The results of a comprehensive analysis of elastic shell behavior under static thermomechanical loads are presented. The study focuses on geometrically nonlinear deformation, buckling, and natural vibrations of shells. Special attention is given to the identification of bifurcation points in the pre-buckling domain of shell deformation.The proposed comprehensive method is implemented as a two-stage algorithm. At each step of the thermomechanical loading, it combines the solution of the geometrically nonlinear static problem for the shell with a modal analysis at the same step. This approach allows the determination of critical states according to both the static criterion (maximum point of the load–deflection curve) and the dynamic criterion (load at which the lowest natural frequency of the shell becomes zero). The method is based on the geometrically nonlinear theory of thermoelasticity, the moment scheme of finite elements, and a universal three-dimensional finite element. We apply the methodology of introducing small non-symmetric perturbations into the initial geometry of the midsurface of the shell to determine bifurcation points iin the pre-buckling domain. This approach enables tracing new solution branches corresponding to adjacent forms of buckling. The presented numerical examples confirm the accuracy, universality, and effectiveness of the proposed method.

Actuality. An analysis of accidents at nuclear power plants and power plants has shown that these incidents are accompanied by high temperatures and high-intensity radiation. In an emergency situation, the technological equipment of the protective shell must ensure the localisation of all radioactive materials released during the accident within its volume, protect the environment from ionising radiation, and counteract high temperature effects. Today, there are various forms and design solutions for protective shells, each of which has its own advantages and disadvantages. Therefore, when choosing protective shell designs, it is necessary to take into account the conditions of construction, operation, and possible emergency impacts. Modern construction encourages the use of new materials such as foam concrete (aerated concrete), which will reduce material consumption and construction costs, as well as improve thermal and ionising protection. Purpose. The main objective of the article is to study the fire protection effectiveness of foam concrete and its γ-absorbing capacity. Main results. Two methods were developed for the research: to determine the fire-retardant properties of foam concrete and to determine the effectiveness of foam concrete in absorbing γ-radiation. It has been established that the fire resistance of foam concrete for steel structures ranges from 130 to 150 minutes for slab thicknesses from 20 mm to 60 mm, accordingly. Studies of the absorption of γ-radiation by foam concrete have shown that foam concrete with a bulk weight of 1200 kg/m3 has a γ-radiation attenuation coefficient similar to that of fine-grained concrete with graphite (with a bulk weight of 1800 kg/m3), which indicates its significant effectiveness (1,5 times). Conclusions. A series of experimental studies has shown that foam concrete is an effective fire-retardant material and can be used for fire protection of steel building structures. It was found that with a foam concrete thickness of 20-60 mm, the fire resistance limit of a steel structure in terms of load-bearing capacity is 130-150 minutes, and in terms of thermal insulation capacity – 80-150 minutes. The effectiveness of using foam concrete to protect technological equipment and its ability to absorb γ-radiation has been substantiated.

Systematic and comprehensive studies of micromodified steels (seven grades) alloyed with vanadium, chromium, cerium, nickel, molybdenum, niobium were carried out, from which reinforcing bars with a diameter of 22 mm were manufactured on a rolling mill. After that, the bars were subjected to heat treatment to obtain various structures, in particular, ferrite-pearlitic, pearlitic, structures of incomplete austenite transformation (bainite transformation) - structures of sorbite and trostite, as well as martensite. After that, samples were prepared from the reinforcing bars for testing fatigue strength (fatigue), static mechanical properties {strength limit σВ , MPa , yield strength σТ , MPa , relative elongation – δ (%), transverse narrowing – ψ (%)}, as well as criteria of modern fracture mechanics {К1С, MPa˖m1/2, δC, mm, RMC , MPa}. In addition, corrosion rate indicators were also determined in corrosion-aggressive environments containing chloride ions, СО2, sulfuric acid anions, as well as in bacterial model environments with bacteria of the SVB, GTB and ZB types. Based on the use of innovative steels, technical re-equipment of energy transport engineering and the hydraulic engineering industry is possible. The resource of such structures for various purposes increases from 50 to 100% compared to standard ones. Therefore, it is necessary to continue work on improving the technologies for obtaining such high-quality materials on a metal basis in order to improve the complex of their properties. The strategy for such a breakthrough of powder metallurgy in the economy should be based on the development of development priorities and the consistent implementation of short-term target programs at the national and regional levels, as well as the development of a long-term comprehensive program at the national level and bringing the work to practical implementation. Therefore, it is also necessary to significantly expand the funding of this area.

The work investigates the stress-strain state of wooden frame elements of buildings with close to zero energy consumption. It is substantiated that wooden frame structures are widely considered as an effective alternative to traditional ones (concrete, steel) from the point of view of ecology and energy efficiency. An analysis of architectural, planning and structural solutions of a low-rise residential energy-efficient building Start TM “Business House” of the NZEB standard for industrial production from typical structural elements was carried out. Using the model of the spatial calculation scheme of the building and the “LIRA” software complex, the stress-strain state of the adopted structural solutions of the building was investigated. An analysis of the level of use of the load-bearing properties of the frame elements (stairs of the first and second floors) and the floor truss (lower belt, braces) at maximum forces from calculated load combinations was carried out. A verification calculation of the frame elements: the first and second floor racks, the floor truss elements for the strength of the sections along the normal to the axis of the load, for chipping, stability, as well as for fulfilling the requirements for ultimate flexibility. The calculation data indicate the rational use of the selected cross-section of the first floor racks and floor truss elements. It is proven that the wooden frame provides both the energy efficiency requirements of the NZEB standard and a high level of operational reliability.

The selection of a method for solving complex engineering problems is an integral part of any calculation process, on which the accuracy and reliability of the obtained results largely depend. At the same time, all methods and approaches, even the most universal, have certain limits of their rational application. In this case, it is important to determine the limits and possibilities of using certain methods. This paper briefly considers the limits of using a combined approach based on the finite element method and graph theory, as well as options for its use as a separate toolkit or in combination with other methods to eliminate their shortcomings or to perform alternative calculations. In addition, the possibility of combining the approach based on graph theory with other numerical methods is considered. The paper also presents the results of practical use of this combined approach in assessing the stability of a non-uniform landslide-prone slope, the calculation and analysis of the stress-strain state of which were carried out using the semi-analytical finite element method in the spatial formulation of the problem, and the stability assessment was carried out using graph theory approaches for the specified calculation sections. In the course of solving this problem, five different settings were considered in stages, from the slope in its natural state to the built-up slope, taking into account a possible option for engineering protection of this area. Accordingly, for one of the calculation sections, the obtained values of the stability coefficients and the shapes of potential sliding surfaces are given in accordance with some of them, shear pressure diagrams were determined and constructed, which can be used as initial data for the placement and calculations of engineering protection structures.

All existing methods for calculating the strength of reinforced concrete elements are based on experimentally established possible types of element failure under certain forces caused by external forces. Thus, under the action of bending moments or the combined action of moments and longitudinal forces, failure occurs as a result of the crushing of the concrete in the compressed zone when the stresses in the longitudinal reinforcement reach or do not reach the limit values for tension (yield strength) and compression. under the action of torsional moments – along a critical spiral crack, when a compressive force is applied over a small area – from the crushing of concrete under the area. The resistance of reinforced concrete elements to shear forces differs significantly from other forces of action, as it is characterized by different types of failure – concrete fragmentation above a critical inclined crack, concrete shear above a critical inclined crack, crushing of concrete in an inclined strip between inclined cracks or a support and a load, loss of adhesion of longitudinal reinforcement to concrete in the tension zone beyond a critical inclined crack, and failure along inclined cracks during punching, which is explained by the influence of the loading pattern, the geometry and design features of the element. Accordingly, to assess strength in the event of possible types of failure, the appropriate calculation tool is used, which is not always implemented within a single calculation model for elements. Therefore, in practice, different calculation methods are used for each of the possible types of failure. This paper presents a method for calculating the strength of I-beam reinforced concrete webs when they fail along a strip between inclined cracks, based on the principles of reinforced concrete plasticity theory, considering the concrete of the web under conditions of plane stress compression-tension when tensile stresses are transferred to the concrete from shear reinforcement. Within the framework of the developed method, the criterion for failure is taken to be the attainment of the main compressive stresses in the concrete strip of the web at the corresponding stress state. The general case of the ultimate equilibrium of a beam within the strip between inclined cracks with arbitrary content and location of transverse reinforcement is considered. Calculated dependencies are obtained for calculating the limit values of stresses in the strip and shear force at wall failure.

Storage of individual bulk materials in containers requires their isolation from external influences, for example, moisture ingress. Waterproofing is provided by maintaining increased pressure in the container. In order to slow down the possible pressure drop, the upper part of the container is made of an elastic two-layer material. One layer provides waterproofing. The second layer provides sufficient strength of the two-layer coating. Its stressed state of the material significantly affects the service life and safety of flexible coatings. Establishing and taking into account the influence of operating conditions, mechanical properties of material layers on the stressed-deformed state of the coating is a relevant scientific and technical problem. Its solution allows to increase the reliability and safety of using pressure vessels. In the article, the layers are considered as isotropic with reduced mechanical characteristics. Using the stress functions (Erie functions) of the classical linear theory of elasticity, a mathematical model of the plane deformed state of the two-layer coating is constructed. The model takes into account the boundary conditions for the external surfaces of a two-layer coating: a uniformly distributed normal load given by Fourier expansion acts on the surface of the first layer. A normal stress acts on the external surface of the second layer. The model also takes into account the conditions for the joint deformation of the layers: equality of the forces of mutual pressure of the layers, tangential stresses arising on the surfaces of interaction of the layers and their displacements. Based on the solution of the mathematical model, an algorithm for determining the stress-strain state of a two-layer coating is formulated. It takes into account the assumption of stress functions, respectively, of the components of the stress-strain state of the material of the coating layers in the form of sums. The dependence of the coating deformations on the mechanical properties of the material of the layers has been established. Thus, an increase from the minimum to practically maximum value of the Poisson's ratio of the layer material that provides waterproofing reduces the coating deflection by almost an order of magnitude.

The main types of connections are welded, riveted, and bolted. Bolted connections have many advantages over other types of connections, namely: high manufacturability, reliability, and speed of installation work, so we will further consider various approaches to modeling bolted connections. One of the most crucial and important points in the design of a structure is the calculation of the connection elements of the components, since the reliability of the structure as a whole depends on the accuracy and reliability of the calculation results. For a wide range of tasks, the finite element method (FEM) is often used in calculations; this numerical method has proven to be one of the most common and versatile. When calculating elements of assemblies such as bolts, rivets, etc., simplified design schemes are usually used, but this approach does not allow for a complete analysis of the distribution of forces. For a complete analysis, it is necessary to create detailed spatial models, which in turn leads to the need to solve systems of high-order equations. To increase the efficiency of the FEM, it is necessary to combine it with the method of distribution of unknowns, as a result, the resulting approach is called the semi-analytical finite element method (SFEM). The bolt, bolt head, and nut were modeled by spatial elements, and the bolt tension was modeled by a load from uniform heating. The obtained results of the stress-strain state using the finite element method and the semi-analytical finite element method allow us to conclude that there is a slight difference in the stress distribution in the spatial formulation of the FEM and SFEM with experimental data and allowed us to identify a rational approach to modeling bolt tension.

The purpose of the article is to publish the procedure for determining the resistance of underground structures to the shock-explosive action of adjusted aircraft bombs.The course of the Russian-Ukrainian war shows that currently one of the most dangerous means of defeating our troops in defensive positions are adjusted aerial bombs. Under such conditions, an effective way to protect personnel and material and technical means from enemy strikes is to shelter them in underground structures that must be resistant to the shock-explosive action of these weapons.The article presents the procedure for determining the resistance of underground structures to the shock-explosive action of adjusted aviation bombs, in particular FAB-500 M62 with a universal planning and adjustment module, using calculations of the required value of the protective of the soil layer of underground structures, which consists of determining the depth of penetration of a corrected aircraft bomb into the soil and calculating the radius of the sphere of destruction of the soil layer of the structure.The scientific novelty of the proposed calculations lies in the comprehensive consideration of indicators, the numerical values of which characterize: the final velocity of the aircraft bomb at the moment of impact; the depth of its penetration, taking into account the inclined position in the protective soil layer of an underground structure; radius of the sphere of destruction of the protective soil the thickness of this structure, taking into account the bomb penetration coefficient; tactical and technical characteristics of the FAB-500 M62.The practical significance of the results obtained lies in the obtained formalized description of the sequence of calculations for determining the resistance of underground structures to the shock-explosive action of adjusted aviation bombs and the ability of commanders (chiefs),military command bodies to more correctly determine the stability of the specified structures and promptly make appropriate decisions regarding effective shelter and protection of personnel and material and technical means from enemy strikes.

In applied and structural mechanics, many examples of optimal design with different objective functions are considered, but there is a need to take research in this area to a new level. The object under study with two or three simultaneous types of optimization is an actual applied problem in the field of construction and applied mechanics. One of the main tasks of designing minimal surfaces is to find the optimal shell shapes for given overall dimensions and shape in plan, taking into account parametric optimization - it is necessary to implement a modern optimization algorithm in the calculation of this structure. Its solution should be brought to ready-made formulas, graphs, tables, calculation examples and practical. The system of solving equations of the finite element method is formed using the Lagrange's variational principle, according to which the total potential energy P of a finite element model of a body is in a state of stability and equilibrium has a minimum value. Within the framework of the study, a methodology for obtaining the ratio of the finite element method with regard to geometric nonlinearity is presented that does not depend on the shape and properties of the finite elements, so it can be implemented for a plate finite element of a shell of minimal surface. To study the multicriteria parametric optimization of the minimum surface shell with regard to geometric nonlinearity, a special additional optimizer module created by the authors is used, which is linked to the Femap with Nastran calculation complex [12]. The computational model is built by the finite element method, which makes it possible to perform a qualitative study of optimization taking into account the objective functions: Mises stress and structural weight. This methodology proves to be effective in the study of multi-criteria parametric optimization with consideration of geometric nonlinearity. Such an approach to the calculation of building structures makes it possible to use structural materials efficiently, and modern calculation complexes based on the finite element method (FEM) can be used in further development at the level of building codes of Ukraine.