Non-linear bending analysis of laminated sector plates using Generalized Differential Quadrature

Abstract Non-linear static analysis of laminated sector plates with any combination of clamped, simply supported and free edges is presented using Generalized Differential Quadrature (GDQ) method. Particular interest of this study is large deformation of asymmetric sector plates with free edges. Based on the first-order shear deformation theory and von Karman type non-linearity, the governing system of equations include a system of 13 partial differential equations (PDEs) in terms of unknown displacements, forces and moments. Successive application of the GDQ technique to the governing equations resulted in a system of non-linear algebraic equations. The Newton–Raphson iterative scheme is then employed to solve the system of non-linear equations. Illustrative examples are presented to demonstrate accuracy and rapid convergences of the method with small number of grid points. Predictions of the presented method show very good agreement with other numerical studies available in the literature. Further results for asymmetric laminated sector plates with free edges are also presented for future references.

[1]  Manouchehr Salehi,et al.  Large deflection analysis of elastic sector Mindlin plates , 1994 .

[2]  C. Shu,et al.  APPLICATION OF GENERALIZED DIFFERENTIAL QUADRATURE TO SOLVE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS , 1992 .

[3]  H. B. Sharda,et al.  Non-linear analysis of moderately thick sector plates , 2005 .

[4]  K. M. Liew,et al.  Differential quadrature element method for static analysis of Reissner-Mindlin polar plates , 1999 .

[5]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE AND LONG-TERM INTEGRATION , 1971 .

[6]  Chang Shu,et al.  Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates , 1999 .

[7]  Hui-Shen Shen,et al.  Non-linear analysis of functionally graded plates under transverse and in-plane loads , 2003 .

[8]  Shear deformation in thermal bending analysis of laminated plates by the GDQ method , 2003 .

[9]  Geoffrey Turvey,et al.  Large deflection analysis of eccentrically stiffened sector plates. , 1998 .

[10]  Geoffrey Turvey,et al.  DR large deflection analysis of sector plates , 1990 .

[11]  A. R. Sobhani,et al.  Elastic linear and non-linear analysis of fiber-reinforced symmetrically laminated sector Mindlin plate , 2004 .

[12]  Faruk Civan,et al.  Differential quadrature for multi-dimensional problems , 1984 .

[13]  A. R. Setoodeh,et al.  Large deformation analysis of moderately thick laminated plates on nonlinear elastic foundations by DQM , 2007 .

[14]  G. Turvey,et al.  Elastic small deflection analysis of annular sector Mindlin plates , 1994 .

[15]  Chang Shu,et al.  Parallel simulation of incompressible viscous flows by generalized differential quadrature , 1992 .

[16]  K. S. Kim,et al.  Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements , 2006 .

[17]  M. Farid,et al.  A DQ large deformation analysis of composite plates on nonlinear elastic foundations , 2007 .

[18]  S.M. Rezaei Niya,et al.  Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions , 2006 .

[19]  R. Srinivasan,et al.  Non-linear bending of annular sector plates using a matrix method , 1984 .

[20]  A. Mufti,et al.  Nonlinear statics and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade , 2006 .

[21]  C. Bert,et al.  Differential quadrature for static and free vibration analyses of anisotropic plates , 1993 .