Three-dimensional quasi-static general solution for isotropic thermoelastic medium with applications

Abstract

An accurate and efficient method for three dimensional quasi-static thermal elastic problems is established. The three-dimensional equations of isotropic quasi-static-thermo-elasticity are simplified by the introduction of two displacement functions. A general solution is derived by virtue of the Almansi's theorem, which is expressed in terms of three functions, satisfying harmonic functions and quasi-static heat conduction equation respectively. Exact and complete fundamental solution would be derived for arbitrary boundary problems subjected to a point heat load. The solution is concise in form which is completely new to the literature. In this paper, the 3D solutions of the isotropic quasi-static medium under dynamic point heat source based on the general solutions are presented by two newly functions. All components of the coupled field are expressed in terms of elementary functions which are convenient to use. The number results for two types of dynamic heat source show the change rules of the thermal stress field. The corresponding analysis can give some theoretical basis for revealing the mechanism of thermal elastic coupling problem and provide guidance for engineering structural design in the future work.