The Analysis of Unbalanced Cross-Plied Elliptic Plates Under Uniform Pressure

Abstract

Unbalanced cross-plied laminated plates with bending-membrane coupling are analyzed for the case of an elliptic planform under uniform pressure. Closed form solutions are presented for two cases of membrane boundary conditions with the bending boundary conditions assumed to be clamped. Comparisons between various approximations and membrane boundary conditions are made for composite plates of glass, Thornel and boron fibers in epoxy matricies. Circular plates are treated as a special case of elliptic plates.

Closed-form solution of an arbitrarily laminated, anisotropic, elliptic plate under uniform pressure

“…It is noted that the w part of the above solution was first suggested for isotropic plates by G. H. Bryan, according to Love [12], while the parts with coefficients U1 and V~ were first used by Kicher [4]. It is believed that the parts with coefficients U2 and V2 are introduced here for the first time.…”

“…Subsequently a few closed-form solutions have appeared for plates of certain specific lamination arrangements, planform geometries, and boundary conditions. Notable among these are the works of Whitney [2] and Whitney and Leissa [3] for both antisymmetric cross-ply and antisymmetric angle-ply rectangular plates with certain kinds of simply supported edges and Kicher's work [4] on antisymmetric cross-ply elliptic plates with certain kinds of clamped edges. Also, the work of [2] was recently extended by Turvey [5] to include the effect of a Winkler-Pasternak elastic foundation.…”