Thermal stresses in an elastic parallelepiped

Abstract

A semi-analytical algorithm is presented for solving a three-dimensional thermoelasticity problem for a parallelepiped with free edges. By implementing the direct integration method, the problem is reduced to the determination of three Vihak key functions introduced as the integrals of the equilibrium equations. The governing equations for the Vihak functions are derived based on the compatibility equations in terms of stresses. Based on original boundary conditions, the integral conditions are derived for the Vihak functions verbalizing their resultant “force” and “momentum.” An approach for separating variables in the governing equations and integral conditions is suggested by implementing special sets of the associated- and eigenfunctions. Numerical case studies are discussed with special attention given to the effect of the Poisson ratio.

Keywords:

• Analytical solution
• direct integration method
• elastic parallelepiped
• exact analysis
• thermoelasticity