Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

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Abstract

Using the model of coupled thermoelasticity, the boundary value problems of the dynamics of a thermoelastic half-space are solved for plane deformation with periodic surface force and thermal effects associated with the desired boundary functions by linear algebraic relations. Green’s tensors are constructed for the stated boundary value problems, using their properties, analytical solutions of these problems are obtained. To solve them, we have used the method of incomplete separation of variables, the Fourier transform, and the properties of fundamental solutions. The presented algorithm solves the classical four boundary value problems of thermoelasticity, as well as non-classical ones with coupled thermal and force characteristics at the boundary of the half-plane.

About the authors

L. A. Alekseyeva

Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Republic of Kazakhstan

Email: alexeeva@math.kz
Казахстан, Алматы

B. N. Alipova

University of Kentucky, 40506, Lexington, KY, USA; International IT University, 050040, Almaty, Republic of Kazakhstan

Author for correspondence.
Email: alipova.bakhyt@gmail.com
США, Лексингтон; Казахстан, Алматы

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