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

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Abstract

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.

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Authors and Affiliations

  1. College of Aerospace Engineering, Chongqing University, Chongqing, 400044, China

    Dan Xie & Kailin Jian

  2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Kailin Jian

  3. College of Engineering, Peking University, Beijing, 100871, China

    Weibin Wen

Authors
  1. Dan Xie
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  2. Kailin Jian
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  3. Weibin Wen
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Correspondence to Kailin Jian.

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Project supported by the National Natural Science Foundation of China (No. 11176035)

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Xie, D., Jian, K. & Wen, W. Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis. Appl. Math. Mech.-Engl. Ed. 37, 1153–1176 (2016). https://doi.org/10.1007/s10483-016-2126-6

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  • DOI: https://doi.org/10.1007/s10483-016-2126-6

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