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A meshfree radial point interpolation method (RPIM) for three-dimensional solids

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Abstract

A meshfree radial point interpolation method (RPIM) is developed for stress analysis of three-dimensional (3D) solids, based on the Galerkin weak form formulation using 3D meshfree shape functions constructed using radial basis functions (RBFs). As the RPIM shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite element method (FEM). Numerical examples of 3D solids are presented to verify validity and accuracy of the present RPIM method, and intensive numerical study has been conducted to investigate the effects of some important parameters. It is demonstrated that the present meshfree RPIM is robust, stable, and reliable for stress analysis of 3D solids.

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Authors and Affiliations

  1. Centre for Advanced Computations in Engineering Science (ACES) Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260

    G. R. Liu, G. Y. Zhang & Y. T. Gu

  2. SMA Fellow, Singapore-MIT Alliance, Singapore

    G. R. Liu

  3. Inst High Performance Comp, Singapore

    Y. Y. Wang

Authors
  1. G. R. Liu
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  2. G. Y. Zhang
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  3. Y. T. Gu
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  4. Y. Y. Wang
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Correspondence to G. R. Liu.

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Liu, G., Zhang, G., Gu, Y. et al. A meshfree radial point interpolation method (RPIM) for three-dimensional solids. Comput Mech 36, 421–430 (2005). https://doi.org/10.1007/s00466-005-0657-6

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  • DOI: https://doi.org/10.1007/s00466-005-0657-6

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