Isogeometric finite element method for buckling analysis of generally laminated composite beams with different boundary conditions

Abstract In this paper, isogeometric finite element method (IGA) based on Non-Uniform Rational B-splines (NURBS) basis function is applied for the buckling analysis of generally laminated composite beam with various boundary conditions. A beam element with four degrees of freedom per control point is investigated, which has considered the bending-torsion deformation. The model for the buckling analysis of laminated composite beam is detailed by the principle of virtual work. Several numerical examples of symmetric and anti-symmetric, cross-ply and angle-ply composite beam are performed. Numerical results of critical buckling loads and mode shapes are presented, and compared with other available results to show the efficiency and accuracy of the present IGA approach. In addition, the impacts of the modulus ratios, slenderness ratios, stacking sequence and the fiber angle, especially the Poisson effect on the critical buckling loads of composite beam are clearly demonstrated. It should be noted the results with the Poisson effect neglected are only suit for the cross-ply composite beams. And the benchmark solutions presented in this work can be used as a reference for the buckling analysis of laminated composite beams in future.

[1]  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 .

[2]  Metin Aydogdu,et al.  Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method , 2006 .

[3]  K. Chandrashekhara,et al.  Free vibration of composite beams using a refined shear flexible beam element , 1992 .

[4]  Hiroyuki Matsunaga,et al.  Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory , 2000 .

[5]  T. Q. Bui,et al.  Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method , 2012 .

[6]  Ahmed A. Khdeir,et al.  Buckling of cross-ply laminated beams with arbitrary boundary conditions , 1997 .

[7]  M. Karama,et al.  Bending, buckling and free vibration of laminated composite with a transverse shear stress continuity model , 1998 .

[8]  Hung Nguyen-Xuan,et al.  Static, free vibration, and buckling analysis of laminated composite Reissner–Mindlin plates using NURBS‐based isogeometric approach , 2012 .

[9]  J. Reddy.  Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates , 2010 .

[10]  Alessandro Reali,et al.  Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint) , 2007 .

[11]  M. Kargarnovin,et al.  An analytical approach for the free vibration analysis of generally laminated composite beams with shear effect and rotary inertia , 2012 .

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

[13]  K. M. Liew,et al.  Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads , 2004 .

[14]  Prabhat Hajela,et al.  Free vibration of generally layered composite beams using symbolic computations , 1995 .

[15]  Huu-Tai Thai,et al.  Static behavior of composite beams using various refined shear deformation theories , 2012 .

[16]  Moshe Eisenberger,et al.  Vibrations and buckling of cross-ply nonsymmetric laminated composite beams , 1996 .

[17]  Huu-Tai Thai,et al.  Vibration and buckling of composite beams using refined shear deformation theory , 2012 .

[18]  Shen Rongying,et al.  Dynamic finite element method for generally laminated composite beams , 2008 .

[19]  Chen Wanji,et al.  An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams , 2008 .

[20]  X. Kong,et al.  Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups , 2014 .

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

[22]  Hiroyuki Matsunaga,et al.  VIBRATION AND BUCKLING OF MULTILAYERED COMPOSITE BEAMS ACCORDING TO HIGHER ORDER DEFORMATION THEORIES , 2001 .

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

[24]  Weiqiu Chen,et al.  Free vibration analysis of generally laminated beams via state-space-based differential quadrature , 2004 .

[25]  Metin Aydogdu,et al.  Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions , 2007 .

[26]  Hiroyuki Matsunaga,et al.  Assessment of a global higher-order deformation theory for laminated composite and sandwich plates , 2002 .

[27]  Metin Aydogdu,et al.  Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method , 2005 .

[28]  Jaehong Lee,et al.  NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature , 2015 .

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

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

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

[32]  J. N. Reddy,et al.  Free vibration of cross-ply laminated beams with arbitrary boundary conditions , 1994 .

[33]  Sébastien Mistou,et al.  Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity , 2003 .

[34]  K. Y. Lam,et al.  A strip element method for the transient analysis of symmetric laminated plates , 2001 .

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