Опір матеріалів і теорія споруд
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Документ Thermoelasticity of elastomeric constructions with initial stresses(КНУБА, 2020) Bazhenov, V. A.; Kozub, Yu. G.; Solodei, I. I.The article presents an algorithm for solving linked problems of thermoelasticity of elastomeric structural elements on the basis of a moment scheme of finite elements. To model the processes of thermoelastic deformation of structures with initial stresses the incremental theory of a deformed solid is used. At each step of deformation, the stiffness matrix is adjusted using an incremental geometric stiffness matrix. The use of triple approximation of displacements, deformations and volume change function allows to consider the weak compressibility of elastomers. The components of the stress tensor are calculated according to the Duhamel-Neumann law. To solve the problem of thermal conductivity, a thermal conductivity matrix considering the boundary conditions on the surface of a finite element is constructed. A sequential approximation algorithm is used to solve the thermoelasticity problem. At each stage of the solution, the characteristics of the thermal stress state are calculated. Based on the obtained components of stress and strain tensors, the intensity of internal heat sources is calculated as the dissipative energy averaged over the load cycle. To calculate the dissipative characteristics of the viscoelastic elastomer the parameters of the Rabotnov’s relaxation nucleus are used. Solving the problem of thermal conductivity considering the function of internal heat sources allows you to specify the heating temperature of the body. At each cycle of the algorithm, the values of the physical and mechanical characteristics of the thermosensitive material are refined. This approach to solving thermoelastic problems is implemented in the computing complex "MIRELA+". Based on the considered approach, the solutions of a number of problems are obtained. The results obtained satisfactorily coincide with the solutions of other authors. Considering the effect of preload and the dependence of physical and mechanical properties of the material on temperature leads to significant adjustments to the calculated values.Документ Kyiv school of the theory of structures(КНУБА, 2020) Bazhenov, V. A.; Perelmuter A.V.; Vorona, Yu. V.The paper presents a review of more than a century-long history of Kyiv school of the theory of structure, the foundation of which was laid by world-famous scientists V.L. Kirpichov and S.P. Tymoshenko. The birth of the Kyiv scientific school of the Theory of structures is associated in this paper with the establishment at the Kyiv Polytechnic Institute the Strength of Materials Department. It is noted that further formation and development of the theory of structures was facilitated by the creation in 1918 of the Ukrainian Academy of Sciences, the Institute of Mechanics of the NAS of Ukraine, expansion of relevant research in higher education institutions, creation of new academic and sectoral research institutions, most of which is located in Kyiv. The contribution of Kiev scientists to the development of methods for analyzing spatial structures of bar and shell type, their inelastic behavior, as well as dynamics and stability is reflected. Particular attention is paid to the fundamentally new opportunities for the development of the theory of structures in the era of numerical analysis. The successes of Kiev mechanics in the field of development and improvement of structure analysis numerical methods, such as the finite difference method and various modifications of finite element methods, are emphasized. Kiev engineers and scientists are also known for their developments in the field of design and calculation of modern cable-stayed structures, as well as optimal design. The activities of the scientific school of structural mechanics of the Kyiv National University of Construction and Architecture are also covered in the review. In the final part of the paper the new issues connected with the justification of calculation models and the analysis of reliability of constructions are considered. Some of this problems are dictated by the demands of practice, in particular those that arosed in the process of Chernobyl New Safe Confinement designing. The publication contains a wide bibliography.