Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications

Abstract

An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM) and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field) are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.

A Brief Review on Polygonal/Polyhedral Finite Element Methods

“…The new method is known as T-Trefftz Voronoi Cell Finite Elements (VCFEM-TTs) [141] and was soon extended to 3D [142]. Recently another novel hybrid FEM has been formulated, by coupling HT-FEM with the idea of the Method of Fundamental Solution (MFS) known as hybrid fundamental solution based FEM (HFS-FEM) [143].…”