Analytical solutions of Lame equations by Galerkin method

This paper deals with the deformation of an elastic solid described by Lame equations satisfying the boundary conditions. By means of the differential operators, we reduce these equations to Poisson equations that we solve using Galerkin method, i.e. we obtain the components of displacement vector. Furthermore, we compute the strain and stress tensors acting on the solid which are important in engineering applications. Numerous examples are given in this work.