Ply number rounding-off in optimization of composite structures using lamination parameters

Abstract

A bi-level optimization strategy for finding the optimal ply numbers and stacking sequence in composite structures has become one of the most popular techniques in recent years. When the optimization technique is based on the use of lamination parameters, the top level optimization has two subsets of design variables for each substructure (e.g., a panel in wing design): lamination parameters treated as continuous design variables, and three integers that define the number of plies of 0, 90 and ±45 degree orientation. When a continuous optimizer is used, there is a need for an algorithm to perform a rounding-off of obtained continuous representation of the number of plies to an integer value that, ideally, does not alter the mechanical performance of a panel. In this paper three schemes based on the lamination parameter matching are introduced to determine the integer values of the ply numbers. The strategy is to use a binary code controlling the ply number rounding-off in order to obtain a discrete number of plies of each orientation per composite panel. An optimization problem is formulated where the objective function (to be minimized) defines how close the lamination parameter values and the panel thickness, obtained in the top level optimization, are to their values when integer ply numbers are considered. Such an optimization problem is solved by a permutation GA for each individual panel. A wing box benchmark problem is used to demonstrate the potential of these methods.