Alternate Hybrid-Stress Elements for Analysis of Multilayer Composite Plates

Abstract

Two quadrilateral-shaped multilayer plate bending/stretching elements based on the assumed-stress hybrid finite-element model are presented. These elements may be applied to the analysis of fiber composite plates and shells composed of an arbitrary number of layers and arbitrary mate rial properties and fiber direction within each layer. Both elements incor porate the effects of transverse shear by including the transverse shear stresses τ xz and τyz, and by assuming independent rotations of the normals to the plate midsurface, so that normals to the midsurface in the un deformed state need not be normal to the midsurface after deformation. In the formulation of an element based on the assumed-stress hybrid model, the stress distribution in the interior of the element is expressed in terms of a finite number of stress parameters such that equilibrium is satisfied, and the displacement distribution on the boundary of the element is expressed in terms of generalized nodal displacements such that interelement displacement compatibility is maintained. The principle difference between the two elements presented is the level of approxima tion incorporated into the stress and displacement assumptions. For one element the stresses within each layer are related to a set of stress param eters within that layer, and the boundary displacement assumption allows for independent cross-sectional rotations within each layer (and is thus capable of modeling the severe cross-sectional warping often associated with thick laminated plates). For the other element, the stresses within each layer are related to a set of stress parameters associated with the entire laminate, and the boundarv displacement assumption allows for a uniform rotation of the cross section of the laminate (not necessarily normal to the plate midsurface). To assess the behavior of the two elements, two laminated composite plate example problems are considered, for which analytic solutions are available. The accuracy of predicted stress and displacement results obtained by using the two hybrid elements are compared with the exact solutions for cases involving both thick and moderately thick plates. Com parisons of the relative accuracy and computing efficiency of the two elements are presented, and the limitations on the use of each element are also discussed.