Lévy‐type solutions for buckling of shear deformable unsymmetrically laminated plates with rotational restraints

The local stability of unsymmetric laminated structures is significantly affected by bending‐extension coupling and the comparatively low transverse shear stiffnesses, which have to be included in the structural analysis. If such structures have flat surfaces in segments, they can be investigated with the discrete plate analysis. In this analysis, the individual segments are considered as plates with rotational restraints that represent the supporting effect of the surrounding structure. The aim of this work is to improve the analytical stability of laminated plates. Therefore, Lévy‐type solutions for the buckling load of the mentioned laminated plates are considered and refined. This offers exact solutions for unsymmetrical cross‐ply laminates as well as antisymmetric angle‐ply laminates. In order to show the influence of shear deformations, the solutions for classical laminated plate theory (CLPT), first‐order shear deformation theory (FSDT), and third‐order shear deformation theory (TSDT) are worked out and compared to each other. In the context of TSDT, a new formulation for the rotational elastic restraint is presented, which affects the rotation and the warping of the plate cross‐section. This investigation presents the influence of shear deformations on different laminates and classifies the benefits of the different laminated plate theories with respect to the stability behaviour under different boundary conditions. In addition, the influence of bending‐extension coupling on different fibre angles and layer sequences is analysed.