Free and forced vibration analysis using the smoothed finite element method ( SFEM )

Smoothed finite element method (SFEM) was recently proposed by the authors to improve the accuracy and convergence rate of the existing standard four-node isoparametric finite element method (FEM) by 2 2 quadrature in the static analysis. In this work, it is further extended to the free and forced analysis of two-dimensional (2D) dynamic problems. It is found that SFEM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements in solving dynamic problems without increasing the computational cost. As only shape function itself is involved in computing the field gradients and no coordinate transformation is required, the method is very easy to implement. Nonlinear elastic forced vibration problem is also examined by using smoothed deformation gradients on each cell. r 2006 Elsevier Ltd. All rights reserved.

[1]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[2]  K. Y. Dai,et al.  A Smoothed Finite Element Method for Mechanics Problems , 2007 .

[3]  Ted Belytschko,et al.  Efficient linear and nonlinear heat conduction with a quadrilateral element , 1983 .

[4]  T. Belytschko,et al.  Efficient implementation of quadrilaterals with high coarse-mesh accuracy , 1986 .

[5]  K. Y. Dai,et al.  Theoretical aspects of the smoothed finite element method (SFEM) , 2007 .

[6]  K. Y. Dai,et al.  A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures , 2002 .

[7]  C. Brebbia,et al.  Boundary Element Techniques , 1984 .

[8]  K. Bathe.  Finite Element Procedures , 1995 .

[9]  K. Y. Dai,et al.  An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics , 2007 .

[10]  Toshio Nagashima,et al.  NODE-BY-NODE MESHLESS APPROACH AND ITS APPLICATIONS TO STRUCTURAL ANALYSES , 1999 .

[11]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[12]  D. V. Griffiths,et al.  Programming the finite element method , 1982 .

[13]  K. Y. Dai,et al.  A LINEARLY CONFORMING POINT INTERPOLATION METHOD (LC-PIM) FOR 2D SOLID MECHANICS PROBLEMS , 2005 .

[14]  Michał Kleiber,et al.  Nonlinear Mechanics of Structures , 1991 .

[15]  K. Y. Dai,et al.  Contact Analysis for Solids Based on Linearly Conforming Radial Point Interpolation Method , 2007 .

[16]  J. M. Kennedy,et al.  Hourglass control in linear and nonlinear problems , 1983 .