Static and vibration analyses of general wing structures using equivalent-plate models

An efficient method, using an equivalent-plate model, is developed for studying the static and vibration analyses of general built-up wing structures composed of skins, spars, and ribs. The model includes the transverse shear effects by treating the built-up wing as a plate following the Reissner-Mindlin theory, the so-called first-order shear deformation theory. The Ritz method is used with the Legendre polynomials being employed as the trial functions. This is in contrast to previous equivalent-plate-model methods, which have used simple polynomials, known to be prone to numerical ill-conditioning, as the trial functions. The present developments are evaluated by comparing the results with those obtained using MSC/NASTRAN, for a set of examples. These examples are 1) free-vibration analysis of a clamped trapezoidal plate with a) uniform thickness and b) nonuniform thickness varying as an airfoil, 2) free-vibration and static analyses (including skin stress distribution) of a general built-up wing, and 3) free-vibration and static analyses of a swept-back box wing. The results obtained by the present equivalent-plate model are in good agreement with those obtained by the finite element method.