Closed‐form buckling analysis of unsymmetrically laminated plates

The local stability of thin‐walled fibre‐reinforced plastic composite beams can be reduced to individual laminates using discrete plate theory. These individual plates receive a supporting effect from their surrounding structure, which is modelled with rotational restraints. In the present investigation, this buckling problem is described by a closed‐form solution. The energy‐based method works with the Rayleigh quotient and the principle of the stationary value of the elastic potential energy. For the analysis of unsymmetrically laminated plates, the classical laminated plate theory (CLPT) considers both the plate deflection and the in‐plane displacements. The first‐order shear deformation theory (FSDT) and third‐order shear deformation theory (TSDT) additionally describe the cross‐sectional rotations and thus take transverse shear deformations into account. In addition to the direct consideration of the bending‐extension couplings, these have also been investigated using the reduced bending stiffness (RBS) method. The investigation shows the influence of bending‐extension coupling on the stability of compressively loaded unsymmetrically laminated plates. Moreover, it is found that the transverse shear stiffness reduces the critical load at relatively high plate thicknesses. The closed‐form analytical solution and the RBS method show good agreement with finite element analyses. The presented closed‐form analytical methods provide explicit solutions for the critical compressive load of unsymmetric laminates under different boundary conditions. Due to the explicit solution, this method is significantly more computationally efficient than numerical, semi‐analytical or exact methods. The present methods are characterised by a simple applicability as well as a very high computational efficiency and are very suitable for preliminary design as well as optimisation of laminated structures.