Variational Formulation of the Problem of Nonstationary Thermoelasticity for Thin Shells Compliant to Shears and Compression

Abstract

On the basis of the variational problem of classical thermoelasticity for three-dimensional bodies of small thickness, we formulate the corresponding variational problem of nonstationary thermoelasticity for shells compliant to shears and compression. The reduction of dimensionality of the original problem is attained by using the Galerkin semidiscretization and the Timoshenko–Mindlin hypotheses on the linearity of variations of displacements and temperature along the thickness of the shell. The problem is formulated in terms of the vector of elastic displacements and rotations of the normal, temperature, and its gradient defined on the middle surface of the shell. The case of quasistatic problem for which the conditions of correctness are established is analyzed in more detail. The results of the finite-element analysis of the problem of thermoelasticity for a steel plate subjected to the action of thermal and force loads are presented.