Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

doi:10.1007/s10483-016-2126-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (9): 1153-1176.doi: https://doi.org/10.1007/s10483-016-2126-6

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

Dan XIE¹, Kailin JIAN^1,2, Weibin WEN³

1. College of Aerospace Engineering, Chongqing University, Chongqing 400044, China;
2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China;
3. College of Engineering, Peking University, Beijing 100871, China

收稿日期:2015-12-19 修回日期:2016-04-07 出版日期:2016-09-01 发布日期:2016-09-01
通讯作者: Kailin JIAN E-mail:cqjian@cqu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11176035)

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

Dan XIE¹, Kailin JIAN^1,2, Weibin WEN³

1. College of Aerospace Engineering, Chongqing University, Chongqing 400044, China;
2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China;
3. College of Engineering, Peking University, Beijing 100871, China

Received:2015-12-19 Revised:2016-04-07 Online:2016-09-01 Published:2016-09-01
Contact: Kailin JIAN E-mail:cqjian@cqu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11176035)

摘要/Abstract

摘要：

A global interpolating meshless shape function based on the generalized moving least-square (GMLS) is formulated by the transformation technique. Both the shape function and its derivatives meet the Kronecker delta function property. With the interpolating GMLS (IGMLS) shape function, an improved element-free Galerkin (EFG) method is proposed for the structural dynamic analysis. Compared with the conventional EFG method, the obvious advantage of the proposed method is that the essential boundary conditions including both displacements and derivatives can be imposed by the straightforward way. Meanwhile, it can greatly improve the ill-condition feature of the standard GMLS approximation, and provide good accuracy at low cost. The dynamic analyses of the Euler beam and Kirchhoff plate are performed to demonstrate the feasibility and effectiveness of the improved method. The comparison between the numerical results of the conventional method and the improved method shows that the proposed method has better stability, higher accuracy, and less time consumption.

关键词: element-free Galerkin (EFG)method, structural dynamics, meshless method, generalized moving least-square (GMLS)

Abstract:

Key words: generalized moving least-square (GMLS), meshless method, element-free Galerkin (EFG)method, structural dynamics

中图分类号:

74S30
81T80

Dan XIE, Kailin JIAN, Weibin WEN. Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1153-1176.

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Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

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