Adaptive nodeless variable finite elements with flux-based formulation for thermal–structural analysis

Abstract

A nodeless variable element method with the flux-based formulation is developed to analyze two-dimensional thermal–structural problems. The nodeless variable formulation provides accurate temperature distributions to yield more accurate thermal stress solutions. The flux-based formulation is used to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element meshes that can adapt and move along with the transient solution behavior. A version of a nearly optimal element size determination is proposed to provide high convergence rate of the predicted solutions. The combined procedure is evaluated by solving several thermal, structural, and thermal stress problems.