Fundamentals of thermoelasticity

The main purpose of the thermoelasticity is the determination of strain and stress states of a continuum deformable body when subjected to a prescribed temperature distribution. Similarly to the classical theory of elasticity, the variables involved in the thermoelasticity are uniquely determined by the solution of the thermoelastic problem including the governing differential equations of motion, the compatibility equations and the constitutive equations. This chapter is mainly devoted to the derivation of the basic equations of the 3D and 2D thermoelasticity. In particular, first the three-dimensional thermoelasticity is introduced and the two classical displacement and stress formulations are proposed. Then the problem is reduced to a two-dimensional one and the concepts of plane strain and plane stress are thoroughly examined.