Analysis of shear deformable laminated composite trapezoidal plates

This paper presents the discrete singular convolution (DSC) method for the free vibration analysis of laminated trapezoidal plates. The plate formulation is based on first-order shear deformation theory (FSDT). The straight-sided trapezoidal domain is mapped into a square domain in the computational space using a four-node element by using the geometric transformation. The frequency parameters are obtained for symmetric angle-ply and cross-ply laminated trapezoidal plate. The accuracy of the present method is demonstrated by comparing with numerical and analytical solutions available in the literature.

[1]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[2]  L. Nallim,et al.  Statical and dynamical behaviour of thin fibre reinforced composite laminates with different shapes , 2005 .

[3]  K. M. Liew,et al.  A Rayleigh-Ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions , 1991 .

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

[5]  Ömer Civalek,et al.  Numerical analysis of free vibrations of laminated composite conical and cylindrical shells , 2007 .

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

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

[8]  Ömer Civalek,et al.  Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method , 2007 .

[9]  Bending Analysis of Classical Symmetric Laminated Composite Plates by the Strip Element Method , 2000 .

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

[11]  A high precision shear deformable element for free vibration of thick/thin composite trapezoidal plates , 2003 .

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

[13]  Yang Xiang,et al.  Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications , 2002 .

[14]  Simon Wang,et al.  Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory , 1997 .

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

[16]  K. M. Liew,et al.  Transverse Vibration Of Trapezoidal Plates Of Variable Thickness: Unsymmetric Trapezoids , 1993 .

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

[18]  Yang Xiang,et al.  Vibration Of Thick Skew Plates Based On Mindlin Shear Deformation Plate Theory , 1993 .

[19]  Abdul Hamid Sheikh,et al.  A high precision shear deformable element for the analysis of laminated composite plates of different shapes , 2002 .

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

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

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

[23]  Abdul Hamid Sheikh,et al.  A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES , 2002 .

[24]  Ömer Civalek,et al.  Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach , 2007 .

[25]  Ömer Civalek,et al.  Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods , 2007 .

[26]  K. M. Liew,et al.  Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method , 2003 .

[27]  Ömer Civalek,et al.  Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method , 2008 .

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

[29]  C. Wang,et al.  Vibration analysis of arbitrarily shaped sandwich plates via Ritz method , 2001 .

[30]  Renato Natal Jorge,et al.  Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions , 2005 .