Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions

The present study is concerned with the thermal buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The requirement of the continuity conditions between layers for symmetric cross-ply laminated beams is satisfied by the use of the shape function incorporated into the theory which also unifies the one dimensional shear deformable beam theories developed previously. The governing equations are obtained by means of minimum energy principle. Three different combinations of clamped and hinged edge boundary conditions are considered. The critical thermal buckling temperatures are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and lay-ups are presented and compared with the ones available in the literature. It is interesting to note that some cross-ply beams buckle upon cooling instead of heating and some of them do not buckle irrespective of whether they are heated or cooled.

[1]  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 .

[2]  A. W. Leissa,et al.  Vibration and buckling of generally laminated composite plates with arbitrary edge conditions , 1987 .

[3]  Carl T. Herakovich,et al.  Mechanics of Fibrous Composites , 1997 .

[4]  T. R. Tauchert,et al.  Thermally Induced Flexure, Buckling, and Vibration of Plates , 1991 .

[5]  Hiroyuki Matsunaga,et al.  Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory , 2005 .

[6]  Kostas P. Soldatos,et al.  A transverse shear deformation theory for homogeneous monoclinic plates , 1992 .

[7]  A. Mannini.  Shear deformation effects on thermal buckling of cross-ply composite laminates , 1997 .

[8]  P. Biswas.  Thermal Buckling of Orthotropic Plates , 1976 .

[9]  Arcangelo Messina,et al.  Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory , 1999 .

[10]  A. A. Khdeir.  Thermal buckling of cross-ply laminated composite beams , 2001 .

[12]  Jaehong Lee.  Thermally induced buckling of laminated composites by a layerwise theory , 1997 .

[13]  Hiroyuki Matsunaga,et al.  Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading , 2007 .

[14]  C. Sophocleous,et al.  ON SHEAR DEFORMABLE BEAM THEORIES: THE FREQUENCY AND NORMAL MODE EQUATIONS OF THE HOMOGENEOUS ORTHOTROPIC BICKFORD BEAM , 2001 .

[15]  A. Messina,et al.  Influence of edge boundary conditions on the free vibrations of cross-ply laminated circular cylindrical panels , 1999 .

[16]  R. Bhat.  Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method , 1986 .

[17]  Lien-Wen Chen,et al.  THERMAL BUCKLING OF LAMINATED COMPOSITE PLATES , 1987 .

[18]  G. Venkateswara Rao,et al.  Thermal buckling of cross-ply composite laminates , 1992 .

[19]  Haim Abramovich,et al.  Thermal buckling of cross-ply composite laminates using a first-order shear deformation theory , 1994 .

[20]  Robert M. Jones.  Thermal buckling of uniformly heated unidirectional and symmetric cross-ply laminated fiber-reinforced composite uniaxial in-plane restrained simply supported rectangular plates , 2005 .

[21]  T. R. Tauchert.  THERMAL BUCKLING OF THICK ANTISYMMETRIC ANGLE-PLY LAMINATES , 1987 .

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

[23]  K. M. Liew,et al.  Vibration analysis of symmetrically laminated thick rectangular plates using the higher-order theory and p-Ritz method , 1997 .

[24]  Kostas P. Soldatos,et al.  A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories , 1993 .

[25]  W. M. Roberts,et al.  Thermal buckling of plates , 1952 .

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

[27]  R. Dhanaraj,et al.  Thermal buckling of laminated composite plates , 1994 .

[28]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[29]  Hiroyuki Matsunaga,et al.  Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory , 2006 .

[30]  Kostas P. Soldatos,et al.  Comparative dynamic studies for symmetric cross-ply circular cylindrical shells on the basis of a unified shear deformable shell theory , 1995 .

[31]  M. Aydogdu.  Free Vibration Analysis of Angle-ply Laminated Beams with General Boundary Conditions , 2006 .

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