THERMOELASTIC DEFORMATION OF A TRANSVERSELY ISOTROPIC AND LAYERED HALF-SPACE BY SURFACE LOADS AND INTERNAL SOURCES

A general method is developed for the study of transient thermoelastic deformation in a transversely isotropic and layered half-space by surface loads and internal sources. A Laplace transform is first applied to the field quantities; Cartesian and cylindrical systems of vector functions are then introduced for reducing the basic equations to three sets of simultaneous linear differential equations. General solutions are obtained from these sets, and propagator matrices from the solutions by a partitioned matrix method. Source functions for a variety of sources are derived in the Cartesian and cylindrical systems, and the Laplace transformed expressions of the field variables at the surface presented explicitly in the two systems in terms of a layer matrix. The effect of gravity is included by multiplying simply an effect matrix resulting from the modification of continuity conditions at the surface and the layer interfaces. It should be noted that the present analytical method has great advantages over either the classical thin plate approach or the finite element method, and that the present result can be reduced directly to the solutions of the corresponding isotropic case. © 1990.