Stability Analysis of Plates With Partial Restraints Using Unconstrained Optimization Techniques

A procedure is presented for stability analysis of thin plates subject to any combination of in-plane shear, biaxial compression, and bending. Unlike finite element or finite strip methods, where the plate is discretized into a set of elements or strips, the plate here is treated as a single element. An energy-based formulation is used to express the buckling coefficient, K, in terms of general functions that describe the longitudinal and transverse displacement profiles. The longitudinal edges are treated as partially restrained against rotation (PRR) and in-plane translation. Unconstrained optimization technique is then used to determine the minimum combinations of pre-selected geometric plate parameters. Accuracy of the derived expressions is compared with the Galerkin method for the limiting simply supported and clamped boundary conditions. Results are then presented for plates PRR and in-plane translation.