Browsing by Author "Zelenyak Volodymyr"

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    Mathematical modeling of stationary thermoelastic state in a half plane containing a periodic system of cracks due to periodic local heating by a heat flux
    (Lviv Politechnic Publishing House, 2019) Zelenyak Volodymyr; Kolyasa Liubov; Klapchuk Myroslava
    Purpose. To determine the two-dimensional thermoelastic state in a semi-infinite solid (half-plane), weakened by a system of periodic internal cracks under conditions of local heating on the edge of the half plane. 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 a practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the period of cracks placement.Methodology. The methods for studying two-dimensional thermoelastic state of a body with crack 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. Findings. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle of orientation and on the relative position of cracks. 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. Originality. The originality of our solution lies in the fact that the new two-dimensional problems of heat conduction and thermoelasticity for a half plane containing a periodic cracks due to local heating by a heat flux are obtained. Practical value. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with cracks 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.
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    Modeling of elastic state for two joined dissimilar semi-infinite plates with crack under the action of pressure on the shores of the crack
    (Lviv Politechnic Publishing House, 2019) Zelenyak Volodymyr; Kolyasa Liubov
    Purpose. A two-dimensional mathematical model for the problem of elasticity theory on joined dissimilar elastic half-planes containing rectilinear crack under the action of mechanical efforts on the shores of a crack is examined. As a consequence, the intensity of stresses in the vicinity of tops of the crack increases, which significantly affects strength of the body. This may lead to the growth of a crack and to the local destruction of a structure. Such a model represents to some extent a mechanism of destruction of the elements of engineering structures with cracks, we determined stress intensity factors (SIF) at the tops of the crack, which are subsequently used to determine critical values of the normal pressure on the shores of the crack. Therefore the aim of present work is to determine the two-dimensional elastic state in joined dissimilar half-endless plates containing a rectilinear randomly-oriented crack under conditions of power load on the shores of the crack. This will make it possible to determine critical values of mechanical load on the shores of a crack in order to prevent crack growth, which will not allow the local destruction of the body. Methodology. The methods of studying two-dimensional elastic state body with crack as stress concentrators based on the function of complex variable method by which the problem of stationary elasticity are reduced to a SIF of the first kind, a numerical solution which was obtained by the method of mechanical quadratures. Findings. In this paper, two-dimensional mathematical model in the form of singular integral equations on the contours of cracks in order to determine perturbed power stresses due to the presence of cracks are obtained; numerical solutions to singular integral equations of the problem of elasticity theory for a specified region under the action of normally distributed pressure on the shores of the crack are found; stress intensity factors at the tops of a crack and to detect the effects of mechanical character are identify and explored. Graphical dependences of SIF, which characterize distribution of the intensity of stresses at the tops of a crack, on the angle of crack inclination and elastic characteristics of half-planes is obtained. This makes it possible to analyze the intensity of stresses in the vicinity of a crack's tops depending on the geometrical and mechanical factors, as well as to determine the limit of permissible values of normal pressure on the shores of the crack at which the growth of the crack starts, as well as the local destruction of the body. It is shown that the proper selection of elastic characteristics of the components of joined dissimilar half-planes can help achieve an improvement in the strength of the body in terms of the mechanics of destruction by reducing SIF at the crack's tops. Originality. Scientific novelty lies in the fact that the solutions of the new two-dimensional problems of elasticity for a specified region ( joined dissimilar half-endless plates containing a rectilinear randomly-oriented crack ) under the action of normally distributed pressure on the shores of the crack are obtained. Practical value. Practical value of the present work lies in the possibility of a more complete accounting of actal stressed-strained state in the piecewise-homogeneous elements of a structure with cracks that work under conditions of different mechanical loads. The results of specific studies that are given in the form of graphs could be used when designing rational operational modes of structural elements. In this case, the possibility is obtained for preventing the growth of a crack through the appropriate selection of composite's components with the corresponding mechanical characteristics.