procedure to design the arrangement of the planar grid of thin elastic rods that deploy to lay on a target surface of uniform gaussian curvature, either spherical or hyperbolic. The out-of-plane deformation of the grid is controlled by a unique degree of freedom as usual in self-deployable gridshells. The procedure is applied to design two quadrilateral units featuring a grid composed of straight elastic rods, differing in the arrangement of rods within the edge quadrilateral. These units start from a planar configuration and deform in such a way to lay on two distinct target surfaces having positive and negative Gaussian curvatures, respectively. Deployment is controlled by the distance between the opposite corners of the base quadrilateral. The procedure is finally validated by verifying the deployment process by employing Finite Element analyses and tabletop models.

This study investigates the optimization of gridshell dome shapes using seismic design demand parameters as the primary objective function. The innovative methodology integrates shape optimization with seismic analysis, deviating from traditional approaches that separate geometric design and seismic performance enhancement. By integrating computational methods, utilizing parametric modeling through Grasshopper, and structural analysis with OpenSees, the framework employs a genetic algorithm for optimization. Nonlinear time-history analysis, incorporating material and geometric nonlinearities, reveals that the optimal shape of the dome is significantly influenced by its seismic response. The results show that the optimal dome shape can vary substantially based on seismic performance criteria, indicating a dynamic interplay between structural form and seismic forces. Moreover, the optimal shape can be further influenced by implementing a supplementary damping system. In this case, both the gridshell shape and seismic dampers arrangement require adjustments to achieve optimal seismic performance. These findings highlight the critical role of integrated seismic analysis in shaping optimization, emphasizing that the ideal dome geometry is not static but evolves in response to seismic demands and damping configurations.

The statics of funicular shells is governed by Pucher’s theory. When external loads are known in advance, the horizontal equilibrium of a membrane shell can be fully handled through the Airy stress function and then decoupled from its vertical equilibrium leading to the form-found geometry. Apart from limiting the solution space investigated during the search, the manual prescription of the potential field tends to become cumbersome when either relatively elaborate free-form shell planar footprints are addressed or functional requirements are considered. In this work, a recently formulated isogeometric form-finding strategy is employed to study the effect of different kinematic boundary conditions on the shape of funicular shells made of a unilateral material. The procedure benefits from a nonlinear programming routine to automatically determine a feasible Airy stress function fulfilling concurrent static and functional constraints. Further, use is made of spline technology allowing for smooth surface modelling and enhanced computational efficiency.

The response of freestanding objects subjected to sliding-rolling induced by dynamic excitations is of interest for several mechanical applications, not least for the stability of museum exhibits of historical and artistic value. A simplest plane geometry for describing pot-like artifacts is the rigid half disc which also provides a basis for understanding more complex mechanical problems, like polygonal-shaped blocks in masonry structures. Besides dependency on excitation frequency, amplitude and phase, the observed response of these objects is also strongly dependent on friction coefficients and finishing of contacting surfaces. Time-history analysis of these systems requires appropriate numerical integration as well as suitable error bounds evaluation. Analytical and numerical analyses are presented in this contribution for the rolling half disc model subjected to an impulsive base excitation. Results are critically examined to appraise the model sensitivity to rolling friction.

Load-bearing interconnected microstructured solids, such as concrete, paper, and bone, have an inherently size-dependent mechanical behavior, that is shown over specific length scales. In peridynamics, this measure is called the horizon and it controls void nucleation, coalescence, and fracture transition. Stemming from a through-thickness dimensionally-reduced bond-based peridynamic model recently proposed, this work analyzes the elastic behavior of thin plates made of highly interlaced solid materials. The internal actions, corresponding to the application of specific loading conditions, have been derived from such a model and compared with (i) FEM analyses, and (ii) with the outcomes of a previously available peridynamic approach.

Mechanical metamaterials, designed to possess unique properties not achieved in conventional materials, offer broad possibilities for applications, ranging from vibration isolation to seismic wave manipulation. Among these, negative stiffness metamaterials emerge as a promising research area due to their unique deformation capabilities, allowing for greater deformation compared to traditional materials. However, lack of comprehensive mathematical modeling and experimental testing still hamper a full comprehension of their mechanical behavior and a mindful design. Specifically, we present a preliminary analysis of the frequency response curves for a negative stiffness metamaterial whose hysteretic behavior is simulated by using the Vaiana-Rosati hysteretic model. Through simulations, we examine its stability and bifurcation characteristics.

Timber connections are crucial to guarantee structural integrity and performance in timber structures, especially under cyclic loading scenarios such as those induced by earthquakes and winds. In addition, understanding the hysteretic behavior exhibited by these connections is essential to accurately predict their response. Researchers typically perform experimental tests to investigate the behavior of various types of connections; the latter typically exhibit different types of hysteresis loop shapes which, consequently, provide different values of stiffness, strength, and energy dissipation. This study aims to categorize and simulate such hysteresis loop shapes by using a recent phenomenological hysteresis model formulated by Vaiana and Rosati. The proposed approach also enables the deduction of crucial information, such as secant stiffness, equivalent damping ratio, and energy dissipation, which are relevant for simplifying the dynamic analysis of timber structures.

Dynamical identification can be a powerful tool in characterizing the behaviour of structures under dynamic excitation, as it allows for the validation of numerical models and for the assessment of structural integrity, highlighting potential flaws in the structural design or construction. In this respect, it is essential to ensure that the dynamic properties of the structure under consideration are accurately captured through calibration processes. The present study investigates the dynamic response of a real-scale building subjected to an electro-mechanical exciter through rigorous testing and numerical analyses. To this scope, a non-standardized vibrodyne exciter was first calibrated and then used to apply controlled vibrations to the real-scale building. The structural response was measured by means of acceleration transducers and compared with the numerical response obtained from a FEM model, with the aim of validation and refinement. By combining experimental testing with numerical analyses, the study contributes to improve the understanding of structural behavior under dynamic loading.

Highly resolved finite element simulations of a laser beam welding process are considered. The thermomechanical behavior of this process is modeled with a set of thermoelasticity equations resulting in a nonlinear, nonsymmetric saddle point system. Newton’s method is used to solve the nonlinearity and suitable domain decomposition preconditioners are applied to accelerate the convergence of the iterative method used to solve all linearized systems. Since a onelevel Schwarz preconditioner is in general not scalable, a second level has to be added. Therefore, the construction and numerical analysis of a monolithic, twolevel overlapping Schwarz approach with the GDSW (Generalized Dryja-Smith-Widlund) coarse space and an economic variant thereof are presented here.

The structural characteristics of Crinckle Crankle walls are a topic of fascination. These unique, corrugated structures can be observed in East Anglia (England), where they were predominantly constructed between the 17th and 19th centuries for purposes such as enclosing orchards or as garden walls. Referred to as Crinckle Crankle walls, some of these distinctive structures still stand in Suffolk and Hampshire. This particular construction technique, often credited to Dutch engineers [1], involves creating a sinuous form that imparts increased bending stiffness and enhances the wall’s ability to withstand horizontal forces. As a result, craftsmen were able to construct slender walls using just a single row of bricks, eliminating the need for traditional supports or buttresses. This discussion aims to shed light on the structural capabilities of these walls and their construction methods. The walls will be analyzed using Discrete Element Method (DEM) analysis. Additionally, considerations will be made regarding their load-bearing capacity and security evaluations when subjected to dynamic loads.

In Italy, a significant portion of the existing building stock consists of masonry structures that are often in poor condition due to inadequate maintenance over time. Consequently, it is crucial to intervene in order to prevent further loss of life during seismic events, which have already caused substantial damage to these buildings. Additionally, these older masonry structures tend to have thermal inefficiencies, with high energy dispersions from indoor environments caused by various factors. The current research proposes an integrated retrofit system designed to simultaneously enhance both the seismic and energy performance of existing structures. This system comprises metal exoskeletons made of an aluminium alloy, complemented by the insertion of sandwich panels. The investigated solution, known as MIL15.s and developed by the Italian company TM Group S.r.l., was also subjected to experimental tests during my Ph.D. studies at the Polytechnic University of Timişoara. Specifically, a preliminary test was conducted on a masonry panel both before and after consolidation using the proposed retrofit technique, demonstrating its effectiveness against out-of-plane mechanisms. Future research will involve a second phase of experimental tests incorporating additional components of the system, as the preliminary phase only evaluated the contribution of the base profiles. Furthermore, numerical simulations of various case studies will be conducted to assess the overall impact of the seismic—energy retrofit on the performance of existing structures.

Numerous studies focus on analysing the dynamic behaviour of URM buildings under horizontal forces and interpreting potential in-plane collapse modes. Understanding the mechanical behaviour of masonry structures remains challenging due to their intrinsic heterogeneity and the various possibilities of material combinations. Consequently, the modelling phase becomes crucial for seismic vulnerability assessments of masonry buildings, particularly concerning differences in the shear-flexural behaviour of piers and spandrels. In this paper, after briefly reviewing the Equivalent Frame (EF) and Finite Element (FE) approaches, simple masonry elements such as piers have been modelled using these methods under various loading and constraint conditions. By comparing the results obtained issues related to shear behaviour were detected. All models were developed in SAP2000 using two different approaches: lumped-plasticity and distributed-plasticity. Notably, the software automatically defines shear behaviour based on flexural behaviour without offering modification options. Therefore, a simplified method for primally considering the shear collapse is proposed. By analysing the stress-state due to vertical loads and evaluating the strength domain of the analysed pier, a layered shell element section with appropriate geometric and mechanical properties can be defined for the pier, based on internal equilibrium conditions. This approach permits determining the minimum strength value for the modelled pier basing on its strength domain, considering the predominant behaviour (either shear or flexure) and enabling visualization of the related deformed shape. Comparisons between theoretical and numerical results are provided with the aim of better calibrating the proposed method.

Masonry bridges are common in many countries and their maintenance is a critical task, to preserve not only architectural heritage but also the embodied carbon invested in their construction. Sensing technologies can offer vital information to engineers responsible for these structures. In this paper, a multi-sensing approach is used to study the behaviour of a skewed, three-span masonry rail bridge in the UK, focusing on its deformation history and the movements at four transverse fractures that extend the full width of the bridge. Specific technologies include laser scan analysis, videogrammetry, and Fibre-Bragg gratings (FBGs) to monitor the multi-dimensional bridge response, which at the transverse cracks is of particular concern to engineers. Based on these data, the distributed nature of the structural behaviour of the bridge is discussed. The results demonstrate that complex masonry bridge degradation can be quantified and tracked, providing crucial insights for bridge maintenance and structural interpretation.

The structural integrity of existing masonry buildings is increasingly important in urban areas, particularly in the Mediterranean region, where such structures are prevalent. This paper addresses the vulnerability of typological residential masonry buildings subjected to vertical ground settlements, a less explored area compared to seismic vulnerability. Previous studies have largely relied on empirical methods for damage assessment due to differential settlements, focusing on criteria like differential settlement ratio and angular distortion. This study aims to fill the gap by applying non-linear analytical approaches to assess the fragility of masonry buildings under these conditions. The methodology involves monotonically increasing differential settlements applied at the base of the building elements, followed by a detailed damage estimation. Five conventional damage states, derived from the stress–strain constitutive relationship of non-linear hinges, are used for this purpose. The European Macroseismic Scale EMS98 provides the framework for defining these damage thresholds. The analysis documents the activation step for each damage state, mapping the progression of damage and identifying critical failure points within the structure. This comprehensive evaluation enhances the understanding of structural response under ground settlements and contributes to the development of more resilient construction and retrofit strategies. The findings highlight the critical stages of damage progression, offering valuable insights for engineers and researchers in the field of civil engineering.

This study proposes a passive structural vibration control strategy employing a sliding variant of the Tuned Liquid Column Damper, termed as STLCD, and investigates both theoretical and experimental aspects. The STLCD configuration features a U-tube container filled with liquid, capable of sliding along a linear guide rail and connected to the primary structure through a spring-dashpot unit. Unlike conventional TLCDs, this setup offers flexibility for tuning short-period systems, utilizing the spring for tuning and the dashpot for additional damping. However, similar to TLCDs, the STLCD exhibits slight nonlinear behavior, necessitating the use of an equivalent linear mechanical model to streamline the analysis for optimal device design. The study delves into the selection process for STLCD optimal design parameters, assuming a Gaussian white noise ground acceleration, with the objective of minimizing the roof displacement variance of the primary system (Hitchcock et al. in Eng Struct 19:126–134, 1997). Experimental tests are carried out at the Laboratory of Experimental Dynamics at the University of Palermo, Italy, with the aim to validate the proposed mathematical formulation. Finally, in order to prove the efficacy of the proposed device the vibration control performance of a scaled model of a two-story structure equipped with an STLCD is evaluated under harmonic excitations against its uncontrolled counterpart.

This study presents the results of several nonlinear dynamic analyses performed on a 2D building structure equipped with different types of rate-independent hysteretic dampers. To simulate their complex hysteretic behavior, the Vaiana-Rosati model of hysteresis is employed. In particular, we compare the experimental and simulated hysteresis loops by evaluating the related amounts of dissipated energy. The results reveal remarkable consistency between them, underscoring the accuracy of the model in describing the complex behavior of the dampers as well as the ease of model calibration. In addition, by performing several nonlinear dynamic analyses in NextFEM Designer®, we examine various types of selected dampers thus delving into their respective advantages and determining the most effective one in reducing building displacements, velocities, and accelerations.

The increasing vibration issues in footbridges highlight the need to consider dynamic behavior in their analysis, in addition to the static loads. This study ponders the vibration performance in the design of a footbridge. Initially, the natural frequencies and modal shapes of three-span footbridge model are identified. Accordingly, a comparison with critical frequency ranges is done. Moreover, design situations are assessed by defining traffic class and comfort level, including acceptable acceleration limits. Different pedestrian stream loads of walking, running and crowded situation are modelled to determine the maximum response acceleration on the deck numerically and compare it with the allowable values. The findings show that, for daily use, human-induced vibrations stay within acceptable acceleration limits for the case study footbridge. This aligns with the design situation set by the owner. Lastly, a sensitivity analysis evaluates the effect of light and heavy concrete deck on the response acceleration due to pedestrian-induced vibrations. It also evaluates how increasing the number of people on the footbridge affects the vibration response.

In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a unified framework, ensuring stability and accuracy. The schemes are derived and analyzed for their consistency and stability properties, showcasing their effectiveness in practical computational scenarios.

This paper introduces the lightning Virtual Element Method for self-adjoint eigenvalue problems in modal analysis of structures. Unlike traditional VEM, the lightning VEM uses lightning rational functions, eliminating the need for stabilization terms and improving stiffness matrix conditioning. We explore the effect of removing the stabilization term on the spectrum of the operator, and we show that the lightning VEM is able to compute the eigenvalues of the problem with the same accuracy as the classical VEM, without suffering the polluting effect of the stabilization.

This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive algorithms based on the interplay of implicit and explicit time schemes fail to capture the fast transient dynamics of pressure fields. We present an algorithm that relies on a temporal error estimator using Backward Differentiation Formulae (BDFk) of order \(k=2,3\). Specifically, we demonstrate that the implicit BDF3 solution can be well approximated by applying a single Newton-type nonlinear solver correction to the implicit BDF2 solution. The difference between these solutions determines our adaptive temporal error estimator. The effectiveness of our approach is confirmed by numerical experiments conducted on a backward-facing step flow CFD test case with Reynolds number 300 and on a two-dimensional haemodynamics FSI benchmark.

Angiogenesis, the formation of new blood vessels, is crucial in both normal and pathological contexts, notably cancer. This complex process involves interactions among endothelial cells, tumor angiogenic factors, matrix metalloproteinases, and inhibitors. In this article, we introduce a preliminary mathematical model of angiogenesis described by a system of partial differential equations. We discretize the model spatially and solve it in time direction using a simple forward method, specifically the Euler method. This approach simplifies the computational process and provides a foundational understanding of the dynamics involved. Numerical tests and results confirm the reliability of proposed numerical procedure.

Augmenting classical epidemiological models with information from the social sciences helps unveil the interplay between contagion dynamics and social responses. However, multidisciplinary integration of social analysis and epidemiological modelling is often challenging, due to scarcity of vast and reliable data sources and because ad hoc modelling assumptions may not reproduce empirically observed patters. Here, we test the hypothesis that awareness and information spreading straightforwardly translate into behavioural responses, analysing empirical data to generate insights about their dynamics and relationships. We employ such results to build a data-informed behavioural-epidemiological model that elucidates the impact of compliant behaviours and the role of centralised regulations in mitigating epidemics. We investigate the model properties and its benefits in integrating theoretical modelling and data.