Variational formulation of non-stationary thermoelasticity problem for thin shells compliant to shears and compression (Q2808461)

In terms of a classical variational thermoelasticity problem for three-dimensional bodies of small thickness, the authors formulate a corresponding variational non-stationary thermoelasticity problem for shells compliant to shears and compression. The dimension of the initial problem is reduced due to the Galerkin semi-discretization and Timoshenko-Mindlin hypotheses on the linearity of displacement and temperature variations with respect to the shell thickness. The problem is stated in terms of vector of elastic displacements and rotations of the normal, temperature and its gradient defined on the shell median surface. The case of a quasi-static problem for which the correctness conditions are established is analyzed in detail. The results of finite element analysis are presented for the thermoelasticity problem of a steel plate under thermal and force loadings.