Special finite elements with arbitrarily-shaped holes for heat conduction analysis of porous materials

Special finite elements are developed which adequately represent the state of heat conduction in the region around an arbitrarily-shaped hole. This is achieved with two assumed temperature fields. The frame field is defined along the element boundary while the intra-element field is independently approximated by using truncated T-complete solutions as trial functions for capturing hole effects. The geometrical irregularity of holes contribute to the difficulty in seeking T-complete solutions. By means of the charge simulation method and numerical conformal mapping technique, the systematic construction of T-complete solutions is shown which satisfy a priori the governing differential equation. Based on the modified variational principle, the two independent temperature fields are linked together at the element level, ensuring conformity across inter-element boundaries. The resultant element stiffness equation involves boundary integrals only, which provides a great flexibility in mesh generation with polygons. Numerical examples for the problems with a single, dual, and multiple holes are given to illustrate the efficiency and accuracy of the proposed method.& COPY; 2023 Published by Elsevier Ltd.