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The complex variable meshless local Petrov–Galerkin method for elastodynamic analysis of functionally graded materials

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  • Dai, Baodong
  • Wei, Dandan
  • Ren, Hongping
  • Zhang, Zhu

Abstract

As an improvement of the meshless local Petrov–Galerkin (MLPG), the complex variable meshless local Petrov–Galerkin (CVMLPG) method is extended here to dynamic analysis of functionally graded materials (FGMs). In this method, the complex variable moving least-squares (CVMLS) approximation is used instead of the traditional moving least-squares (MLS) to construct the shape functions. The main advantage of the CVMLS approximation over MLS approximation is that the number of the unknown coefficients in the trial function of the CVMLS approximation is less than that of the MLS approximation, thus higher efficiency and accuracy can be achieved under the same node distributions. In implementation of the present method, the variations of the FGMs properties are computed by using material parameters at Gauss points, so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method (FEM) for the FGMs. Several numerical examinations for dynamic analysis of FGMs are carried out to demonstrate the accuracy and efficiency of the CVMLPG.

Suggested Citation

  • Dai, Baodong & Wei, Dandan & Ren, Hongping & Zhang, Zhu, 2017. "The complex variable meshless local Petrov–Galerkin method for elastodynamic analysis of functionally graded materials," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 17-26.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:17-26
    DOI: 10.1016/j.amc.2017.03.042
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    1. Wei, Dandan & Zhang, Weiwei & Wang, Linghui & Dai, Baodong, 2015. "The complex variable meshless local Petrov–Galerkin method for elasticity problems of functionally graded materials," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1140-1151.
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    Cited by:

    1. Ma, Xiao & Zhou, Bo & Xue, Shifeng, 2021. "A meshless Hermite weighted least-square method for piezoelectric structures," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    2. Ma, Xiao & Zhou, Bo & Xue, Shifeng, 2022. "A Hermite interpolation element-free Galerkin method for functionally graded structures," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    3. Liu, Zheng & Wei, Gaofeng & Qin, Shaopeng & Wang, Zhiming, 2022. "The elastoplastic analysis of functionally graded materials using a meshfree RRKPM," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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