Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method

The present study is concerned with the 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 are 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 free, clamped and simply supported edge boundary conditions are considered. The critical buckling loads are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results were obtained for different length-to-thickness ratios and lay-ups are presented and compared with the ones available in the literature.