Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method

The elastic bending of unstiffened and stiffened corrugated plates is studied in this paper, and a mesh-free Galerkin method is presented for the analyses. A corrugated plate is treated as an orthotropic plate that has different flexure properties in two perpendicular directions. The equivalent flexure properties are estimated by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plate is considered as a composite structure of an orthotropic plate with beams. By superimposing the strain energy of the orthotropic plate and the beams, and imposing the displacement compatibility conditions between the plate and the beams, the stiffness matrix of the structure is obtained. Because no mesh is needed in the proposed method, there is no limitation to the position of the stiffeners (beams). Changes in the positions of the stiffeners do not require the re-meshing of the plate. Several numerical examples are employed to show the accuracy and convergence of the proposed method. The computation results demonstrate good agreement with the solutions given by ANSYS, and different profiles of corrugated plates are considered.

[1]  C.M.C. Roque,et al.  Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method , 2003 .

[2]  Eiichi Watanabe,et al.  Shear buckling of corrugated plates with edges elastically restrained against rotation , 2004 .

[3]  M. Mukhopadhyay,et al.  Finite element static and dynamic analyses of folded plates , 1999 .

[4]  A. Ferreira,et al.  Radial basis functions and higher-order shear deformation theories in the analysis of laminated composite beams and plates , 2004 .

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

[6]  J. N. Reddy,et al.  Theory and analysis of elastic plates , 1999 .

[7]  N. P. Semenyuk,et al.  On Design Models in Stability Problems for Corrugated Cylindrical Shells , 2002 .

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

[9]  Arthur H. Nilson,et al.  Finite Element Analysis of Metal Deck Shear Diaphragms , 1974 .

[10]  J. Ren,et al.  Mesh-Free Method Revisited: Two New Approaches for the Treatment of Essential Boundary Conditions , 2002, Int. J. Comput. Eng. Sci..

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

[12]  John T. Easley.  Buckling Formulas for Corrugated Metal Shear Diaphragms , 1975 .

[13]  Demetres Briassoulis,et al.  Equivalent orthotropic properties of corrugated sheets , 1986 .

[14]  R. A. Shimansky,et al.  Transverse Stiffness of a Sinusoidally Corrugated Plate , 1995 .

[15]  K. M. Liew,et al.  Boundary element‐free method (BEFM) for two‐dimensional elastodynamic analysis using Laplace transform , 2005 .

[16]  K. M. Liew,et al.  Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method , 2004 .

[17]  K. Liew,et al.  Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method , 2006 .

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

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

[20]  J. Lau.  Stiffness of Corrugated Plate , 1981 .

[21]  António J.M. Ferreira,et al.  Thick Composite Beam Analysis Using a Global Meshless Approximation Based on Radial Basis Functions , 2003 .

[22]  António J.M. Ferreira,et al.  Polyharmonic (thin-plate) splines in the analysis of composite plates , 2004 .

[23]  Bo Edlund,et al.  Shear capacity of plate girders with trapezoidally corrugated webs , 1996 .

[24]  D. E. McFarland,et al.  Buckling of Light-Gage Corrugated Metal Shear Diaphragms , 1969 .

[25]  K. M. Liew,et al.  Meshfree method for large deformation analysis–a reproducing kernel particle approach , 2002 .

[26]  Guirong Liu,et al.  A point interpolation meshless method based on radial basis functions , 2002 .

[27]  K. M. Liew,et al.  Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads , 2004 .

[28]  J M Davies.  Calculation of Steel Diaphragm Behavior , 1976 .

[29]  K. M. Liew,et al.  Numerical simulation of thermomechanical behaviours of shape memory alloys via a non‐linear mesh‐free Galerkin formulation , 2005 .

[30]  K. M. Liew,et al.  Elasto‐plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming , 2002 .

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

[32]  Guirong Liu,et al.  A LOCAL RADIAL POINT INTERPOLATION METHOD (LRPIM) FOR FREE VIBRATION ANALYSES OF 2-D SOLIDS , 2001 .

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

[34]  K. Liew,et al.  Buckling of folded plate structures subjected to partial in‐plane edge loads by the FSDT meshfree Galerkin method , 2006 .

[35]  António J.M. Ferreira,et al.  A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates , 2003 .