Coupled Thermoelasticity

Abstract

The problems of coupled linear thermoelasticity are among those classes of mechanics which seldom have analytical solution even for simple structures such as beams and rods. Therefore, finite element method is one of the most reliable numerical methods to handle the solution of structural members. The chapter begins with the Galerkin method to obtain the finite element equations of the coupled problems for general three-dimensional case. The members of each related matrice in the resulting finite element equations are calculated and given. The method is then applied to a number of problems. The function-ally graded layer under thermal shock load is analyzed in the next section. Thick spherical vessels under radially symmetric thermal shock load applied to its inside surface is dis-cussed in the next section. The coupled thermoelastic equations for an axisymmetrically loaded disk with different approximation orders is presented in the last section. Elements with various orders are employed to investigate the effects of the number of nodes in an element IntroductionDue to the mathematical complexities encountered in the analytical treatment of coupled thermoelasticity problems, the finite element method is often preferred. The finite element method itself is based on two entirely different approaches: the variational approach based on the Ritz method, and the weighted residual methods. The variational approach, which for elastic continuum is based on the extremum of the total potential and kinetic energies, has deficiencies in handling coupled thermoelasticity problems due to the controversial functional relation of the first law of thermodynamics. On the other hand, the weighted residual method based on the Galerkin technique, which is directly applied to the governing equations, is quite efficient and has a very high rate of convergence [1][2][3][4].