A finite element formulation for thermal stress analysis. Part I: Variational formulation

• Published in: Nuclear engineering and design 1976, Vol.39 (2), p.267-275
• Main Authors: Keramidas, George A., Ting, Edward C.
• Format: Article
• Language: English
• ISSN: 0029-5493; 1872-759X
• DOI: 10.1016/0029-5493(76)90075-3

This paper deals with the development of a variational principle which can be used for solving problems related to the thermoelastic behavior of solids and is the first of the two part series. The formulation is based on the introduction of a new quantity defined as heat displacement and related to temperature in the same manner as the mechanical displacement is related to strain. The introduction of such a quantity allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The obtained equations are used to write a variational formulation which, together with the concept of generalized coordinates, yield a set of differential equations with the time as the independent variable. These equations can be used to formulate a finite element solution for thermoelastic problems. This is done in the second part.