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A linearly conforming point interpolation method (LC-PIM) for three-dimensional elasticity problems

Authors

  • G. Y. Zhang,

    Corresponding author
    1. Department of Mechanical Engineering, Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
    • Department of Mechanical Engineering, Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
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  • G. R. Liu,

    1. Department of Mechanical Engineering, Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
    2. The Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore 117576, Singapore
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  • Y. Y. Wang,

    1. Institute of High Performance Computing, Singapore, Singapore
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  • H. T. Huang,

    1. Six Tee Engineering Groups Pte Ltd, Singapore, Singapore
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  • Z. H. Zhong,

    1. State Key Laboratory of Advanced Technology for Vehicle Body Design and Manufacturing, Hunan University, Hunan, People's Republic of China
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  • G. Y. Li,

    1. State Key Laboratory of Advanced Technology for Vehicle Body Design and Manufacturing, Hunan University, Hunan, People's Republic of China
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  • X. Han

    1. State Key Laboratory of Advanced Technology for Vehicle Body Design and Manufacturing, Hunan University, Hunan, People's Republic of China
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Abstract

Linearly conforming point interpolation method (LC-PIM) is formulated for three-dimensional elasticity problems. In this method, shape functions are generated using point interpolation method by adopting polynomial basis functions and local supporting nodes are selected based on the background cells. The shape functions so constructed have the Kronecker delta functions property and it allows straightforward imposition of point essential boundary conditions. Galerkin weak form is used for creating discretized system equations, and a nodal integration scheme with strain-smoothing operation is used to perform the numerical integration. The present LC-PIM can guarantee linear exactness and monotonic convergence for the numerical results. Numerical examples are used to examine the present method in terms of accuracy, convergence, and efficiency. Compared with the finite element method using linear elements, the LC-PIM can achieve better efficiency, and higher accuracy especially for stresses. Copyright © 2007 John Wiley & Sons, Ltd.

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