THERMAL EFFECTS IN MINDLIN-TYPE PLATES
Peter Schiavone, Robert J. Tait · The Quarterly Journal of Mechanics and Applied Mathematics · 1993
We derive a linear thermoelastic plate model based on a Mindlin-type assumption on the displacements. Initial-boundary-value problems of the Dirichlet, Neumann and mixed type are formulated and appropriate uniqueness results are obtained. The exterior problems are solved in special classes of finite-energy functions having a specific ‘far-field pattern’ which allow some divergence at infinity. These are larger than the class of admissible functions used in classical elasticity. We also indicate how results on existence and uniqueness are obtained in problems of static equilibrium and steady thermoelastic oscillations. The latter are governed by systems of elliptic equations and can be solved numerically using a generalized Fourier-series technique developed earlier for thin micropolar plates. Finally, we mention the generalization to a theory of thermoelastic micropolar plates.