Abstract
We propose a new method for laminate stacking sequence optimization based on a two-level approximation and genetic algorithm (GA), and establish an optimization model including continuous size variables (thicknesses of plies) and discrete variables (0/1 variables that represent the existence of each ply). To solve this problem, a first-level approximate problem is constructed using the branched multipoint approximate (BMA) function. Since mixed-variables are involved in the first-level approximate problem, a new optimization strategy is introduced. The discrete variables are optimized through the GA. When calculating the fitness of each member in the population of GA, a second-level approximate problem that can be solved by the dual method is established to obtain the optimal thicknesses corresponding to the each given ply orientation sequence. The two-level approximation genetic algorithm optimization is performed starting from a ground laminate structure, which could include relatively arbitrarily discrete set of angles. The method is first applied to cylindrical laminate design examples to demonstrate its efficiency and accuracy compared with known methods. The capacity of the optimization strategy to solve more complex problems is then demonstrated using a design example. With the presented method, the stacking sequence in analytical tools can be directly taken as design variables and no intermediate variables need be adopted.
Highlights
Because of their high strength-to-weight and high stiffnessto-weight ratios, composite materials have been widely used in structures in the aerospace industry over recent decades
An efficient stacking sequence optimization strategy for composite structures is presented in this paper
This strategy is based on a two-level multi-point approximation and genetic algorithm (GA)
Summary
Because of their high strength-to-weight and high stiffnessto-weight ratios, composite materials have been widely used in structures in the aerospace industry over recent decades. Laminated composite materials are usually fabricated from unidirectional plies of a given thickness with fiber orientations limited to a small set of angles, for example 0◦, +45◦, −45◦ and 90◦ Designing such laminates for various strength and stiffness requirements involves an integerprogramming problem for selecting the best number of plies of each orientation, and determining an optimal stacking sequence. One major shortcoming of GAs is their high computational cost for the large number of objective and constraint evaluations For this reason, several modifications to GAs have been proposed, such as parallel computing (Henderson 1994; Punch et al 1994; Kere and Lento 2005), multi-level optimization (Punch et al 1994), approximation methods for function evaluation (Liu et al 1998; Gantovnik et al 2002; Todoroki and Ishikawa 2004), as well as a combination of these methods (Park et al 2008). The new method is applied to weight minimization problems of a composite cylinder and a composite cone-cylinder, for which the computational cost is demonstrated at the level of optimization calculations with only continuous variables
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