Вип. 104

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Basic relationships for physically and geometrically nonlinear problems of deformation of primatic bodies
(КНУБА, 2020) Maksimyuk, Yu. V.; Pyskunov, S. O.; Shkril, A. A.; Maksimyuk, O. V.
The initial relations of thermo elastic-plastic deformation of prismatic bodies are given in the paper. The basic concepts, indifference of deformation tensors, with the condition of energy conjunction in description of the shaping process are laid out on the basis of classical works.
Boundary element approaches to the problem of 2-d non-stationary elastic vibrations
(КНУБА, 2020) Vorona, Yu. V.; Kozak, A. A.
Two boundary element approaches are used to solve the problem on non-stationary vibrations of elastic solids. The first approach is based on the transition to the frequency domain by means of a Fourier series expansion. The second approach is associated with the direct solution of a system of time-dependent boundary integral equations, with a piecewise constant approximation of the dependence of the unknowns on time. In both cases, a collocation scheme is used to algebraize the integral equations, and the difficulties associated with the calculation of singular integrals are overcome by replacing the kernels with the initial segment of the Maclaurin series. After such a replacement, the kernels take the form of a sum, the first term of which is the corresponding fundamental solution of the statics problem while other terms are regular. Since integration of static kernels is not difficult the problem of calculating the diagonal coefficients of the SLAE turns out to be solved. The developed techniques are compared in the process of dynamics analysis solving of elastic media with two cylindrical cavities. The boundary of one of the cavities is subjected to a radial impulse load, which varies according to the parabolic law. Both approaches have shown the similar effectiveness and qualitative consistency.
Buckling and vibrations of the shell with the hole under the action of thermomechanical loads
(КНУБА, 2020) Bazhenov, V. A.; Krivenko, O. P.
The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and vibrations of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, under complex thermomechanical loading. The technique is based on the geometrically nonlinear equations of three-dimensional thermoelasticity, the finite element formulation of the problem in increments, and the use of the moment finite-element scheme. A thin shell is considered by this method as a threedimensional body. We approximate a shell by one spatial universal finite element (FE) throughout the thickness. The universal FE is based on an isoparametric spatial FE with polylinear shape functions for coordinates and displacements. The universal element has additional variable parameters introduced to expand its capabilities. The method of modal analysis of the shell is based on an approach that at each current stage of thermomechanical loading takes into account the stresses accumulated at the previous stages. The developed algorithm allows one to study geometric nonlinear deformation and buckling of elastic shells of an inhomogeneous structure with a thin and medium thickness, as well as to study small vibrations of the shells relative to the reference deformed state caused by static loading, taking into account large displacements and a prestressed state. An analysis of the stability and vibration of the spherical panel with the hole is carried out. The effect on the frequencies and mode shapes of the shell of the sequential action of thermal and mechanical loads is investigated.
Creation of mathematical model of platformvibrator with shock, designed for concrete products compaction and molding
(КНУБА, 2020) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.
Platform-vibrators are the main molding equipment in the production of precast concrete elements. Shock-vibration technology for the precast concrete production on low-frequency resonant platform-vibrators significantly improves the quality of the products front surfaces and the degree of their factory readiness. This technology is used to produce large elements. We describe the creation of a mathematical model for platform-vibrator that uses shock to produce asymmetric oscillations. The values of the upper and lower accelerations of the mold with concrete have different values with shock-vibration technology. The created mathematical model corresponds to the two-body 2-DOF vibro-impact system. It is strongly nonlinear non-smooth discontinuous system. It has some peculiar properties, namely: the upper body with very large mass breaks away from the lower body during vibrational motion; both bodies move separately; the upper body falls down onto the soft constraint; the impact that occurs is soft one due to the softness and flexibility of the constraint. The soft impact simulation requires special discussion. In this paper, we simulate a soft impact by a nonlinear contact force in accordance with the Hertz quasistatic contact law. The numerical parameters for this system were chosen in such a way that: firstly they provide the fulfillment of requirements for real machine, and secondly they allow analyzing its dynamic behavior by nonlinear dynamics tools. The created model is well enough to fulfill a number of requirements, namely: T-periodic steady-state movement after passing the transient process; the appropriate value of mold oscillations amplitude; the satisfactory value of the asymmetry coefficient that is the ratio of lower acceleration to the upper acceleration. We believe that the created model meets all the necessary requirements.
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.
The parametric oscillations of rotating rods under action of the axial beat load
(КНУБА, 2020) Nedin, V. O.
The paper presents the results of investigation of the axial beat loads’ influence on the transverse rotating rods’ oscillations and their stability. The perforator's long drills are considered as objects of investigation. The analysis of different author’s papers that are studded the dynamics of oscillations of shafts and rotating rods is carried out. The relevance of the research topic is substantiated. The model of the considered dynamic system is described and equations of oscillations in space are given. The technique for investigation is presented. This technique is based on search for new bend forms of rotating rod by solving the equations of oscillations with using the Hubbolt time integration method and the polynomial functions (splines) that are described the current bend form. In it, the spline functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points. Described technique was realized in a computer program with graphic user interface that is developed by author. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation. Diagrams with regions of stable and instable motion of the rods, that were found by different parameters and boundary conditions are shown. The analysis of the results is obtained and the conclusion about possibility of operating the equipment in certain frequency ranges is done. The space oscillating process of rotating rods is considered with account of the gyroscopic loads and geometric nonlinearity.
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.