Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method

The main objective of this study is to give a numerical solution of three-dimensional analysis of thick rectangular plates. The analysis uses discrete singular convolution (DSC) method. Free vibration, bending and buckling of rectangular plates have been studied in this paper. Regularized Shannon's delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The obtanied results are compared with those of other numerical methods. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers.

[1]  G. Wei,et al.  Conjugate filter approach for solving Burgers' equation , 2002 .

[2]  S. Srinivas,et al.  An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates , 1970 .

[3]  C. Wang,et al.  Frequency relationship between levinson plates and classical thin plates , 1999 .

[4]  K. M. Liew,et al.  Three-dimensional vibration of rectangular plates : Variance of simple support conditions and influence of in-plane inertia , 1994 .

[5]  Yang Xiang,et al.  Transverse vibration of thick rectangular plates—I. Comprehensive sets of boundary conditions , 1993 .

[6]  Decheng Wan,et al.  Numerical solution of incompressible flows by discrete singular convolution , 2002 .

[7]  K. Liew,et al.  Three-dimensional static solutions of rectangular plates by variant differential quadrature method , 2001 .

[8]  Irwan Katili,et al.  A new discrete Kirchhoff-Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—part II: An extended DKQ element for thick-plate bending analysis , 1993 .

[9]  Guo-Wei Wei,et al.  Discrete singular convolution for the sine-Gordon equation , 2000 .

[10]  S. Srinivas,et al.  Flexure of Simply Supported Thick Homogeneous and Laminated Rectangular Plates , 1969 .

[11]  K. M. Liew,et al.  Three-Dimensional Vibration Analysis of Rectangular Plates Based on Differential Quadrature Method , 1999 .

[12]  Ö. Civalek.  Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation , 2006 .

[13]  Y. Cheung,et al.  Free vibration of thick, layered rectangular plates by a finite layer method , 1972 .

[14]  Guo-Wei Wei,et al.  DSC‐Ritz method for high‐mode frequency analysis of thick shallow shells , 2005 .

[15]  F.-L. Liu,et al.  Differential quadrature element method for buckling analysis of rectangular Mindlin plates having discontinuities , 2001 .

[16]  Raymond D. Mindlin,et al.  FLEXURAL VIBRATIONS OF RECTANGULAR PLATES , 1955 .

[17]  Guo-Wei Wei,et al.  A comparison of the spectral and the discrete singular convolution schemes for the KdV-type equations , 2002 .

[18]  Yang Xiang,et al.  A NOVEL APPROACH FOR THE ANALYSIS OF HIGH-FREQUENCY VIBRATIONS , 2002 .

[19]  Yang Xiang,et al.  Research on thick plate vibration: a literature survey , 1995 .

[20]  Y. Xiang,et al.  On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates , 2005 .

[21]  K. M. Liew,et al.  Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates , 1999 .

[22]  K. Liew,et al.  Vibration Analysis of Corner Supported Mindlin Plates of Arbitrary Shape Using the Lagrange Multiplier Method , 1994 .

[23]  Yang Xiang,et al.  Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm , 2002 .

[24]  Guo-Wei Wei,et al.  A new algorithm for solving some mechanical problems , 2001 .

[25]  Arthur W. Leissa,et al.  On the three‐dimensional vibrations of the cantilevered rectangular parallelepiped , 1983 .

[26]  Yang Xiang,et al.  Discrete singular convolution for the prediction of high frequency vibration of plates , 2002 .

[27]  Charles W. Bert,et al.  Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method , 1998 .

[28]  S. Srinivas,et al.  Buckling of thick rectangular plates. , 1969 .

[29]  K. Liew,et al.  Numerical aspects for free vibration of thick plates part I: Formulation and verification , 1998 .

[30]  Ö. Civalek.  The determination of frequencies of laminated conical shells via the discrete singular convolution method , 2006 .

[31]  K. M. Liew,et al.  Three-dimensional vibration of rectangular plates: Effects of thickness and edge constraints , 1995 .

[32]  Ö. Civalek,et al.  Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates , 2004 .

[33]  Guo-Wei Wei,et al.  Discrete singular convolution for the solution of the Fokker–Planck equation , 1999 .

[34]  Siyang Yang,et al.  Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral method for solving partial differential equations , 2002 .

[35]  Arthur W. Leissa,et al.  The free vibration of rectangular plates , 1973 .

[36]  K. M. Liew,et al.  A continuum three-dimensional vibration analysis of thick rectangular plates , 1993 .

[37]  Yang Xiang,et al.  The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution , 2001 .

[38]  Guo-Wei Wei,et al.  VIBRATION ANALYSIS BY DISCRETE SINGULAR CONVOLUTION , 2001 .

[39]  Ding Zhou,et al.  Vibrations of moderately thick rectangular plates in terms of a set of static Timoshenko beam functions , 2000 .

[40]  Tarun Kant,et al.  Numerical analysis of thick plates , 1982 .

[41]  Ding Zhou,et al.  Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method , 2002 .

[42]  Yang Xiang,et al.  Plate vibration under irregular internal supports , 2002 .

[43]  Guo-Wei Wei,et al.  Solving quantum eigenvalue problems by discrete singular convolution , 2000 .

[44]  K. M. Liew,et al.  A differential quadrature procedure for three-dimensional buckling analysis of rectangular plates , 1999 .

[45]  Ömer Civalek,et al.  An efficient method for free vibration analysis of rotating truncated conical shells , 2006 .

[46]  Ö. Civalek.  Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns , 2004 .

[47]  G. Wei.  Discrete singular convolution for beam analysis , 2001 .

[48]  Irwan Katili,et al.  A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields. I - An extended DKT element for thick-plate bending analysis. II - An extended DKQ element for thick-plate bending analysis , 1993 .

[49]  Yun Gu,et al.  Parameter optimization in the regularized Shannon's kernels of higher-order discrete singular convolutions , 2003 .

[50]  K. Liew,et al.  Modeling via differential quadrature method: Three-dimensional solutions for rectangular plates , 1998 .

[51]  W. H. Wittrick.  Analytical, three-dimensional elasticity solutions to some plate problems, and some observations on Mindlin's plate theory , 1987 .

[52]  Y. Xiang,et al.  DSC analysis of free-edged beams by an iteratively matched boundary method , 2005 .

[53]  G. Wei,et al.  DSC ANALYSIS OF RECTANGULAR PLATES WITH NON-UNIFORM BOUNDARY CONDITIONS , 2002 .