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.
Highlights
A novel hybrid finite element formulation, called the hybrid fundamental solution based FEM (HFS-FEM), was recently developed based on the framework of hybrid Trefftz finite element method (HT-FEM) and the idea of the method of fundamental solution (MFS) [1,2,3,4,5]
Compared to the functional employed in the conventional FEM, the present variational functional is constructed by adding a hybrid integral term related to the intraelement and element frame displacement fields to guarantee the satisfaction of displacement and traction continuity conditions on the common boundary of two adjacent elements
The homogeneous solution is obtained by using the hybrid fundamental solution based finite element method (HFS-FEM) and the particular solution associated with body force is approximated by using the strong form of basis function interpolation
Summary
A novel hybrid finite element formulation, called the hybrid fundamental solution based FEM (HFS-FEM), was recently developed based on the framework of hybrid Trefftz finite element method (HT-FEM) and the idea of the method of fundamental solution (MFS) [1,2,3,4,5]. The HFS-FEM has simpler expressions of interpolation functions for intraelement fields (fundamental solutions) and avoids the coordinate transformation procedure required in the HT-FEM to keep the matrix inversion stable. This approach has the potential to achieve high accuracy using coarse meshes of high-degree elements, to enhance insensitivity to mesh distortion, to give great liberty in element shape, and to accurately represent various local effects (such as hole, crack, and inclusions) without troublesome mesh adjustment [17,18,19,20]. Concluding remarks and future development are discussed at the end of this paper
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