Semi-analytic solutions for a thermoelastic problem with cubic anisotropy

In this paper, a semi-analytic thermal stress solution is obtained for cylindrical crystals with cubic anisotropy. Based on a suitable splitting of the differential operators, a convergent series for a general elasticity problem with cubic anisotropy is derived. Each term of the series is related to an isotropic elasticity problem, which may be solved analytically. Using the analytic solution to the two-dimensional isotropic elasticity problem, a semi-analytic solution of the elasticity problem with cubic anisotropy in a disk is obtained. The novel feature of this splitting method is its ability to generate higher order terms without difficulty, unlike the perturbation solutions obtained previously where the assumption of weak anisotropy has to be made. Furthermore, for materials with cubic anisotropy the method is guaranteed to converge.