A Localized Radial-Basis-Function Meshless Method Approach to Axisymmetric Thermo-Elasticity

Current methods for solving thermoelasticity problems involve using finite element analysis, boundary element analysis, or other meshed-type methods to determine the displacements under an imposed temperature/stress field. This paper will detail a new approach using localized meshless methods based on multi-quadric radial basis function interpolation to solve these types of coupled thermoelasticity problems. Here, a point distribution is used along with a localized collocation method to solve the Navier equation for the components of the displacement vector. The specific application considered in this paper is that of axisymmetric thermo-elasticity. With rapidly increasing availability and performance of computer workstations and clusters, the major time requirement for solving a thermoelasticity model is no longer the computation time, but rather the problem setup. Defining the required mesh for a complex geometry can be extremely complicated and time consuming, and new methods are desired that can reduce this time. The proposed meshless method features the complete elimination of a mesh, be it structured or unstructured, and the associated complexities involved in its generation and control. The reduction of initial model setup time makes the meshless approach an ideal method of solving coupled thermoelasticity problems. Several examples with exact solutions are used to verify this method for various geometries and boundary condition combinations.