Зведення двовимірних задач термопружності для тіл з кутовими точками до ключових інтегро-диференціальних рівнянь

R. M. Kushnir; Yu. V. Tokovyi; M. Y. Yuzvyak; A. V. Yasinskyi

doi:10.37863/umzh.v73i10.6784

R. M. Kushnir Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
Yu. V. Tokovyi Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
M. Y. Yuzvyak Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
A. V. Yasinskyi Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine

DOI: https://doi.org/10.37863/umzh.v73i10.6784

Keywords: direct integration method, analytical solutions, two-dimensional problems, rectangular domain, annular sector, finite-length cylinder, integro-differential equations

Abstract

UDK 539.3

A generalization of the direct integration method is given with regard to solving the original equations of two-dimensional thermoelasticity problems for solids with corner points (i.e., plane problems for a rectangular domain and an annular sector and the axisymmetric problem for a solid cylinder of finite length). The problems are thereby reduced to a governing integrodifferential equation for a key function, which is unique for each problem. By making use of equilibrium equations, the expressions for stress-tensor components are derived in terms of the key function, while the complete sets of boundary conditions are identically reduced to the corresponding sets of integral conditions for the key function. The algorithms for separating variables in the derived governing equations are suggested by utilizing the complete sets of the eigen- and associated functions in order to construct the solutions to the formulated problems in the form of explicit dependencies on thermal loading in view of the boundary conditions.

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Reduction of the two-dimensional thermoelasticity problems for solids with corner points to key integrodifferential equations

Abstract

References