On energy-derived difference equations in thermal stress problems

Abstract

This paper is concerned with the analysis and solution of variationally-derived finite difference equations in mixed boundary value problems of plane thermoelastic stress and thermoelastic strain. The relationship between these equations at the boundary and the natural boundary conditions is derived, and convergence to the explicit boundary equations with decreasing grid size is shown. Efficient decomposition and solution techniques for the positive definite, quasi-tridiagonal coefficients matrix are presented. Numerical studies are included for a finite, thin plate subjected to a parabolic temperature field.