Buckling of shear-deformable unsymmetrically laminated plates

Abstract

The couplings of unsymmetric laminated structures and the comparatively low transverse shear stiffnesses significantly influence their stability behaviour. The aim of this work is to improve the purely analytical stability analysis of unsymmetric laminated structures. This problem can be reduced to one single plate with the use of the discrete plate theory. In this study, laminates under uniaxial compressive load are considered that are simply supported at all edges and have rotational restraints on the unloaded edges (SRSR) or have a free edge (SFSR). Therefore, the present study provides explicit solutions for the buckling load in two ways. Firstly, the first explicit solution for the buckling load of unsymmetric laminates with the mentioned boundary conditions is developed, which takes the bending–extension couplings into account in a direct way. The method is an energy-based method in the form of the Rayleigh-quotient for classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and third order shear deformation theory (TSDT). Secondly, the reduced bending (RBS) method is investigated for the first time in the framework of TSDT. The comparison of unsymmetric cross-ply and angle-ply laminates shows a good agreement with finite element analysis (FEA). Due to the high computational efficiency of the presented methods, they are excellently suited for pre-design and optimization of composite structures, with simultaneous high usability in practical application.