Natural frequencies of FSDT cross-ply composite shells by multiquadrics

The first-order theory of Donnell is applied to evaluate the natural frequencies of doubly curved cross-ply composite shells. In this paper a meshless method based on multiquadric radial basis functions is used for discretization of equations of motion and boundary conditions. It is shown that natural frequencies obtained by this approach are very accurately determined.

[1]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[2]  S. T. Mau,et al.  A Refined Laminated Plate Theory , 1973 .

[3]  Hidenori Murakami,et al.  Laminated Composite Plate Theory With Improved In-Plane Responses , 1986 .

[4]  J. Ren,et al.  A new theory of laminated plate , 1986 .

[5]  Stanley B. Dong,et al.  On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation , 1972 .

[6]  Stanley B. Dong,et al.  On the Theory of Laminated Anisotropic Shells and Plates , 1962 .

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

[8]  E. Carrera,et al.  Zig-Zag and interlaminar equilibria effects in large deflection and postbuckling analysis of multilayered plates , 1997 .

[9]  C. Sun,et al.  A higher order theory for extensional motion of laminated composites , 1973 .

[10]  J. N. Reddy,et al.  A higher-order shear deformation theory of laminated elastic shells , 1985 .

[11]  J. Whitney,et al.  A Refined Theory for Laminated Anisotropic, Cylindrical Shells , 1974 .

[12]  E. Carrera.  Historical review of Zig-Zag theories for multilayered plates and shells , 2003 .

[13]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[14]  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 .

[15]  E. Carrera.  C0 REISSNER–MINDLIN MULTILAYERED PLATE ELEMENTS INCLUDING ZIG-ZAG AND INTERLAMINAR STRESS CONTINUITY , 1996 .

[16]  E. Reissner,et al.  Stress Strain Relations in the Theory of Thin Elastic Shells , 1952 .

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

[18]  M. Di Sciuva,et al.  An Improved Shear-Deformation Theory for Moderately Thick Multilayered Anisotropic Shells and Plates , 1987 .

[19]  L. Schumaker,et al.  Surface Fitting and Multiresolution Methods , 1997 .

[20]  Jack R. Vinson,et al.  Laminated Transversely Isotropic Cylindrical Shells , 1971 .

[21]  J. Carleone,et al.  Transverse shear in laminated plate theories. , 1973 .

[22]  Erasmo Carrera,et al.  Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis , 1998 .

[23]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[24]  António J.M. Ferreira,et al.  Analysis of Composite Plates Using a Layerwise Theory and Multiquadrics Discretization , 2005 .