Optimization of Buckling and Yield Strengths of Laminated Composites

Abstract

Theme F laminates possess two important features highly desirable in aerospace structural applications. These are: 1) the high stiffness to weight ratio, and 2) the anisotropic property which can be tailored through the variation of fiber orientations and the stacking sequence. The latter feature provides the structural designer with an additional dimension in the constraint space that could lead to a substantial change in the design procedure. Furthermore, as a result of the additional variables, the structural optimization becomes an integral part of a good design work involving laminates of advanced composite materials. Under in-plane loads, a laminated plate can fail as a result of structural instability (buckling) or material yielding. In this report we are concerned with the optimum fiber orientation for a set of combined loadings. The laminates considered are the angle-ply laminates with symmetric layups. A direct search technique is employed to solve the optimization problems. Although the optimum fiber directions are determined independently according to the buckling and the strength constraints, the results can be easily placed in the respective regions where they are meaningful. The buckling loads for a plate depend on the geometry and size of the structure, while the strength criterion usually depends only on the state of stress at a point. It is conceivable that, for practical purposes, a marginal size for the laminated plate can be defined so that when the plate is larger than this size the laminate should be optimized according to the buckling criterion. For a plate size smaller than the marginal size, the strength criterion should be followed. This design procedure is discussed in some detail in this report.