ISOGEOMETRIC SIMULATION FOR BUCKLING, FREE AND FORCED VIBRATION OF ORTHOTROPIC PLATES

Buckling, free and forced vibration analyses of orthotropic plates are studied numerically using Isogeometric analysis. The present formulation is based on the classical plate theory (CPT) while the NURBS basis function is employed for both the parametrization of the geometry and the approximation of plate deflection. An efficient and easy-to-implement technique is used for imposing the essential boundary conditions. Numerical examples for free and forced vibration and buckling of orthotropic plates with different boundary conditions and configurations are considered. The numerical results are compared with other existing solutions to show the efficiency and accuracy of the proposed approach for such problems.

[1]  A. V. Lopatin,et al.  Buckling of clamped orthotropic plate in shear , 2006 .

[2]  A. Kerr,et al.  NATURAL VIBRATION ANALYSIS OF CLAMPED RECTANGULAR ORTHOTROPIC PLATES , 1996 .

[3]  A. Rao,et al.  Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates , 1970 .

[4]  S. M. Dickinson,et al.  On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates , 1986 .

[5]  Bo Liu,et al.  Exact solutions for free vibrations of orthotropic rectangular Mindlin plates , 2011 .

[6]  Tinh Quoc Bui,et al.  A novel meshfree model for buckling and vibration analysis of rectangular orthotropic plates , 2011 .

[7]  N. S. Bardell,et al.  Free vibration analysis of thin coplanar rectangular plate assemblies — Part I: theory, and initial results for specially orthotropic plates , 1996 .

[8]  Achchhe Lal,et al.  STOCHASTIC THERMAL POST-BUCKLING RESPONSE OF LAMINATED COMPOSITE CYLINDRICAL SHELL PANEL WITH SYSTEM RANDOMNESS , 2012 .

[9]  N. Li,et al.  Forced vibration analysis of the clamped orthotropic rectangular plate by the superposition method , 1992 .

[10]  J. Surdenas,et al.  Buckling of Rectangular Orthotropic Plates Under Biaxial Loading , 1987 .

[11]  R. L. Taylor Isogeometric analysis of nearly incompressible solids , 2011 .

[12]  Mohammad Talha,et al.  Thermo-Mechanical Buckling Analysis of Finite Element Modeled Functionally Graded Ceramic-Metal Plates , 2011 .

[13]  Y. Z. Chen,et al.  Evaluation of fundamental vibration frequency of an orthotropic bending plate by using an iterative approach , 1998 .

[14]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[15]  E. Morozov,et al.  Buckling of the SSFF rectangular orthotropic plate under in-plane pure bending , 2009 .

[16]  Guirong Liu,et al.  An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape , 2003 .

[17]  Zhigang Suo,et al.  ANALYTICAL SOLUTIONS OF POLYMERIC GEL STRUCTURES UNDER BUCKLING AND WRINKLE , 2011 .

[18]  Charles W. Bert,et al.  Fundamental frequency analysis of single specially orthotropic, generally orthotropic and anisotropic rectangular layered plates by the differential quadrature method , 1993 .

[19]  Romesh C. Batra,et al.  Natural frequencies of thick plates made of orthotropic, monoclinic, and hexagonal materials by a meshless method , 2009 .

[20]  R. E. Rossi,et al.  Vibrations of a rectangular orthotropic plate with a free edge: a comparison of analytical and numerical results , 1998 .

[21]  Romesh C. Batra,et al.  Natural frequencies of thick square plates made of orthotropic, trigonal, monoclinic, hexagonal and triclinic materials , 2004 .

[22]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[23]  Maenghyo Cho,et al.  The application of geometrically exact shell elements to B-spline surfaces , 2004 .

[24]  F. Auricchio,et al.  The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations , 2010 .

[25]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[26]  E. Morozov,et al.  Buckling of the CCFF orthotropic rectangular plates under in-plane pure bending , 2010 .

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

[28]  K. Y. Dai,et al.  Free and forced vibration analysis using the smoothed finite element method (SFEM) , 2007 .

[29]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[30]  D. J. Gorman Accurate Free Vibration Analysis of the Completely Free Orthotropic Rectangular Plate by the Method of Superposition , 1993 .

[31]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[32]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[33]  Sung-Kie Youn,et al.  Isogeometric contact analysis using mortar method , 2012 .

[34]  T. Sakiyama,et al.  Free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions , 2005 .

[35]  Victor M. Calo,et al.  The role of continuity in residual-based variational multiscale modeling of turbulence , 2007 .

[36]  Yufeng Xing,et al.  New exact solutions for free vibrations of thin orthotropic rectangular plates , 2009 .

[37]  Ali Akbar Jafari,et al.  An efficient mixed methodology for free vibration and buckling analysis of orthotropic rectangular plates , 2011, Appl. Math. Comput..

[38]  Rama B. Bhat,et al.  Natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation , 1996 .

[39]  K. Bhaskar,et al.  Accurate and elegant free vibration and buckling studies of orthotropic rectangular plates using untruncated infinite series , 2008 .

[40]  W. Wall,et al.  Isogeometric structural shape optimization , 2008 .

[41]  Peter Wriggers,et al.  Contact treatment in isogeometric analysis with NURBS , 2011 .

[42]  Erasmo Carrera,et al.  Influence of in-plane axial and shear loading on the vibration of metallic plates , 2011 .

[43]  Flexural vibration and buckling analysis of orthotropic plates by the boundary element method , 1990 .

[44]  E. Morozov,et al.  Buckling of the SSCF rectangular orthotropic plate subjected to linearly varying in-plane loading , 2011 .

[45]  Guirong Liu,et al.  A smoothed Hermite radial point interpolation method for thin plate analysis , 2011 .

[46]  T. Hughes,et al.  B¯ and F¯ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements , 2008 .

[47]  Huu-Tai Thai,et al.  Levy-type solution for buckling analysis of orthotropic plates based on two variable refined plate theory , 2011 .

[48]  R. L. Ramkumar,et al.  Free vibration solution for clamped orthotropic plates using Lagrangian multiplier technique , 1987 .

[49]  J. Giri,et al.  Buckling of Rotationally Restrained Orthotropic Plates Under Uniaxial Compression , 1977 .

[50]  T. Hughes,et al.  Isogeometric fluid-structure interaction: theory, algorithms, and computations , 2008 .

[51]  D. J. Gorman Accurate free vibration analysis of clamped orthotropic plates by the method of superposition , 1990 .

[52]  Guirong Liu Mesh Free Methods: Moving Beyond the Finite Element Method , 2002 .

[53]  Yoshihiro Narita,et al.  Vibration studies for simply supported symmetrically laminated rectangular plates , 1989 .

[54]  Y. Hon,et al.  A meshfree Hermite‐type radial point interpolation method for Kirchhoff plate problems , 2006 .

[55]  L. M. Cook,et al.  Upper and lower bounds to the natural frequencies of vibration of clamped rectangular orthotropic plates , 1978 .

[56]  Yuri Bazilevs,et al.  The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches , 2010 .

[57]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

[58]  A. N. Bercin Letter to the Editor: Free Vibration Solution for Clamped Orthotropic Plates Using the Kantorovich Method , 1996 .

[59]  R. Batra,et al.  Natural frequencies of orthotropic, monoclinic and hexagonal plates by a meshless method , 2005 .