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## Über dieses Buch

This book gathers the latest advances, innovations, and applications in the field of civil, environmental and construction engineering, as presented by researchers and engineers at the XXX Annual Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering (RSP), held in September 2021. Co-organized by six universities from Russia, Poland and Slovakia, the event covered diverse topics such as structural mechanics; building structures; geodesy and geotechnics; transport and environmental issues in civil engineering. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaborations.

## Inhaltsverzeichnis

### Dynamic Actions of a Two-Layer Freely Supported Beam

The article deals with the issues of studying the stress-strain state of a structure presented in the form of a multilayer system made of various materials. A solution to the theory of elasticity and a classical solution based on Kirchhoff's hypotheses are presented. Formulas for determining the frequencies of free vibrations of the plate are determined. The results obtained are used in the construction of refined technical theories for the calculation of two-layer plates and shells. However, the problem that lies in the classical theory is significantly important, namely, this definition of the stress-strain state when a multilayer plate is investigated. The results obtained do not give any more accurate values ​​that are required in the first place, but get an approximate solution, which significantly reduces the quality of the produced process. Thus, the developed calculation methodology is presented, which makes it possible to obtain accurate and high-quality calculations applicable for any number of layers and plate sizes.

O. V. Ratmanova, M. A. Kalmova

### Parametric Study of Saw-Cut Method

Knowledge of the level of residual prestressing is a crucial basis for determining the load-carrying capacity of prestressed concrete structures. The value of prestressing force decreases over time because of expected but sometimes also unexpected factors. Expected factors include prestress losses according to available standards. On the other hand, prestress losses that are not considered in standards can be attributed to environmental distress or conceptual problems of prestressed concrete structures. In Europe, we are challenging ageing infrastructure. Thus, we need to decide whether old bridges should be replaced, or their structural state facilitates to preserve them in service. The level of prestressing can be evaluated, e.g., using indirect methods for determining the value of residual prestressing force. These methods are based on the measurements of deflection, the width of the crack, or stress (strain) and subsequently, it is possible to determine the actual state of prestressing indirectly using obtained results. This paper introduces the parametric study of Saw-cut method which is generally considered as a non-destructive indirect method. A presented study is performed for the determination of factors that could influence the application of Saw-cut methods in practice. The studied factors include the value of prestressing force, depth and axial distance of saw-cuts, and FE mesh. For numerical analysis, a 2D finite element model with the assumption of nonlinear material behavior is performed in ATENA 2D Software. Finally, the conclusions of the parametric study are discussed and summarized.

Jakub Kral’ovanec, Martin Moravčík, Peter Koteš, Andrej Matejov

### Homogenization in the Problem of Long-Term Loading of a Layered Elastic-Creeping Composite

The paper presents analytical estimates of the proximity of solutions to boundary value problems for elastic-creeping layered composite materials, which are widely used in construction, and must withstand loads for a long time, and the corresponding averaged model for such a material. The estimates show the possibility of using the averaged model over a long time interval for the problem of loading by a constantly acting force action. Previously, this statement was substantiated by numerical experiments comparing the solutions of boundary value problems for the effective (averaged) model and direct numerical calculation using the original model for a highly inhomogeneous layered material. Analytical estimates are based on previously obtained estimates of the proximity of solutions to stationary problems of elasticity theory. The problem under consideration is reduced to such problems using the Laplace transform in time. Next, we analyze analytically the dependence of the estimates for stationary problems with a complex parameter of the Laplace transform on this complex parameter, and the reverse transition to the original variables (time and spatial coordinate) is performed. The method used in this work for estimating the proximity of solutions for the averaged and original boundary value problems can also be used in the study of dynamic problems of viscoelasticity. It should also be noted that for the one-dimensional model considered in this work, an interesting property has been established: if the constitutive relations for various phases are written as dependences of deformations on stresses, then the coefficients for the same form of writing the constitutive relation of the averaged model are obtained as simple weighted averages of similar coefficients for individual phases.

T. Bobyleva, A. Shamaev

### Problems of Design of Reinforced Concrete Columns of Circular Cross-Section

The aim of the work is to consider the problems of calculating and design of reinforced concrete columns of circular cross-section, the development of proposals for a simplified analytical calculation of such columns. Studying these problems was carried out by methods of analysis, comparison, description, generalization; the calculation of such columns was carried out by the numerical method using the LIRA software package, by the analytical method using the method of simplifying the mathematical model (algorithm), as well as the graphical method. The investigation showed the presence of problems in the design of reinforced concrete columns of circular cross-section, made of both pipe-concrete and having a solid circular cross-section. The set of rules for the design of steel-reinforced concrete structures, introduced in 2016, contains only general recommendations for the design, in which issues such as the joint operation of the shell-pipe and the concrete core during eccentric compression of the concrete are not considered. The existing methods do not fully take into account the properties of building materials, the real stress-strain state of the concrete core and the steel shell, the peculiarities of their joint work. There are also difficulties in analytical calculation of solid circular columns according to the algorithm, recommended by building codes, which complicates the verification of numerical and analytical calculation methods by comparing them with experimental results. The article presents a simplified graphical method, developed by the authors, for calculating columns of solid circular cross-section, based on the algorithm, recommended by the norms.

### Disinfection and Sterilization of Air and Internal Surfaces of Industrial Premises

These studies are relevant for production facilities that are subjected to the destructive action of biologically active media during operation in various fields of industry, construction, agriculture and other industries. The article deals with the problem of negative impact of microorganisms on human health. There are promising ways to disinfect premises. We study both Russian and foreign disinfectants used to fight microorganisms that settle inside the premises. Promising areas of protection from microbiological damage, such as the integrated use of chemical and physical methods of protection, are considered. It is noted that the improvement of technology for creating and maintaining optimal microclimatic conditions in premises should be aimed at the development of improved heating and ventilation systems, which consists in the calculation and design of the latter with controlled air exchange. Authors propose a fundamentally new ventilation system, combined with heating for preventive treatment of premises. The technological scheme of disinfection of enclosing structures with the help of this system, which provides more effective treatment, is justified. The proposed method of preventive treatment is shown on the example of a livestock room. The stages of preparation and maintenance of preventive treatment are considered.

D. A. Svetlov, A. S. Boriskin, A. V. Dergunova, M. V. Vildaiva, V. T. Erofeev

### The Way of Testing Models of Buildings for Seismic Impacts

Methods of experimental modeling of seismic impact on buildings and their models under force impacts, characters and basic parameters that correspond to loads occurring during real earthquakes are considered. The main methods of seismic impact on buildings and structures were analyzed using seismic platforms of software control, directed powerful underground explosion and vibration machines. The advantage of the vibration method is proved, which allows relatively fast and easy and low-cost testing of both full-scale buildings and structures, as well as their models. Experimental installation and method of testing of buildings and their models for seismic impact, excited with the help of simultaneously acting several vibration machines, are presented. Oscillograms of superposition of the first II–III vibration modes were obtained when testing a model of the frame of a 9-storey building. In order to assess the degree of accuracy of the proposed method of simulating seismic impact from the accelerogram earthquakes, floor movements of a building model were determined theoretically and experimentally. The comparison of the results of theoretical and experimental studies showed that the discrepancy between them is on average 10–15%.

Avetik Abovyan, Aleksandr Marutyan, Gurgen Abovyan

### Design and Modelling of Storage Tanks Exposed to Thermal Actions

This paper presents results of a research on the effect of a high temperature, resulting from the storage technology, on the utilization level of stresses in selected individual structural components of a cylindrical, above-ground steel tank with a vertical axis and a fixed roof. Computational simulations were performed for the geometry of an existing facility that had failed during the service life. The analyses conducted resulted in specifying members, in the case of which taking into account thermal effects in the dimensioning process is desirable, undesirable or negligible from the point of view of operational safety.

### Quatrefoil Motif in Slovakia – Gothic Roots of the Parametric Architecture

Geometric elements are the basis of various forms of creating architecture at present - parametric modeling, the use of BIM, adaptable architecture. The basis for all of them are simple constructions by a combination of lines and circles, which also have their roots in Gothic motifs and geometric constructions. The article deals with the geometric procedures of creating one of the motifs - quatrefoil and examples of its application in the Gothic architecture of Slovakia. The quatrefoil is created by an additive combination of 4 circular or oval shapes, centrally symmetrical, visually attractive, contains symbolic, religious connotations. It occurs as a mass - floor plan, cross-section of architectural elements - and as a negative space - openings.

Zuzana Grúňová, Michaela Holešová

### Ventilated Air Cavity – Annual Evaluation

The restricting regulations in European legislation lead to significant changes in building designs in order to reduce energy consumption. Possible approach to this phenomenon is to design passive wooden houses which provide high thermal resistance whilst maintaining relatively small structure thickness. Scientists engaged in these wooden structures focus nowadays on issues linked to the timber-framed wall structures, amongst others durability, heat capacity, or summer overheating. This paper focuses on measurements of a light-weight wooden wall assembly with ventilated air cavity which is one of possible solutions not only to reduce the influence of weather changes, but also to reduce overheating of interior space. This specific assembly is implemented in pavilion research of Department of Civil Engineering and Urban Planning within UNIZA campus in Zilina, Slovakia. It summarizes annual measurements of temperature and relative humidity in the sample center and near the wooden studs. Contribution describes the potential of using ventilated air cavity to maintain steady conditions thorough whole year.

Daniela Michálková, Pavol Ďurica

### Controversy Over Cracks in Glued Laminated Timber Beams

The analysis and evaluation of cracks in three different case studies of glued laminated timber structures is presented in the paper. The analysis is performed from the point of view of possible failure due to crack defects.

Anna Al Sabouni-Zawadzka, Wojciech Gilewski, Paweł A. Król, Jan Pełczyński

### Features of the Calculation of Composite Beams with Constrained Torsion and the Presence of Corrosion Damage

In the process of operation in the construction metal structures are subject to intensive physical wear, manifested in the form of mechanical, corrosion damage, the formation and development of deformation damage in the form of cracks. The essential influence of the constructive form on structure durability is obvious from the analysis of steel structures corrosion damages. Studies of the influence of various elements, assemblies and conjugations of structures can prevent the corrosion damage in the design process. Knowing the quantitative indicators and regularities of this influence on the value of corrosion resistance of the structure as a whole, one can already pre-determine and choose possible constructive form which would least contribute to the emergence and development of factors increasing the intensity of corrosion damage. Usually, the influence of several factors is summed up at the same surface area and causes particularly accelerated destruction.

A. V. Soloviev, L. Y. Rybakova, O. N. Solovieva

### Fire Dynamics Simulation in an Apartment of a Timber Building Depending on the Ventilation Parameter

In modern buildings are also currently used the wooden-based construction systems. A wide range of uses the timber constructions in apartment buildings is a vision of the countries of the EU. The use of timber and the other recyclable materials in apartment buildings creates the precondition for the implementation, operation and disposal of environmental impacts of the EU 2020 Strategy. In the long term is important to transform the construction of buildings to a sustainable standard. Currently, the fire height of timber apartment buildings in majority of EU countries is limited to 5 storeys. This paper deals with the influence of the ventilation parameter in the time and the intensity of the gas temperature during a fire in a model of an apartment building with a timber supporting structure. FDS (Fire Dynamics Simulator – PyroSim software) is used for dynamic simulations of fire in the model apartment.

Agnes Iringová, Dominika Vandličková

### Introduction to the Green Roof Research

Green roof is one of the best answers to the global climate change problems in urban areas with the possibility to reduce urban heat islands. It can reduce the temperature maximum and daily variance of temperatures, which has the positive effect on durability of the waterproof membrane. Retention of the rainwater enables the possibility for evapotranspiration. In this paper, the experimental measurement of various extensive green roof fragments is described with their possibilities and limitations. Temperature and water retention regime of the fragments are monitored as well. Temperature measurement results during autumn, winter and spring days are stated. The result is that daily temperature variance is reduced by use of green roof.

Peter Juras

### Influence of Ice Cover on Operation of Concrete Dams’ Gates

The experience of operating emergency gates under freezing conditions at a number of hydroelectric power plants has shown the insufficient efficiency of the applied methods of fighting against frost structure damage. The rules for the maintenance of spillway dams’ gates in wintertime imply the heating of structures along their grooves, threshold and enclosure, combined with measures for the maintenance of hatches before the beginning of construction. However, heating the gates and arranging ice-free areas are not always sufficiently substantiated and justified. In order to obtain field data and scientific information for the development of recommendations on operation modes and for taking into account when designing, field research of stresses and deflections in the bearing elements of spillway dams’ gate has been carried out. The results of the field research in comparison with the design values are presented in this article. This research is a source of information about the static operation of plane gates under wintertime conditions, which is of theoretical and practical interest. The materials can be used to clarify the rules of maintenance and to clarify the regulatory documents for the design of hydromechanical equipment at hydroelectric power plants.

Sergey V. Evdokimov, Vladimir A. Seliverstov, Tatyana V. Dormidontova

### Reinforced Concrete Matrices Under Impulse Loads

Reinforced concrete matrices are used in the method of hydro explosion stamping for the manufacture of sheet metal products. Reinforced concrete matrices have a number of advantages that ensure the effectiveness of their use. However, there is a problem – low durability under repeated explosive loads. The analysis of scientific publications makes it possible to set the goal and objectives of the research. Thus, the paper analyses ways of improving the constructive of reinforced concrete ring-shaped matrices for hydro explosion stamping and methods of calculating matrices. The author describes the developed design of the matrix, to which he additionally install a compensation layer and a hydraulic chamber. The paper further describes the developed method of calculating ring-shaped reinforced concrete matrices. The author's proposed method for calculating strength and deformation is based on the method of finite integral transformations. A theoretical calculation was performed using various mathematical models. Experimental researches of a series of matrices samples under explosive loads have been carried out. Comparison of theoretical and experimental results is made. Moreover, both our own research and other authors. As a result, a calculation method was obtained that allows one to determine the values of stresses and deformations in the matrix under the action of impulse loads at any time and in any part of the matrix.

Dmitriy Kretov

### Long-Term Window Evaluation: Comparison of Pavilion Laboratory and Climate Chamber Measurement

In the pavilion laboratory there are three different windows evaluated since 2011. These windows are suitable for low-energy or passive houses. Two different plastic based windows were modelled and the temperatures were compared to the real measurement with different outdoor temperatures. One of the windows, with the theoretically worst properties was recently removed and another one was mounted into the laboratory. Than the window was tested in the climate chamber. Result is the comparison of temperature courses with simulation of the same winter day as recorded with the weather station. Similar results were obtained and the degradation of thermal properties of the window were confirmed.

Peter Juras, Pavol Durica, Marek Bartko

### Impact of Sun-Shading Devices in Daylight Assessment with Daylight Ratio in Energy Efficiency Building Design

The research presented the correction for daylight calculation under the real sky condition with the Daylight Ratio for the Russian standard in consider impact of horizontal shading devices. In this research, the method for daylight calculating was improved with the proposal of two coefficients Kshad and Kref that consider the influence of the shading device and replaced the approximate factor τ4, which consider the shading in the exits Russian standards. The research also reveals the assessment of daylight in a room under an intermediate sky is characterized by a reflection of direct sunlight. The results show that a significant effect from the reflection coefficient when the first reflecting surface has a high reflectance and sky condition with high diffuse radiation. Correcting the shading and reflecting coefficients shading device under the Intermediate Sky was associated with the availability of Climate Based Daylight Modelling. With this approach, it is possible to complete the criteria for a dynamic daylight assessment, by combining an artificial lighting system with a touch mode, it will guarantee the requirements of indoor illuminance and energy efficiency.

Ashot G. Tamrazyan, N. T. K. Phuong

### Finite Element Method Modelling of Long and Short Hyperelastic Cylindrical Tubes

The paper presents a study on modelling a rubber cylindrical tube in the finite element method software. It begins with a definition of stored energy functions of considered hyperelastic models. The main part of the paper concerns the problem under the plane deformation assumption, which physically may accurately approximate a sufficiently long tube. It is modelled in ABAQUS using two approaches. The first one consists of a quarter of the cross-section with boundary conditions that impose symmetry. The other FEM model involves an axially symmetric stress formulation. Results are compared with values obtained analytically. The paper ends with an example of numerical solutions for a short cylindrical tube without plane strain assumption.

Stanisław Jemioło, Aleksander Franus

### Mathematical Modeling of the Collapse Form of the Borehole Walls

The paper considers the methodology for determining the critical angle to the horizon when the borehole walls in the bases, composed of underconsolidated sandy soils collapse. The purpose of the paper is to develop a criterion by which ground collapse occurs in a borehole. The paper considers the determination of geometric form parameters of the soil that lost stability and weight. The proposed mathematical modeling of the collapse form shows that the stability of the borehole walls depends not only on the angle of internal friction of the soil, but also on its specific weight and the diameter of the borehole itself. The geometric form of the borehole collapse and its weight obtained in the process of modeling will allow to determine the crimping pressure acting on the outer surface of the casing under the protection of which the drilling is carried out in under consolidated sandy bases in the next stages of research. Knowing the amount of pressure compressing the casing pipe, we can calculate it by the material and the optimal wall thickness. It is possible to calculate the cross-section of the pipe for geometric invariance. It is able to calculate the cross-section of the pipe for geometric invariance. Calculation of the casing pipe material will allow the implementation of modern, light and durable materials in the construction, which significantly reduce the cost of construction of zero cycle structures. The geometric invariance of the casing pipe cross section is an important condition responsible for the geometric dimensions of the future pile in the project documentation. It should also be noted that according to the results of preliminary calculations on the proposed mathematical model, it was found that the sand base cannot have a verticality of 90-degree slope. Drilling of boreholes in the described soils cannot be carried out without the use of casing.

Dmitriy V. Popov

### The “Floating Foundation” Method in Calculating the Settlement of Foundation Slabs

The problem of determining the active zone of the base below the foundation and calculating the settlement of the foundation is still of scientific and practical interest. In most cases, in design, the theory of a homogeneous isotropic linearly deformable medium is used to determine the deformations of soil foundations. In the article, the authors propose to use the one-dimensional problem of the theory of compression soil compaction to calculate the settlement of large-area foundation slabs. As the arguments of the proposed methodology, the finding of the lower boundary of the compressible thickness soil is specified. The author's formula for calculating the slab foundation settlement is presented. Comparison of the calculation results according to the author's methodology and the methodology from the current building standards is given. The comparison showed that when using the theory of a linearly deformable half-space, the depth of the compressible soil thickness (and, accordingly, the value of settlement) increases with an increase in the area of the foundation at the same load. When calculating according to the authors' method, the settlement of slab foundations depends only on the magnitude of the compaction pressure and on the specific gravity of the soil. The advantages and disadvantages of the “floating foundation” method are presented.

Veniamin Isaev, Andrey Maltsev, Andrey Karpov

### Organic Soil Stiffness – Local Experience from Northern Poland

This paper shows an example relationship between CPTU cone resistance and oedometric modulus determined in laboratory tests. The coefficient $$\alpha$$ α for weak soils is proposed on the basis of local experience by comparing the results of laboratory incremental loading oedometer and in-situ cone penetrometer (CPTU) tests. Laboratory tests served as a reference, while the interpretation of CPTU results was based on averaging the values of resistance on the cone qc for a given layer. Moreover, the authors showed how large the discrepancies in the obtained value may arise during the interpretation, only due to the selection of the coefficient $$\alpha$$ α . As cost-effective designing of the reinforcement of the soil nowadays is a difficult challenge the accurate determination of the coefficient $$\alpha$$ α seems to be an essential part of geotechnical surveys.

Maciej Maślakowski, Karol Brzeziński, Monika Płudowska-Zagrajek, Kazimierz Józefiak

### Deformation Resistance of the Sub-ballast Layers of a Selected Modernized Line Section

The constant improvement of the safety and reliability of railway transport and the interoperability of railways are the basic pillars of the emerging European integrated railway area, of which the Slovak Republic is, regarding its geographical location, an integral part. Three corridors of the basic TEN-T network pass through the territory of the Slovak Republic, two of them crossing the Žilina Region.Namely, these are the Baltic-Adriatic and Rhine-Danube corridors, with the joint section Púchov-Žilina, on which modernization works are currently being completed. As the line in question was built in the 1970s and only the necessary funds were spent on its maintenance or reconstruction during its existence, its modernization was highly desirable. Following the above facts, the presented article deals with the analysis of deformation characteristics of structural parts of the sub-ballast layers, obtained within the quality inspection of the work performed on the modernized line section Púchov-Považská Teplá. As part of the quality inspection, static load tests were performed.Their result was an assessment of the deformation resistance at the level of the subgrade surface and the sub-ballast upper surface. Following the article conclusions, the line section in question finally meets the quality parameters corresponding to the standards of the developed European countries. The conclusions also include a summary of experience from several implemented construction projects that can be applied in the further modernization of ŽSR (Railways of the Slovak Republic) infrastructure.

Libor Ižvolt, Peter Dobeš, Martin Mečár

### Rehabilitation of Railway Track Quality in Relation to Diagnostic Data

The railway is a strategic part of the industrial infrastructure of many countries. The overall quality of the railway track structure is affected individually and in various combinations of geometric and material parameters in the form of an extensive set of quality indicators. The quality of a railway track structure during its service life goes through several phases of utilisation (quality degradation) and repairs (quality rehabilitation). Quality indicators represent parameters and factors that are in individual technical groups of the structure capable to objectively describe the quality of their condition and behaviour. At the border of the degradation and rehabilitation phases, the railway manager decides on the implementation of the optimal technical, technological, time and economic format of quality rehabilitation. The decision-making process is subject to the structure and result of the evaluation of the diagnostic data. Although various factors of mechanical properties of the track structure have been investigated for its operational quality in the recent period, the quality of track geometry represented by geometric parameters remains the focus in the decision-making process on the rehabilitation of track quality. This article examines the quality of a specific test section of a railway track from the point of view of the quality of the track geometry. The structure of diagnostic data, the method of their collection, determination of quality indicators and their evaluation are described. The evaluation of quality indicators is connected with models for predicting the future state of track geometry quality using regression and correlation analysis of the dependence of the development of determining quality indicators on time.

Janka Šestáková, Andrej Matejov, Alžbeta Pultznerová

### Terrestrial Laser Scanning Application for General Plane Position Estimation

The method of terrestrial laser scanning (TLS) data acquisition becomes the widely applicable method for the miscellaneous analyses. Its application in the civil engineering field still increases. The deformation and translation processes may be captured, calculated and interpreted after the visualization of collected data from the laser scanner. The detailed and mainly redundant data provided by the TLS method enable reliable analysis with sufficient precision and related application of estimation models and analysis. It is possible to estimate and examine the chosen object’s parameter and observe its behavior and course. This research is devoted to the estimation of the plane in the general position folded by the examined construction parameter which was laser-scanned by the terrestrial laser scanner Leica ScanStation C10. For the estimation of plane parameters, the combined Gauss-Mark model is used. The estimated plane calculation and interpretation contributes to the construction parameter’s course observation with the application of TLS data.

Jakub Chromčák, Daša Bačová, Anna Seidlová, Peter Danišovič, Ingrid Zuziaková

### Method for Determining the Casing Pressure in Uncompacted Sandy Bases When Installing Bored Piles

The article deals with the method of calculating pressure on the outer surface of the casing at the device of bore drilling wells on the basis of the results obtained during the experiments carried out in laboratory conditions. The purpose of the work is to reduce the material capacity and, consequently, to reduce the cost of foundations made with the use of bored piles.

D. V. Popov, E. V. Savinova

### Models of Deformation of Plates with Double Anisotropy

Special cases of transverse bending of structurally orthotropic annular plates made of materials whose deformation and strength characteristics depend on the type of stress state are considered. Such plate materials can be characterized as structures with anisotropy of a twofold nature. The plates were loaded with a uniformly distributed transverse load. In addition, when setting the problem of structural mechanics of plates, it was taken into account that all structures are operated not in an inert space, but in an environment with variable temperature parameters. The connectedness of thermomechanical problems is noticeable only in the short initial time interval of the heat transfer process before the steady-state temperature drop is stabilized. Therefore, in the present study, the problem of thermal force loading of annular plates was considered in an unrelated formulation. In this case, the general problem is divided into two independent ones: structural mechanics and thermodynamics. Given that the generally accepted theories of plates, in the case of anisotropy of a twofold nature, do not allow us to obtain acceptable results, and the known models intended for calculating their stress-strain states have gross non-physical limitations and disadvantages, the presented work is focused on the use of the normalized stress method. The system of differential equations for the problem of transverse bending of annular plates made of materials with complicated thermomechanical properties is obtained below. Particular solutions with characteristic results of calculating the stress-strain state of plates are presented, and their brief analysis is carried out.

Alexander Anatolyevich Treschev, Yulia Andreevna Zavyalova, Maria Alexandrovna Lapshina, Alexander Anatolyevich Bobryshev

### On the Calculation of Thin Shells Beyond the Elastic Limit

This paper presents the results of the calculation of a thin spherical shell, the material of which operates beyond the elastic limit. Thin isotropic shells of rotation of constant thickness h are considered. The complete system of the equations contains the equilibrium equations, the geometric relations of linear theory, and the physical relations of the small elastic-plastic deformations theory. The problem is solved using the elastic decisions method. By decomposing the functions of forces, deformations, displacements, and loads into Fourier series in the circumferential coordinate θ and then converting the complete system of equations, the system of eight first-order differential equations with respect to the Fourier series coefficients of the selected resolving functions is obtained. The integration of the resolving system of differential equations is carried out by the run-through method with discrete orthogonalization. In this paper, we study the change in the stress-strain state and the region of occurrence of plastic deformations when changing the place of application of three ring loads. A significant role in the formation of plastic deformations is played not only by the size of the ring loads, but also by their location on the surface of the shell.

Avgustina Astakhova

### Influence of the Connectedness of Thermoelastic Fields on the Stress-Strain State of a Circular Rigidly Fixed Plate

In the case of heating the upper and lower surfaces of a circular rigidly fixed plate, a new closed solution to the dynamic problem of thermoelasticity is constructed. To obtain the calculated ratio, the method of finite biorthogonal transformation is used, which is used for arbitrary external temperature effects in time (the boundary condition for thermal conductivity of the first kind). The software was developed to analyze the effect of thermoelastic fields on the temperature field and the stress-strain state of the structure. Numerical analysis of the calculation results shows that for a given external temperature effect, the rigidity (physical and mechanical properties and geometric dimensions) of the elastic system has a significant effect on its thermoelastic field. At the same time, taking into account the rate of change in the volume of the plate, the temperature and mechanical stress during the heating of the plate decrease. In the future, under constant temperature conditions, field coupling will not be observed.The calculated ratios obtained make it possible to determine the stress-strain state of a rigidly fixed circular plate under an arbitrary axisymmetric temperature external action.

Zhanslu M. Kusaeva, Dmitrii A. Shlyakhin

### Adhesive Problem in the Mechanics of Materials

The essence of the method of anisotropic contact layer, which forms the basis of the direction called adhesion mechanics, is presented. The effectiveness of the approach is demonstrated by solving an important model problem of multiple fibre fracture under tension of the Kargin-Malinsky reinforced polymer model (fibre in a matrix). The method allows us to satisfy the initial equations and all boundary conditions, i.e. to solve the Cauchy problem strictly. The unusual experimental results are explained by the peculiarities of the stress distribution in the region of their concentration, i.e. near the fibre break.

Robert Turusov, Vladimir Andreev, Nikita Tsybin

### Asymptotic Solution of Elasticity Problem in the Vicinity of Irregular Boundary Point

The present paper presents a study of the stress-strain state (SSS) in the vicinity of an irregular boundary point. The distinctive feature of the solution of the boundary problem of the elasticity theory is stipulated by the boundary form: angular notches, cuts, and by the finite discontinuity (leap) of forced deformations in terms of the contact of the parts constituting the area coming to an irregular point of the area boundary. Stress-strain state in an irregular boundary point area is determined by solving the uniform elastic boundary value problem. For SSS analysis, strain and stress intensity factors are introduced in the vicinity of the irregular boundary point. The stress-strain state is analyzed in the area of an irregular boundary point, to be written by means of strain and stress intensity factors under recognition of their differences. The obtained SSS expression in the boundary notch area allows to write down the dominant term of the asymptotic behavior of the uniform boundary elasticity problem under recognition of the strain and stress intensity factors.

Lyudmila Frishter

### Uncoupled Problem of Thermoelectroelasticity for a Cylindrical Shell

A new closed solution of the coupled dynamic problem of thermoelasticity for a long cylinder in the case of a change in temperature on its front surfaces is constructed. The mathematical formulation of the problem under consideration includes the linear equations of motion and heat conduction relative to the radial component of the displacement vector, as well as the function of changing the temperature field. The problem is solved using the method of separation of variables in the form of a generalized finite integral transformation (CIF). The constructed design ratios make it possible to determine the stress-strain state and the temperature field of an elastic element under an arbitrary temperature external effect.

D. A. Shlyakhin, M. A. Kalmova

### Equivalence of Soils Under Limiting Stress State

Through a calculation model from the theory of limiting equivalence, from a corresponding system of equations for a two-dimensional problem set, the equivalence of limiting stress state of granular soil is determined to within a triaxial uniform compression equivalent to the coherence. The authors note the possible use of the result for the reduction of restrictions substantiated by the soil coherence (the routine studies do not assume any change in the soil coherence and in its own weight in accordance with the simulation conditions in the process of the experiment, hence the realization of these conditions with the change in the geometric scale similarity factor cannot be guaranteed for any choice of the force similarity factor. To illustrate the suggested method, based on the equivalence of soils in limiting stress state, the authors consider an example of determination of the active pressure onto the embankment wall caused by the own weight of the coherent soil.

### Hybrid Finite Element Formulation for Geometrically Nonlinear Buckling Analysis of Truss System Under Mechanical and Thermal Load

This paper introduces a novel approach to establish the nonlinear buckling problem of truss systems under mechanical and thermal load due to constant temperature change based hybrid FEM. In geometrical nonlinear displacement-based finite element analysis, the thermal deformation of truss element is dependent on the incremental element length and requires the implementation of additional thermal deformation constraints. For escaping the implementation process the research proposed to build the hybrid finite model assembling two types of truss finite elements with different numbers of unknowns (common truss element and thermal truss element). Both common truss element and thermal truss element are established based on the large displacement theory. The hybrid global equilibrium equations are developed by assembling constructed common and thermal truss elements. For solving geometrically nonlinear buckling analysis of truss under mechanical and thermal load the incremental-iterative algorithm is established using the arc-length method. The calculation program is written for investigating the effect of thermal load on the buckling behavior of plan truss.

Vu Thi Bich Quyen, Dao Ngoc Tien, Tran Thi Thuy Van

### Lagrange Multiplier Method for Treatment of Nonlinear Multi Freedom Constraints in Dynamic Finite Element Analysis of Truss System Subjected to Harmonic Load

The dynamic finite element analysis of truss with multi freedom nonlinear constraints requires the implementation of constraints to producing the modified dynamic system of equations. Generally, in finite element analysis the mathematical technique for imposing nonlinear boundary constraints based on optimization methods such as the penalty augmentation method and Lagrange multiplier adjunction method. This paper presents an approach to treat the nonlinear multi freedom constraints in dynamic finite element analysis of truss based on the Lagrange multiplier method. Using the Lagrange multiplier method the modified dynamic equilibrium equation is constructed by extremizing the Hamiltonian function and converting a constrained problem into an unconstrained problem. To solve the dynamic equilibrium equation of system under time-dependent harmonic force, the algorithm is established based on the combining Newmark integration method and Newton Raphson method. Using the proposed algorithm the calculation program for dynamic analysis of truss subjected to harmonic load is written. The illustration of numerical example shows the efficiency of the established algorithm.

Vu Thi Bich Quyen, Dao Ngoc Tien, Tran Thi Thuy Van, Pham Van Dat

### Methodology for Assessing Seismic Resistance of a 5-Storey Reinforced Cross-wall Concrete Building

The application of a simplified approach with the introduction of K1 to take into account the nonlinear behaviour of buildings and structures of some structural layouts when designing buildings and structures in seismically hazardous areas can result in a lack of seismic resistance. The use of nonlinear dynamic methods that allow the combined performance of reinforcement and concrete using finite solid elements to be explicitly considered can provide for more reliable results. The work evaluates the value of the allowable damage accounting factor K1 and assesses the actual level of seismic resistance of a 5-storey reinforced concrete cross-wall building given a seismic impact with an intensity of 9 points on the MSK-64 scale.For the building under consideration, a bearing capacity safety factor of Ksaf = 0.9 was obtained. The results of nonlinear dynamic analysis show that for a given building, low-frequency influences make a greater energy contribution to the system response than high-frequency ones.The values of the coefficient given in SP 14.13330.2018 ‘Seismic building design code’ to consider allowable damage K1 for buildings and structures of the corresponding structural layouts should be clarified, including using nonlinear dynamic methods.The results obtained in this work should be taken into account when calculating and designing multi-storey cross-wall buildings in earthquake-prone areas.

Oleg Mkrtychev, Mikhail Andreev

### Considerations on Tensegrity Shell-Like Structures Based on 4-strut Simplex Module

The analysis and evaluation of possible application of 4-strut Simplex tensegrity module for creation of shell-like lattice structures is presented in the paper. Separate modules are analyzed from the point of view of infinitesimal mechanisms and self-equilibrated systems of forces. Further analysis is performed for shell-like spherical, cylindrical and hyperboloidal paraboloid (the shells of positive, zero and negative Gaussian curvature).

Kamila Martyniuk-Sienkiewicz, Wojciech Gilewski

### The Prediction of Railway Induced Vibration Effects on Planned Building

The paper describes the analysis of the dynamic effects of the railway transport on the planned structures in its vicinity. It describes attention to the current problems concerning the technical seismicity involved by rail transport with high-intensity. This analysis is based on results of real case study in Milochov village near main Slovak railway corridor. It describes the process of experimental measurement, evaluation of measured data and the obtained results of the dynamic response of the subsoil from random excitation. This analyzed random excitation is caused by trains running on a heavy loaded railway line.

Zuzana Papánová, Daniel Papán

### Critical Issues in Designing Controllable Deployable Tensegrity Structures

The present paper discusses most critical issues that engineers encounter while designing deployable tensegrity structures for real applications. A thorough literature study is performed to indicate various problems in designing tensegrity structures and their control systems. A step-by-step process of designing a controllable deployable tensegrity system is analyzed on three levels: mechanical design, control design and global layout design. Special focus is put on the description of possible problems that are expected in the design process of morphing or deployable tensegrities, such as the proper design of joints, choice of control algorithms, actuators positioning, collisions between structural members and entanglement of cables. This paper shows the most critical issues that need to be addressed during developing a tensegrity structure for real application. The authors created a roadmap of problems that will occur at different stages of the design process.

### Dynamic Stability of the Plate at the Second Resonance with Creep Taken into Account

The problem of determining the side regions of dynamic stability of a rectangular plate, the material of which obeys the linear creep law, is considered. The solution of the differential equation of vibrations of a plate loaded with constant and variable periodic loads in the plane of the plate is presented as a series with separated variables, which satisfies the conditions for fixing the plate. As a result of using the Bubnov-Galerkin method, differential equations of the third order with variable periodic coefficients are obtained for finding functions that depend on time. To construct even domains of dynamic instability, a solution in the form of a trigonometric series was used. As a result, a system of equations was compiled for the coefficients of the series. To calculate the even regions of instability of the plate, an equation of critical frequencies was obtained in the form of a system determinant. This equation allows us to construct the boundaries of the regions of instability. The study of the influence of the relaxation time and the ratio of long-term and instantaneous moduli of elasticity on the position of the second region of dynamic instability has been carried out.

E. Kosheleva

### COMSOL Multiphysics Implementation of SMA Bracing for Multi-story Structure

This article describes the implementation of a material model of shape memory alloy (SMA) in COMSOL Multiphysics software. Authors discuss different possibilities of modeling SMA within this system and present the approach that is continuation of their previous work. The behaviour of material is described with a set of explicit differential equations that derive from the rheological scheme of the SMA. The equation interpreter within the software allows straightforward implementing equations to the Partial Differential Equation Module coupled with Structural Mechanics Module. This modeling strategy was illustrated with analysis of a five-story steel frame subjected to the Loma Prieta earthquake. The structure was equipped with buckling resistant braces with SMA dampers. Due to the unique characteristic of superelasticity this kind of dampers enhance performance of the setup. Presented results show the benefits of the approach to material modeling by using rheological schemes and possibilities of its application within a commercial software.

Kacper Wasilewski, Artur Zbiciak

### Forced Vibrations of a Thin-Walled Rod of a Symmetric Profile

The paper provides an analytical solution to the problem of natural and forced vibrations of a thin-walled elastic rod with a symmetric profile. The mathematical model also considers the forces of viscous resistance, which, in accordance with the frequency-independent Voigt hypothesis, are introduced in the process of solving the problem. The solution is constructed for an arbitrary dynamic load and two types of boundary conditions: hinged support in constrained torsion and free warping of the end sections of the rod; rigid fastening with constrained torsion and the absence of warping. A feature of the problem is the presence of a complete system of inertial terms, which determines the specifics of the application of the method of finite integral transformations, which serves as an effective way to solve problems in mechanics. The spectrum of circular frequencies of vibrations of the rod, expressions for linear displacements and angles of twisting are obtained.

Elena N. Elekina, Elena S. Vronskaja

### Nonlocal Numerical Damping Model in Beam Dynamics Simulation

The numerical model of material damping adaptable to the finite element structural dynamic analysis is proposed in the paper. In comparison to the classic external damping model used in this research internal damping model is considered nonlocal in time according to the hereditary mechanics concept. Efficiency of the nonlocal model, its advantages over the classic Kelvin-Voight hypothesis and its flexibility is considered on the example of the composite beam dynamic analysis. The example of nonlocal in time damping model key parameters using the 3Dnumerical simulation results is shown. The 3D numerical simulation was implemented in Simulia Abaqus considering the orthotropic properties of the material.

### Method of Stabilization of Resonant Parametric Vibrations

From a practical point of view, the most important feature of parametric vibration systems is the phenomenon of so-called parametric resonance. Parametric resonance occurs when a point specified in a parameter space of a differential equation system describing parametric vibrations is inside one of the instability areas of that equation. There are vibrations with exponentially increasing amplitude. According to linear vibration theory, this increase is unlimited, and therefore the only possible variant of eliminating this, generally negative, phenomenon is to change the parameters of the system to be outside the area of instability. According to Floquet's theory, the stability or instability of the parametric system is determined by the absolute values of the system multipliers, which are complex eigenvalues of monodromy matrix (Floquet transient matrix). If the module of the largest multiplier is less than unity – the system is stable, if it is greater than unity – the system is unstable. The work presented a method of automatic stabilization of resonant parametric vibrations. A procedure based on the concept of directional derivative was used. The idea is that, of all possible options for changing the value of the design parameters of the system, the system should be automatically selected as it will ensure that the modular value of the largest multiplier decreases as soon as possible. The method also uses algorithms of first and second order sensitivity analysis of continuous and discontinuous parametric periodic systems presented in the previous two years at the RSP Seminar in two works by Wójcicki [1, 2].

Zbigniew Wójcicki

### Absorbers Impact on the Reliability of Bridge Abutments

One way to reduce vibrations of a bridge abutment is to add an absorber tuned to the structure. It is important to properly design an absorber, which the most common design is a sprung mass because of its simple structure. A new parameter optimization criterion was proposed - consisting in minimizing the probability of the maximum vibrations of the structure exceeding a certain permissible value of displacements. This criterion means maximizing the reliability of the vibrating structure with regard to the maximum vibration amplitudes. The authors analyzes when vehicles are passing by a bridge abutment in two situations: there is a lot of traffic and the movement is small. In both the cases random vibrations of the bridge abutment are emulated by a filtered Poisson process. When traffic is so small that excitations can be considered separately, in the other way – a series of impulses. Numerical solutions and selection of optimum absorber parameters are presented for both situations.

Monika Podwórna, Jacek Grosel

### Resuspension of Road Traffic Related Particulate Matter to the Environment

An important source of suspended particles PM in urban air is the resuspension of road dust. The aim of the described study was to collect road dust at sampling points and to determine its size distribution by a classical screening test. Grains of road dust passed through a 0.125 mm sieve (sub-sieve fraction) are subjected to X-ray fluorescence spectroscopy to determine the chemical composition. At the measuring station, measurements of particulate matter PM10, PM2.5 and PM1 were performed by the gravimetric method (sampling of particulate matter on filters). In addition, measurements were performed with SMPS and APS particle size spectrometers, which monitored the distribution of aerosol in the range of 12 nm to 20 µm. The amount of selected chemical elements in the particulate samples obtained by the gravimetric method was determined by inductively coupled plasma mass spectrometry (ICP-MS). Based on chemical analyzes of collected road dust and particulate matter collected from the air, the concept of the possible contribution of road dust resuspension to the concentration of particulate matter in the air was determined.

Dusan Jandacka, Daniela Durcanska

### Multicriteria Assessment of HLC (Hemp-Lime Composite) Technology with Different Criteria Weights Estimation Methods

One of the most important issue in multicriteria assessment is finding proper way of criteria weights estimation. It is especially problematic in assessment of newly introduced building materials, when almost none historic data is available. In this paper various methods of weights estimation are compared in valuation of various HLCs (Hemp-lime composites), commonly referred to as hempcrete. New method based on standard deviation of ratings in each criterion is proposed and compared with traditional, well-known algorithms such as Simos method, both variants of calculation proposed by Hokkanen and Salminen and REMBRANDT system.

Łukasz Rosicki, Wojciech Piątkiewicz, Michał Krzemiński

### Mathematical Modeling of Jet Aeration Process for Ecological Purification of Ponds

The problem of oxygen enrichment of polluted water bodies and volumes of liquids is considered. For this purpose, the counter vortex aerator created at the National Research Moscow State University of Civil Engineering is used. The principle of its operation is based on the interaction of two oppositely rotating flows of water, which makes it possible to form a two-phase gas-liquid jet. For the mathematical modeling of the aerated jet propagation process, the method of integral relations, based on the balance of mass, momentum, and interfacial interaction forces is used. The resulting system of ordinary differential equations is integrated numerically by the Runge-Kutta method of the fourth order of accuracy. The principal kinematic characteristics of the jet flow and the optimal operating conditions of the counter vortex aerator are determined. A comparison of the numerical results with experimental data obtained on a hydraulic device is carried out. Generalized dependencies for the engineering calculation of the depth of development in the water body are presented.

### Analysis of Traffic Relations Based on Mobile Operator Data

The article deals with the current issue of processing mobility data from SIM cards. The introduction of the article presents the issue and description of the basic methodology of data processing. The basic source of data is data from mobile operators. The database contains records completely evaluated according to the node system (network of transmitters). The operator is responsible for the anonymity of the data. The trips are evaluated based on several boundary conditions from the point of view of the mobility study. The overall results point to the advantages and disadvantages of such a data source. Two areas are analyzed in the article. The database file of the first area covers the territory of the Žilina self-governing region. The second area is the territory of the Slovak Republic, where five routes across the country (east-west) were analyzed. The study aimed to locate the origins and destinations of the trips, the preferred route, and the share of transit, origin, or destination traffic from the point of view of the region, or district, respectively. The main advantage of using data from SIM cards is the non-invasive form. The data can be located based on the position of the transmitter. A big disadvantage is the possibility of wrong node localization, especially in difficult terrain conditions. The article gives an example of several examples of evaluation taking into account the goal of the study area.

Marek Drliciak, Jan Celko

### The Risk Indicators of Construction Projects’ Cost Overruns Assessed with PCA, Decision Trees, and Pearson’s Correlations

The execution of 55 road construction contracts is examined. The created database comprises the three type of data collected: physical properties of the erected objects, financial data and scheduled periods of work execution. The contractor’s cost overruns are noted for a significant part of the analysed contracts. To find the most influential indicators that can help in assessing the size of a cost overrun or in warning against it, the following three tools are applied: Pearson’s correlations, principal component analysis (PCA) and decision trees (classification and regression trees C&RT). The article is aimed at calculating the three rankings based on these tools. The analysed, ranked independent variables do not cause the cost overruns but they may indicate the possibility of the cost increase. The applied tools are selected for their varied types of results: the relations of the output with the singular type of input in Pearson’s correlations, the variability of different types of inputs analysed jointly (but excluding the output) in PCA and the influence of the different types of data analysed jointly on the output in C&RT.

Hubert Anysz, Magdalena Dąbrowska

### On the Use of Self-oscillations Excited by the Deformation of Polymer Films in the Actuators of Nanomechanical Devices

There are a number of tasks that require the creation of executive micro - or nanomechanical devices that allow you to convert one type of mechanical movement (for example, displacement) into another (for example, into oscillatory). Such devices that convert the energy of the input signal (electrical, optical, mechanical, etc.) into an output signal (for example, in controlled motion) are called actuators. Work on the creation of actors is underway in the UK, USA, Japan and a number of other countries. There are prototypes of actuators, but the problem of their autonomy has not yet been solved. In order for the actuator to become a real device suitable for practical use, it is necessary to solve a number of fundamental issues (to develop microminiature energy sources for their drive; to determine the methods and modes of activation of actuators that generate vibrations). Existing experimental and theoretical research in the field of self-oscillation of polymers allows us to hope for a solution to these problems in a simpler way. The studies performed below show that in accordance with the proposed rules for the selection of polymers for actuator drive polymethyl styrene and polycarbonate can be used as polymer systems in which self-oscillations will be excited in the frequency range of 200–250 Hz. The stretching rates at which the self-oscillations of the above polymers begin to be excited have been determined. The heat generated in this case can be used to maintain self-oscillations for a long time. The proposed approach can be considered as an alternative to mechanochemical actuators using methanol as a fuel. The ways of increasing their operating time and thermal effects when self-oscillations are excited in the frequency range of 200–250 Hz are considered.The glass transition temperatures Tg are calculated using the equation $$T_{g} = \frac{{\left( {\sum\limits_{i} {\Delta V_{i} } } \right)_{p} }}{{\sum\limits_{i} {a_{i} \Delta V_{i} + \sum\limits_{j} {b_{j} } } }},$$ T g = ∑ i Δ V i p ∑ i a i Δ V i + ∑ j b j , where $$\left( {\sum\limits_{i} {\Delta V_{i} } } \right)_{p}$$ ∑ i Δ V i p is the van der Waals volume of the repeating unit of the polymer; ai is a set of atomic constants characterizing the energy of a weak dispersive interaction as the average contribution of each atom to this interaction; bj is a set of constants characterizing the energy of a strong specific intermolecular interaction, such as dipole-dipole interactions and hydrogen bonds.