Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method

Abstract This paper presents an element-free Galerkin (EFG) method for the static analysis of concentrically and eccentrically stiffened plates based on first-order shear deformable theory (FSDT). The stiffened plates are regarded as composite structures of plates and beams. Imposing displacement compatible conditions between the plate and the stiffener, the displacement fields of the stiffener can be expressed in terms of the mid-surface displacement of the plate. The strain energy of the plate and stiffener can be superimposed to obtain the stiffness matrix of the stiffed plate. Because there are no elements used in the meshless model of the plate, the stiffeners need not to be placed along the meshes, as is done in the finite element methods. The stiffeners can be placed at any location, and will not lead to the re-meshing of the plate. The validity of the EFG method is demonstrated by considering several concentrically and eccentrically stiffened plate problems. The present results show good agreement with the existing analytical and finite element solutions. The influences of support size (denoted by a scaling factor d max ) and order of the complete basis functions ( N c ) on the numerical accuracy are also investigated. It is found that larger support size and higher order of basis function will furnish better convergence results.

[1]  Shaker A. Meguid,et al.  Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method , 2002 .

[2]  K. M. Liew,et al.  Free vibration analysis of rectangular plates using orthogonal plate function , 1990 .

[3]  K. M. Liew,et al.  Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells , 2002 .

[4]  K. C. Biswal,et al.  Finite element analysis for stiffened laminated plates using higher order shear deformation theory , 1994 .

[5]  K. M. Liew,et al.  Application of two-dimensional orthogonal plate function to flexural vibration of skew plates , 1990 .

[6]  K. M. Liew,et al.  Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates , 2004 .

[7]  K. M. Liew,et al.  Bending and buckling of thick symmetric rectangular laminates using the moving least-squares differential quadrature method , 2003 .

[8]  Ming Jen Tan,et al.  Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method , 2002 .

[9]  K. M. Liew,et al.  Moving least squares differential quadrature method and its application to the analysis of shear deformable plates , 2003 .

[10]  Mark P. Rossow,et al.  Constraint method analysis of stiffened plates , 1978 .

[11]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[12]  K. Liew,et al.  Formulation of Mindlin-Engesser model for stiffened plate vibration , 1995 .

[13]  K. M. Liew,et al.  Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method , 2004 .

[14]  Wing Kam Liu,et al.  Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures , 1996 .

[15]  A. Deb,et al.  Finite element models for stiffened plates under transverse loading , 1988 .

[16]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

[17]  Edward A. Sadek,et al.  A finite element model for the analysis of stiffened laminated plates , 2000 .

[18]  K. M. Liew,et al.  Analysis of rectangular laminated composite plates via FSDT meshless method , 2002 .

[19]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[20]  K. M. Liew,et al.  A spline strip kernel particle method and its application to two‐dimensional elasticity problems , 2003 .

[21]  Yang Xiang,et al.  VIBRATION OF CIRCULAR AND ANNULAR MINDLIN PLATES WITH INTERNAL RING STIFFENERS , 1996 .