Static equilibrium of a thermoelastic half-plane: Green’s functions and solutions in integrals

Abstract

This article presents in a closed form new influence functions of a unit point heat source on the displacements for three boundary value problems of thermoelasticity for a half-plane. We also obtain the corresponding new integral formulas of Green’s and Poisson’s types that directly determine the thermoelastic displacements and stresses in the form of integrals of the products of specified internal heat sources or prescribed boundary temperature and constructed already thermoelastic influence functions (kernels). All these results are presented in terms of elementary functions in the form of three theorems. Based on these theorems and on derived early by author the general Green-type integral formula, we obtain in elementary functions new solutions to two particular boundary value problems of thermoelasticity for half-plane. The graphical presentation of the temperature and thermal stresses of one concrete boundary value problems of thermoelasticity for half-plane also is included. The proposed method of constructing thermoelastic Green’s functions and integral formulas is applicable not only for a half-plane, but also for many other two- and three-dimensional canonical domains of different orthogonal coordinate systems.