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A novel twice-interpolation finite element method for solid mechanics problems

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Abstract

Formulation and numerical evaluation of a novel twice-interpolation finite element method (TFEM) is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.

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Authors and Affiliations

  1. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, 610065, Chengdu, China

    C. Zheng, X. H. Tang & J. H. Zhang

  2. State Key Laboratory of Digital Manufacturing and Equipment Technology, Huazhong University of Science and Technology, 430074, Wuhan, China

    S. C. Wu

  3. Department of Mechanical Engineering, Centre for Advanced, Computations in Engineering Science (ACES), National University of Singapore, Singapore, 117576, Singapore

    S. C. Wu

Authors
  1. C. Zheng
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  2. S. C. Wu
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  3. X. H. Tang
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  4. J. H. Zhang
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Corresponding author

Correspondence to S. C. Wu.

Additional information

The project supported by the National Natural Science Foundation of China (50474053, 50475134 and 50675081) and the 863 project (2007AA042142).

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Zheng, C., Wu, S.C., Tang, X.H. et al. A novel twice-interpolation finite element method for solid mechanics problems. Acta Mech Sin 26, 265–278 (2010). https://doi.org/10.1007/s10409-009-0265-3

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  • DOI: https://doi.org/10.1007/s10409-009-0265-3

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