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The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(1):27-39; doi:10.1093/qjmam/46.1.27
© 1993 by Oxford University Press
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THERMAL EFFECTS IN MINDLIN-TYPE PLATES

PETER SCHIAVONE1 and R. J. TAIT2

( 1Department of Electrical Engineering and Applied Mathematics Institute, University of Alberta Edmonton, Alberta, Canada T6G 2G1
2Department of Mathematics, University of Alberta Edmonton, Alberta, Canada T6G 2G1 )

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.


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