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

This paper is written in response to the recently published paper (hit. 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; hit. J. Numer Meth. Engng 2008; 74:175208; 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 (hit. 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 (hit. 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; hit. J Numer Meth. Engng 2007; 71:902-930; hit. 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 Oil future numerical methods. Copyright (C) 2009 John Wiley & Sons, Ltd.