Ukrainian Journal of Mechanical Engineering and Materials Science
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Item A brief overview of stationary two-dimensional thermoelastic state models in homogeneous and piecewise-homogeneous bodies with cracks(Видавництво Львівської політехніки, 2023-02-28) Zelenyak, Volodymyr; Kolyasa, Liubov; Klapchuk, Myroslava; Lviv Polytechnic National UniversityPurpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks. Methodology. Based on the method of the function of a complex variable we have studied the two-dimensional thermoelastic state for the body with crack as stress concentrators. As result, the problem of thermoelasticity was reduced to a system of two singular integral equations (SIE) of the first and second kind, a numerical solution of which was found by the method of mechanical quadratures. Findings. The two-dimensional mathematical model of the thermoelastic state has been built in order to determine the stress intensity factors at the top of the crack and inclusion. The systems of singular integral equations of the first and second kinds of the specified problem on closed (contour of inclusion) and open (crack) contours are constructed. The influence of thermophysical and mechanical properties of inclusion on the SIF sat the crack types was investigated. The dependences of the stress intensity factor which characterizes the distribution of the intensity of stresses at the vertices of a crack have been built, as well as its elastic and thermoelastic characteristics of inclusion. This would make it possible to analyze the intensity of stresses in the neighborhoods of crack vertices depending on the geometrical and mechanical factors. As a result, this allows to determine the critical values of temperature in the three-component plate containing a crack in order to prevent the growth of the crack, as well as to prevent the local destruction of the body. It was found that the appropriate selection of mechanical and thermophysical characteristics of the components of a three-component plate containing a crack can be useful to achieve an improvement in body strength in terms of the mechanics of destruction by reducing stress intensity factors at the crack’s vertices. Originality. The solutions of the new two-dimensional problem of thermoelasticity for a specified region due to the action of constant temperature as well as due to local heating by a heat flux were obtained. The studied model is the generalization of the previous models to determine the two-dimensional thermoelastic state in a piecewise homogeneous plate weakened by internal cracks. Practical value. The practical application of this model is a more complete description of the stress-strain state in piecewise homogeneous structural elements with cracks operating under temperature loads. The results of numerical calculations obtained from the solution of systems of equations and presented in the form of graphs can be used in the design of rational modes of operation of structural elements. This takes into account the possibility of preventing the growth of cracks by the appropriate selection of composite components with appropriate mechanical characteristics.Item Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack(Видавництво Львівської політехніки, 2023-02-28) Zelenyak, Volodymyr; Kolyasa, Liubov; Klapchuk, Myroslava; Lviv Polytechnic National UniversityA mathematical model to determine the two-dimensional thermoelastic state in a semi-infinite solid weakened by an internal crack under conditions of local heating is examined. Heat flux due to frictional heating on the local area of the body causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the crack placement. The methods for studying the two-dimensional thermoelastic state of a body with cracks as stress concentrators are based on the method of complex variable function. Reducing the problem of stationary heat conduction and thermoelasticity to singular integral equations (SIE) of the first kind, the numerical solution by the method of mechanical quadrature was obtained. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle orientation of the crack as well as forms of the intensity distribution of the local heat flux. The obtained results will be used later to determine the critical value of the intensity of the local heat flux from equations of limit equilibrium at which crack growth and the local destruction of the body occur. The scientific novelty lies in the fact that the solutions to two-dimensional problems of heat conduction and thermoelasticity for a half-plane containing a crack due to local heating by a heat flux were obtained. This would make it possible to obtain a comparative analysis of the intensity of thermal stresses around the top of the crack, depending on the form of distribution of the intensity of the heat flow on the surface of the body. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with the crack that operate under conditions of heat stress (frictional heat) in various industries, particularly in mechanical engineering. The results of specific values of SIF at the crack tip in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.Item Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source(Видавництво Львівської політехніки, 2019-03-20) Zelenyak, Volodymyr; Kolyasa, Liubov; Lviv Polytechnic National UniversityPurpose. To determine the two-dimensional thermoelastic state in a circular plate, weakened by an edge or internal crack induced by a stationary heat sourse. This paper proposes using singular integral equation (SIE) to investigate thermostressed intensity in the vicinity of the crack tip, depending on the local heat source placement and identify typical mechanical effects. Numerical results for the stress intensity factors (SIFs) can be potentially used to identify (with the limit equilibrium equations) critical values of the intensity of the local heat source at which crack begin to grow and the local destruction of the body. Methodology. The methods of studying two-dimensional thermoelastic state body with crack as stress concentrators based on the function of complex variable method by which the problem of stationary thermoelasticity are reduced to a SIE of the first kind, a numerical solution which was obtained by the method of mechanical quadratures. Findings. In this paper graphic dependences of stress intensity factors at the crack tip on the relative position of crack and local heat source placement and on the length of crack are obtained. Originality. Scientific novelty lies in the fact that the solutions of the new two-dimensional problems of thermoelasticity for a circular plate containing a crack under the influence of local heating of heat source. Practical value. The practical value is the ability to more fully take into account the real situation in the thermoelastic elements of engineering structures with cracks that operate under conditions of heat stress in various industries, particularly in mechanical engineering. The results of specific values in the crack tip SIF in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.Item Determination of stresses and ultimate loads for composite plates with elastic inclusions(Lviv Politechnic Publishing House, 2017-10-19) Jaroszewicz, Jerzy; Maksymovych, Olesya; Dzyubyk, Andrii; Nazar, Ihor; Bialystok University of Technology; Lviv Polytechnic National UniversityIn the article, the algorithm for determination of stresses in anisotropic plates with elastic inclusions of another anisotropic material was developed on the basis of complex singular integral equations. The solving of integral equations has been carried out numerically using the method of mechanical quadratures. The strength analysis (calculation of strength) of composite plates with inclusions has been performed using the Hoffman criterion.