Overlapping finite element analysis for structures under thermal loads with spatially varying gradients

The accuracy of thermal stress analysis is dependent primarily on the mesh pattern and the temperature distribution. To capture the effect of spatially varying temperature accurately, we need to use a fine mesh in that region, but it increases computational cost. Here, we propose an overlapping finite element method with an adaptive shape function considering temperature distribution in order to improve the solution accuracy and reduce the meshing effort in thermal stress analysis. The shape functions are constructed adaptively by adjusting interpolation weights based on the temperature distribution within an element. The performance of the proposed method is investigated by solving 1D and 2D representative problems. It provides more accurate solutions than the original overlapping finite element method without any increase in computational cost. It is effective particularly when a coarse mesh is used in the region of high temperature gradient.