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Generalized finite integration method for 2D elastostatic and elastodynamic analysis

Author

Listed:
  • Shi, C.Z.
  • Zheng, H.
  • Hon, Y.C.
  • Wen, P.H.

Abstract

In this paper, the elastostatic and elastodynamic problems are analyzed by using the meshless generalized finite integration method (GFIM). The idea of the GFIM is to construct the integration matrix and the arbitrary functions by piecewise polynomial with Kronecker product, which leads to a significant improvement in accuracy and convenience. However, the traditional direct integration in the GFIM is difficult to deal with a large number of arbitrary functions generated in elastic problems. In order to tackle this problem, a special technique is proposed to construct relationships among arbitrary functions in this paper. Also, the Laplace transform method and the Durbin’s inversion technique are adopted to deal with the variables of time in the elastodynamic problem. Several numerical examples are presented to demonstrate the accuracy and stability of the GFIM.

Suggested Citation

  • Shi, C.Z. & Zheng, H. & Hon, Y.C. & Wen, P.H., 2024. "Generalized finite integration method for 2D elastostatic and elastodynamic analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 580-594.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:580-594
    DOI: 10.1016/j.matcom.2024.02.013
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    References listed on IDEAS

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    1. Yun, D.F. & Wen, Z.H. & Hon, Y.C., 2015. "Adaptive least squares finite integration method for higher-dimensional singular perturbation problems with multiple boundary layers," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 232-250.
    2. Soradi-Zeid, Samaneh & Mesrizadeh, Mehdi, 2023. "On the convergence of finite integration method for system of ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
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