Some basic boundary value problems of the plane thermoelasticity with microtemperatures

The present paper is devoted to the two-dimensional version of statics of the linear theory of elastic materials with inner structure whose particles, in addition to the classical displacement and temperature fields, possess microtemperatures. Some results of the classical theories of elasticity and thermoelasticity are generalized. The Green's formulas in the case under consideration are obtained, basic boundary value problems are formulated, and uniqueness theorems are proved. The fundamental matrix of solutions for the governing system of the model and the corresponding single and double layer thermoelastopotentials are constructed. Properties of the potentials are studied. Applying the potential method, for the first and second boundary value problems, we construct singular integral equations of the second kind and prove the existence theorems of solutions for the bounded and unbounded domains.This paper describes the use of the LaTeX2E mmaauth.cls class file for setting papers for Mathematical Methods in the Applied Sciences. Copyright (c) 2012 John Wiley & Sons, Ltd.