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

At the preliminary design stage of wing structures, though highly desirable for its high accuracy, a detailed finite element analysis is often not feasible. This is because of the high cost of preparing a large number of finite element models. Moreover, the detailed structural layout is still being finalized. Often equivalent beam models are used at this stage. However, for wings with low aspect ratio, the use of equivalent beam models, as opposed to using an equivalent plate model, is questionable. An efficient method, using equivalent plate model, is developed in this paper for studying the static and vibration analysis of general 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 (FSDT). Previous studies have shown the need for including the transverse shear effect, especially in the analysis of a class of wings. The Ritz method is used. The Legendre polynomials are employed as the trial functions. This is in contrast to previous equivalent plate model methods, which have simple polynomials, known to be prone to numerical ill-conditioning problems, 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: (i) free-vibration analysis of a clamped trapezoidal plate with (a) uniform thickness, and (b) non-uniform thickness varying as an airfoil, (ii)free-vibration and static analysis (including skin stress distribution) of a general wing, and (iii)free-vibration and static analysis of a swept-back box wing. The results obtained by the present equivalent plate model are found to be in good agreement with those obtained by the finite element method.