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.