Post-Buckling of Composite Panels with Isogrid Stiffeners

Abstract

The postbuckling behavior of isogrid stiffened panels is investigated by employing a flat triangular stiffened shell element. This element utilizes the Mindlin plate and Timoshenko beam theories to define the kinematics of the flat shell and the stiffeners of the element. The kinematics of the stiffeners are expressed in terms of those of Mindlin displacements and slopes such that the plane sections passing through the shell and beam sections remain coplanar after deformation. Because the stiffeners are treated as an integral part of the shell element, the influence of the presence of stiffeners during the mesh generation is readily avoided. In this study, this concept is effectively used to perform instability analysis of composite and isotropic panels supported by stiffeners whose configurations form an isogrid pattern. Particularly, the effect of varying shell thickness and eccentric location of stiffeners on the pre- and postbuckling responses of an isogrid stiffened spherical cap is investigated. I. Introduction RAME-STIFFENED panels are widely used in aircraft and aerospace vehicle construction in order to achieve significant weight and cost savings. The weight saving is a direct result of the ability to use thin skins and space the stiffeners farther apart. The reduction in the number of stiffeners that results from wider spacing also translates into lower manufacturing costs. The traditional design approach of stiffened panels is based on explicit design formulas, and they are limited to simple stiffener arrangements. For complex stiffener arrangements, such as an isogrid pattern, a finite element analysis is unavoidable. In a finite element analysis of stiffened shell structures, existing shell finite elements can be grouped as plate and shell elements for models with detailed discretization, conventional beam-shell finite element models, and stiffened shell element models. The accuracy of the finite element solution method depends upon the type and number of finite elements used to model the structural behavior. The solution process can be expensive if several such iterations are needed. The solutions of problems involving large deflections are iterative in nature by themselves, and this added iteration can make the solution economically unfeasible. The efficiency of the finite element solution depends on the nature of the problem and also the mesh size used to model the structure. An accurate finite element model of stiffened panels can be obtained by discretizing both the skin and the stiffeners with plate and shell finite elements. In the absence of repeated symmetry conditions, the finite element method becomes very demanding because of the extensive number of elements and the geometric nonlinearities inherent in the analysis. In such an analysis based on plate and shell elements and utilizing the symmetry conditions, Starnes et al. 1 employed a finite-element-method-based program, STAGS (Structural Analysis of General Shells), along with an energy-based program, PASCO (Panel Analysis and Sizing Code), for buckling and postbuckling analysis of stiffened flat laminates under compressive edge loading. In their analysis, an eight-noded quadrilateral plate element was used to discretize both the panel and part of the stiffeners (i.e., webs and flanges), and a beam element was used to model the stiffeners. Using STAGS with plate and shell elements, Knight and Starnes 2 examined the postbuckling response of a curved stiffened panel by tracing the stable and unstable equilibrium paths of the curved panel under axial edge loading. Sobel and Sharp 3 investigated the postbuckling response of stiffened