The Extended Ritz Method Applied to Transient Coupled Thermoelastic Boundary-Value Problems

摘要

A method for obtaining approximate solutions to initial-boundary-value problems in the linear theory of coupled thermoelasticity is developed. This procedure is a direct variational method representing an extension of the Ritz method. As an illustration of the procedure, it is applied to a class of one-dimensional, transient problems involving weak thermal shocks. The problems considered are: (1) rapid heating of a half-space through a thermally conducting boundary layer, and (2) gradual heating of the boundary surface of a half-space. The solutions generated by the extended Ritz method are compared, for accuracy, to solutions obtained from a numerical inversion scheme for the Laplace transform based on Gaussian quadrature. These comparisons indicate that the variational procedure developed here can yield accurate results. (Author)