Stacking sequence optimization with genetic algorithm using a two-level approximation

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.

Improved Genetic Algorithm with Two-Level Approximation Method for Laminate Stacking Sequence Optimization by Considering Engineering Requirements

“…The basic principles of GATLA method will be briefly described in this section. For more details the reader could refer to the literature [18].…”

“…In a recent study, we have proposed a genetic algorithm using a two-level approximation (GATLA) [18] method for optimizing laminates stacking sequences. Essentially, this approach adopts an optimization strategy that the genetic algorithm is integrated within the sequential approximation optimization problems, without using any intermediate variables.…”

“…For practical engineering stacking sequence optimizations, more than two laminates need to be optimized simultaneously, as practical aerospace structural components usually comprise multiple panels and the stacking sequences of them can remarkably affect structural mechanical properties like strength and stiffness performances [5,19]. Even though the GATLA method has been deemed to be able to deal with the optimizations of multiple laminates in simple structures [18], it has not been extended to practical engineering optimizations with multiple laminates. Moreover, the standard GA used in the strategy has relatively high dependence on some genetic parameters, which brings the burden of determining control parameters to the designers or users.…”

Two-level layup optimization of composite laminate using lamination parameters

“…0 + 45 + −45 + 90 = (14) 0 − 90 = 1 (15) 0 − 45 − −45 + 90 = 2 (16) 45 − −45 = 3 (17) where the non-negative integers and represent the total number of plies and the number of plies with orientation , respectively. The minimum percentage constraint can be expressed as…”

“…In Almeida and Awruch's work [13] GAs were improved for optimizing a laminate's weight and deflection simultaneously. Chen et al [14] used GAs with a two-level approximation in which the first level approximation was used for optimizing stacking sequences, and the related ply thicknesses were obtained during the second level approximation.…”