Formulation of the Analytical Method of Three-Dimensional Thermoelastic Problems in Finite Deformations

Abstract

We apply the conventional consideration of an analytical method in linear thermoelastic problems to nonlinear thermoelastic problems in the second-order theory. The basic equations of nonlinear thermoelastic problems are formulated by using Adkins perturbation method. Thermoelastic potentials applying the Helmholtz theorem are also introduced for analyzing nonlinear thermoelasticity problems. Moreover, by applying these thermoelastic potentials, we propose a formulation of the analytical method to solve boundary-value problems of axisymmetrical uncoupled quasi-static thermoelasticity in finite deformations. Finally, some potentials for axisymmetrical thermoelastic problems of finite deformations are shown.