Hybrid fundamental solution based finite element method for axisymmetric potential problems with arbitrary boundary conditions

Abstract

A hybrid fundamental solution based finite element method (HFS-FEM) is proposed to analyze axisymmetric potential problems with arbitrary boundary conditions. The axisymmetric geometry is simplified from the three-dimensional (3D) to the two-dimensional (2D) by expanding boundary conditions into the summation of Fourier series. In the proposed approach, the interior potential field is constructed by utilizing a linear combination of fundamental solutions at source points as intra-element trial functions. And the frame potential field is independently introduced to enforce the continuity between adjacent elements. And then the two assumed fields are expanded into a series of symmetric and asymmetric components as done for the boundary conditions. For each component, the element stiffness equation involving boundary integrals only is established by means of the axisymmetric form of Hellinger-Reissner functional. Finally, the superposition principle is employed for the final solution. To assess the performance of HFS-FEM, three numerical examples are investigated and comparisons are conducted between the proposed approach and ABAQUS. The results show that the HFS-FEM exhibits insensitivity to mesh distortion.