Abstract
This paper examines three-dimensional boundary value problems in the theory of heat conduction and thermoelasticity for layered transversely isotropic rectangular plates with variable thicknesses acted on by a nonuniform temperature field. It is assumed that known temperature and heat flux at the surfaces of the plate or temperature of the surrounding medium allow a representation of the solution in terms of double trigonometric series. An approximate analytic method has been developed for solving this class of problems which makes it possible to reduce the initial boundary value problem for a plate of variable thickness to a recurrence sequence of the corresponding problems for plates with constant thicknesses.
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