Mehmet A. Akgün

Permutation genetic algorithm for stacking sequence design of composite laminates

Abstract Stacking sequence design of a composite laminate with a given set of plies is a combinatorial problem of seeking an optimal permutation. Permutation genetic algorithms optimizing the stacking sequence of a composite laminate for maximum buckling load are studied. A new permutation GA named gene–rank GA is developed and compared with an existing Partially Mapped Permutation GA, originally developed for solving the travelling salesman problem. The two permutation GAs are also compared with a standard non-permutation GA. It is demonstrated through examples that the permutation GAs are more efficient for stacking sequence optimization than a standard GA. Repair strategies for standard GA and the two permutation GAs for dealing with constraints are also developed. It is shown that using repair can significantly reduce computation cost for both standard GA and permutation GA.

Composite wing structural optimization using genetic algorithms and response surfaces

A two level optimization procedure is proposed for wing design subject to strength and buckling constraints. At the upper level the design variables are the amounts of 0°, ±45°, and 90° material and the objective function is the weight. Continuous optimization is used. At the panel level, the number of plies of each orientation (rounded to integers) as well as the in-plane loads are specified and a genetic algorithm is used to optimize the stacking sequence so as to maximize the buckling load. The process is started by performing a large number of panel genetic optimizations for a range of loads and number of plies. Next a cubic polynomial response surface is fitted to the optimum buckling load as a function of the loads and number of plies. This response surface is then used at the wing level optimization in lieu of the lower level panel optimization. A simple wing example is used to demonstrate the effectiveness of the procedure. In the example, errors due to the response surface approximation, as well as due to rounding the number of plies prove to be minimal.

Post-Buckling of Composite I-Sections. Part 2: Experimental Validation:

An experimental investigation was conducted in order to verify the theoretical model described in Part 1 as well as to obtain experimental insight and to generate a database for the post-buckling behavior of composite I-sections. The experiments were performed using a combination of the shadow moiré technique, strain gages, LVDTs (linear variable differential transformer), and dial gages. A total of twenty carbon-fiber/epoxy I-section columns were manufactured and tested with seven specimens from woven fabric and thirteen from unidirectional (UD) tape. The initial buckling load, lateral deflection of the web and flange as well as the crippling load were measured. The experimental results were compared with those of the theoretical model described in Part 1. Agood agreement was observed.

SENSITIVITY OF STRESS CONSTRAINTS USING THE ADJOINT METHOD

Adjoint sensitivity calculation of stress and displacement functional may be much less expensive than direct sensitivity calculation when the number of load cases is large. However, efficient implementation is problem dependent and requires strategies for reducing the number of constraints used. The study shows that for truss and plane-stress elements it is easy to implement the adjoint method. Also an example demonstrates that even an extreme form of constraint lumping can work well in optimization of a wing structure allowing us to keep only a small number of constraints.