Postbuckling of Compressively Loaded Imperfect Composite Plates: Closed-Form Approximate Solutions

In this paper, closed-form approximate solutions for the geometrically nonlinear behaviour of rectangular laminated plates with °exural orthotropy under longitudinal compression are presented. Based on the governing Marguerre-type di®erential equations postulated for imperfect plates, two plate con¯gurations are discussed in detail, representing important application cases in practical engineering work. The ¯rst con¯guration is a laminated plate that is simply supported at all four edges (the so-called SSSS plate), while for the second con¯guration clamped unloaded longitudinal edges are considered (denoted as the SSCC plate). For both plate con¯gurations, rather simple closed-form approximations in the form of trigonometric shape functions are employed for the description of the out-of-plane postbuckling plate de°ections. Based on the chosen shape functions, the compatibility condition with respect to the in-plane strains is ful¯lled exactly, while the out-of-plane equilibrium condition for a de°ected plate element is not, but is solved using a Galerkin-type formulation instead. Eventually, very simple closed-form solutions for all postbuckling state variables (de°ections, in-plane edge displacements, and e®ective widths) are derived that can be used very conveniently in engineering practice. The high accuracy of the presented analysis methods is established by comparison with the results of other authors.