Uncoupled thermoelasticity problem for a finite rectangular composite

Abstract

The stretching of a composite specimen taking into account temperature influence is modelled in terms of tensile stress applied at the opposite boundaries of the elastic rectangular domain. Two other boundaries are supposed to be fixed, it allows to formulate the stated problem as a boundary value problem. The analytical solution is realized with the help of the integral transform method. According to it, the problem is reduced to the one‐dimensional non‐homogeneous ordinary differential equations with corresponding boundary conditions in the transform's domain. The apparatus of Green's matrix‐function was applied to solve it. It let to the system of two singular integral equations, which was solved with the help of orthogonal polynomials method. The final formulae for displacements and stress were used to analyze the stress state of the rectangular elastic specimen. Obtained numerical results were compared with some experimental data for the stretching rectangular ceramic specimen.