Development of new thermoelastic Petrov–Galerkin finite elements with enhanced precision and distortion tolerance

Abstract

The finite element method (FEM) serves as a crucial tool for addressing problems involving thermoelastic coupling. However, most current thermoelastic elements inherit shortcomings from the conventional finite element models, such as the sensitivity problem in relation to mesh distortion. The aim of this article is to extend some recent element techniques to thermoelastic analysis by developing new Petrov–Galerkin finite elements with high precision and distortion tolerance. This includes a plane 4-node 12-DOF (two displacements and one temperature per node) quadrilateral element US-ATFQ4T and a 3D 8-node 32-DOF (three displacements and one temperature per node) hexahedral element US-ATFH8T. The coupling stiffness matrices of the elements are meticulously assembled by the derivation from the virtual work principle. The mechanical part employs two different sets of shape functions: the isoparametric interpolation for test functions and the interpolation with a sequence of general solutions of homogenous control equations in linear elasticity, named by analytical trial functions (ATFs), for trial functions. The thermal part follows the traditional isoparametric interpolation mode. Numerical examples demonstrate high performance of the proposed elements with quality results even under coarse and distorted meshes.