section characteristics with accuracy one order higher than that indicated by the nonlinear Prandtl lifting-line theory. Any kind of mechanical high lift devices can be included in the analysis without theoretical difficulty.
IntroductionM EMBRANE quadrilateral finite elements having a partially linearj strain field have been shown 1 to be superior to the constant strain triangular element 2 for planar problems. Thus, to achieve the same accuracy, many more degrees of freedom are needed when a planar membrane structure is modeled with constant strain triangular elements than when it is modeled with quadrilateral elements.Membrane elements are often used in conjunction with shear web elements to model built-up wing structures 3 ; the wing skin is modeled by membrane elements and the ribs and spars by shear web elements. Because the surface of a wing is, in general, not planar, it is usually not feasible to divide the wing skin into Received October 19, 1972. Index category: Structural Static Analysis. * NRC-NASA Resident Research Associate. t Aerospace Engineer, Design Studies Section, Structures Division. J Without introducing midside nodes it is impossible to have a general linear strain field, so different formulations are based on different assumed strain fields.Fig. 1 Configuration definition.-SHEAR FINITE ELEMENTS a quadrilateral mesh such that the four vertices of each quadrilateral are in the same plane. No such problem exists with a triangular mesh because three points are always in a plane. When the quadrilaterals are small, and the four points are "almost" on the same plane, it is tempting to use quadrilaterals, which are more accurate for planar problems. This Note examines the effect of using plane quadrilateral membrane elements to model nonplanar structures. The effect was assessed by analyzing a simplified finite element model with the SNAP program. 4 -5 A particular linear-strain quadrilateral element formulation was selected to obtain most of the results, but two other such elements were tested to determine the extent of element-dependence of the results. In addition to the linear strain element results, calculations were made using the quadrilateral membrane element in NASTRAN 6 which is built up of constant strain triangles.
Problem DefinitionThe structure analyzed in this study is shown in Fig. 1. It is composed of a quadrilateral element, defined by nodes 5,6, 7, and 8, which is clamped along the side 5-8 and supported by shear webs along the other three sides. Nodes 5, 6, and 8 are in a plane parallel to the X-Y plane and point 7 is out of this plane by an amount A/z. The structure is loaded in the X direction at point 6. The shear webs are constrained to zero X, Y motion at points 1, 2, 3, 4 which are in the X-Y plane and which form a square. The Z displacements of these four points are constrained to be equal to those of the respective upper points. The model simulates a small part of a built-up wing having a symmetric profile and undergoing pure bending with no stretching of its midplane....
