Abstract In this manuscript, we solve an asymmetric 2D problem for a long cylinder. The surface is assumed to be traction free and subjected to an asymmetric temperature distribution. A direct approach is used to solve the problem in the Laplace transformed domain. A numerical method is used to invert the Laplace transforms. Graphically results are given and discussed.

Abstract In this work we consider a problem in the context of the generalized theory of thermoelasticity for a half space. The material of the half space is functionally graded in which Lamé's modulii are functions of the vertical distance from the surface of the medium. The surface is traction free and subjected to a time dependent thermal shock. The problem was solved by using the Laplace transform method together with the perturbation technique. The obtained results are discussed and compared with the solution when Lamé's modulii are constants. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.