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A cell-based smoothed radial point interpolation method with virtual nodes for three-dimensional mid-frequency acoustic problems |
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| Authors: | Guiyong Zhang Zecong Chen Zhixiang Sui Dongsong Tao Zhicheng He Qian Tang Lei Sun |
| Affiliation: | 1. Liaoning Engineering Laboratory for Deep-Sea Floating Structures, School of Naval Architecture, Dalian University of Technology, Dalian, China;2. China Ship Development and Design Center, Shanghai, China;3. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China;4. Department of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan, China
Hunan Provincial Key Laboratory of Vehicle Power and Transmission System, Xiangtan, China;5. Liaoning Engineering Laboratory for Deep-Sea Floating Structures, School of Naval Architecture, Dalian University of Technology, Dalian, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai, China |
| Abstract: | It is well known that the finite element method (FEM) encounters dispersion errors in coping with mid-frequency acoustic problems due to its “overly stiff” nature. By introducing the generalized gradient smoothing technique and the idea of condensed shape functions with virtual nodes, a cell-based smoothed radial point interpolation method is proposed to solve the Helmholtz equation for the purpose of reducing dispersion errors. With the properly selected virtual nodes, the proposed method can provide a close-to-exact stiffness of continuum, leading to a conspicuous decrease in dispersion errors and a significant improvement in accuracy. Numerical examples are examined using the present method by comparing with both the traditional FEM using four-node tetrahedral elements (FEM-T4) and the FEM model using eight-node hexahedral elements with modified integration rules (MIR-H8). The present cell-based smoothed radial point interpolation method has been demonstrated to possess a number of superiorities, including the automatically generated tetrahedral background mesh, high computational efficiency, and insensitivity to mesh distortion, which make the method a good potential for practical analysis of acoustic problems. |
| Keywords: | condensed shape functions dispersion error gradient smoothing stiffness |