Special circular hole elements for thermal analysis in cellular solids with multiple circular holes

This paper presents a new hybrid finite element approach with fundamental solutions (HFS-FEM) as a trial function for modeling thermal behavior in perforated or cellular solids containing multiple randomly distributed circular holes with arbitrary sizes and locations, using special elements to reduce mesh effort. Based on the independent intra-element field in the element consisting of fundamental solutions and the frame field defined on the element boundary, the approach has characteristic features of elementary boundary integrals and versatile element construction by virtue of combining the new hybrid functional. Special purpose hole elements and regular elements are constructed using the special fundamental solution satisfying the specified hole boundary conditions and the conventional fundamental solution, respectively, such that the circular hole region can be modeled with a much smaller number of elements. Numerical examples including problems with single, double and randomly distributed multiple holes are considered and the results demonstrate the versatility, accuracy, and efficiency of the approach presented.