On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM)

Authors

  • G. R. Liu,

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

    Corresponding author
    1. Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
    2. Faculty of Mathematics and Computer Science, University of Science HCM, Vietnam
    • Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
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  • H. Nguyen-Xuan,

    1. Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore 117576, Singapore
    2. Faculty of Mathematics and Computer Science, University of Science HCM, Vietnam
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  • K. Y. Dai,

    1. IntecSEA, WorleyParsons Pte. Ltd, Singapore
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  • K. Y. Lam

    1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
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Abstract

This paper is written in response to the recently published paper (Int. J. Numer. Meth. Engng 2008; 76:1285–1295) at IJNME entitled ‘On the smoothed finite element method’ (SFEM) by Zhang HH, Liu SJ, Li LX.

In this paper we

  • (1)repeat briefly the important essence of the original SFEM presented in (Comp. Mech. 2007; 39: 859–877; Int. J. Numer. Meth. Engng 2007; 71:902–930; Int. J. Numer. Meth. Engng 2008; 74:175–208; Finite Elem. Anal. Des. 2007; 43:847–860; J. Sound Vib. 2007; 301:803–820), and
  • (2)examine further issues in the evaluation of the shape functions used in the SFEM.

It will be shown that the ‘SFEM’ presented in paper (Int. J. Numer. Meth. Engng 2008; 76:1285–1295) is not at all our original SFEM presented in (Comp. Mech. 2007; 39:859–877; Int. J. Numer. Meth. Engng 2007; 71:902–930; Int. J. Numer. Meth. Engng 2008; 74:175–208; Finite Elem. Anal. Des. 2007; 43:847–860; J. Sound Vib. 2007; 301:803–820). Therefore, all these ‘Theorems’, ‘Corollaries’ and ‘Remarks’ presented in paper (Int. J. Numer. Meth. Engng 2008; 76:1285–1295) have nothing to do with our original SFEM. The properties of the original SFEM stand as they were presented in our original papers (Comp. Mech. 2007; 39:859–877; Int. J. Numer. Meth. Engng 2007; 71:902–930; Int. J. Numer. Meth. Engng 2008; 74:175–208; Finite Elem. Anal. Des. 2007; 43:847–860; J. Sound Vib. 2007; 301:803–820). Finally, we brief on our advancements made far beyond our original SFEM and our visions on future numerical methods. Copyright © 2009 John Wiley & Sons, Ltd.

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