Closed-form analysis of the buckling loads of symmetrically laminated orthotropic plates considering elastic edge restraints

The initial buckling loads of symmetrically laminated rectangular orthotropic plates under uniaxial compression are determined in a closed-form analytical manner. The considered laminates are simply supported at all edges and furthermore subjected to elastic rotational restraints at the unloaded edges. The analysis approach which is based on the assumptions of Classical Laminate Plate Theory employs a representation for the transverse displacements consisting of a system of trigonometric functions in both inplane coordinate directions. Due to its simplicity, a closed-form solution for the critical buckling load is possible which is useful for preliminary design purposes. The presented approach is compared to closed-form analytical and numerical data available in the literature and is found to be in favorable agreement.