Minimum Weight Design of Symmetric Angle-Ply Laminates With Incomplete Information on Initial Imperfections

Abstract

An angle-ply laminated plate is optimized with the objective of minimizing its weight subject to maximum deflection and buckling constraints. The plate has an initial deflection the shape of which is not known a priori, i.e., the initial deflection is not specified in a “deterministic” manner and as such it is “uncertain.” The weight is proportional to the laminate thickness which is minimized taking the ply angles as design variables and under the least favorable conditions of initial imperfections. The convex modeling approach is employed to analyze the uncertain initial deflection with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirement that these variations are bounded in L 2 norm. The results are given for both single load and multiple load cases and the effect of uncertainty on the optimal design is investigated. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.