Efficient post-buckling analysis of variable-stiffness plates using a perturbation approach

The present work discusses the development of a formulation for efficiently analyzing variable-stiffness plates operating in the post-buckling regime. The approach relies upon the combined use of a single-mode Koiter's perturbation strategy along with a mixed variational formulation expressed in terms of Airy stress function and out-of-plane displacement, where the unknowns are approximated using global trial functions based on Legendre polynomials. A highly efficient numerical tool is achieved, which allows the initial post-buckling field to be analyzed with the ease of closed-form solutions, but a much wider field of employ in terms of elastic couplings, boundary and loading conditions. The quality of the predictions is illustrated by means of a comprehensive set of comparisons against results from the literature. Possible applications of the approach are shown, where the exploration of the design space offered by curvilinear fibers requires thousands of non-linear post-buckling analyses to be run.