A cell-based smoothed radial point interpolation method with virtual nodes for three-dimensional mid-frequency acoustic problems

被引：34
作者：
Zhang, Guiyong [1 ,2 ,3 ]
Chen, Zecong [1 ]
Sui, Zhixiang [4 ]
Tao, Dongsong [1 ]
He, Zhicheng [5 ]
Tang, Qian [6 ,7 ]
Sun, Lei [1 ,3 ]
机构：
[1] Dalian Univ Technol, Sch Naval Architecture, Liaoning Engn Lab Deep Sea Floating Struct, Dalian 116024, Peoples R China
[2] Dalian Univ Technol, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China
[3] Collaborat Innovat Ctr Adv Ship & Deep Sea Explor, Shanghai 200240, Peoples R China
[4] China Ship Dev & Design Ctr, Shanghai, Peoples R China
[5] Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha, Hunan, Peoples R China
[6] Hunan Inst Engn, Dept Mech Engn, Xiangtan, Peoples R China
[7] Hunan Prov Key Lab Vehicle Power & Transmiss Syst, Xiangtan, Peoples R China
来源：
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING | 2019年 / 119卷 / 06期
基金：
中国国家自然科学基金;
关键词：
condensed shape functions; dispersion error; gradient smoothing; stiffness; FINITE-ELEMENT SOLUTION; ES-FEM; FORMULATION; ERROR; PIM;
D O I：
10.1002/nme.6062
中图分类号：
T [工业技术];
学科分类号：
08 ;
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.
引用
收藏
页码：548 / 566
页数：19
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