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论文类型：期刊论文

发表时间：2019-08-10

发表刊物：INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

收录刊物：SCIE、EI

卷号：119

期号：6

页面范围：548-566

ISSN号：0029-5981

关键字：condensed shape functions; dispersion error; gradient smoothing; stiffness

摘要：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.