Analysis of plates and shells using an edge-based smoothed finite element method

In this paper, an approach to the analysis of arbitrary thin to moderately thick plates and shells by the edge-based smoothed finite element method (ES-FEM) is presented. The formulation is based on the first order shear deformation theory, and Discrete Shear Gap (DSG) method is employed to mitigate the shear locking. Triangular meshes are used as they can be generated automatically for complicated geometries. The discretized system equations are obtained using the smoothed Galerkin weak form, and the numerical integration is applied based on the edge-based smoothing domains. The smoothing operation can provide a much needed softening effect to the FEM model to reduce the well-known “overly stiff” behavior caused by the fully compatible implementation of the displacement approach based on the Galerkin weakform, and hence improve significantly the solution accuracy. A number of benchmark problems have been studied and the results confirm that the present method can provide accurate results for both plate and shell using triangular mesh.

[1]  G. Dhatt,et al.  An efficient triangular shell element , 1970 .

[2]  Guirong Liu.  A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS , 2008 .

[3]  K. Bathe,et al.  A four‐node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation , 1985 .

[4]  Guirong Liu.  ON G SPACE THEORY , 2009 .

[5]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[6]  P. Lardeur,et al.  A discrete shear triangular nine D.O.F. element for the analysis of thick to very thin plates , 1989 .

[7]  Guirong Liu,et al.  An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids , 2009 .

[8]  H. Nguyen-Xuan,et al.  A smoothed finite element method for plate analysis , 2008 .

[9]  K. Bathe,et al.  Development of MITC isotropic triangular shell finite elements , 2004 .

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

[11]  J. A. Stricklin,et al.  A rapidly converging triangular plate element , 1969 .

[12]  Phill-Seung Lee,et al.  Insight into 3-node triangular shell finite elements: the effects of element isotropy and mesh patterns , 2007 .

[13]  Chen Wanji.  Refined 15‐DOF triangular discrete degenerated shell element with high performances , 2004 .

[14]  E. Ramm,et al.  A unified approach for shear-locking-free triangular and rectangular shell finite elements , 2000 .

[15]  G. Liu.  A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems , 2010 .

[16]  Irwan Katili,et al.  On a simple triangular reissner/mindlin plate element based on incompatible modes and discrete constraints , 1992 .

[17]  Chen Wanji,et al.  Refined 9‐Dof triangular Mindlin plate elements , 2001 .

[18]  Guirong Liu,et al.  Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM) , 2008 .

[19]  R. J. Alwood,et al.  A polygonal finite element for plate bending problems using the assumed stress approach , 1969 .

[20]  Jong H. Kim,et al.  Three-node macro triangular shell element based on the assumed natural strains , 2002 .

[21]  A. Ugural.  Stresses in plates and shells , 1981 .

[22]  Rezak Ayad,et al.  A new hybrid‐mixed variational approach for Reissner–Mindlin plates. The MiSP model , 1998 .

[23]  G. Liu.  A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory , 2010 .

[24]  Jean-Louis Batoz,et al.  An explicit formulation for an efficient triangular plate‐bending element , 1982 .

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

[26]  Klaus-Jürgen Bathe,et al.  A study of three‐node triangular plate bending elements , 1980 .

[27]  Jong Hoon Kim,et al.  A three-node C0 ANS element for geometrically non-linear structural analysis , 2002 .

[28]  K. Y. Sze,et al.  A quadratic assumed natural strain curved triangular shell element , 1999 .

[29]  K. Bathe,et al.  The MITC7 and MITC9 Plate bending elements , 1989 .

[30]  T. Belytschko,et al.  A C0 triangular plate element with one‐point quadrature , 1984 .

[31]  Xiangyang Cui,et al.  A Smoothed Finite Element Method (SFEM) for Linear and Geometrically Nonlinear Analysis of Plates and Shells , 2008 .

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

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

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

[35]  E. Hinton,et al.  A study of quadrilateral plate bending elements with ‘reduced’ integration , 1978 .

[36]  Guiyong Zhang,et al.  Analysis of elastic-plastic problems using edge-based smoothed finite element method , 2009 .