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Multi-Objective Optimization for Coupled Mechanics-Dynamics Analyses of Composite Structures



Fiber reinforced composites are increasingly used in advanced applications due to advantageous qualities including high strength-to-weight ratio. The ability to tailor composite structures to meet specific performance criteria is particularly desirable. In practice designs must often balance multiple objectives with conflicting behavior. Objectives of this work were to optimize lamina orientations of a three-ply carbon fiber reinforced composite structure for the coupled solid mechanics and dynamics considerations of minimizing max principal stress while maximizing fundamental frequency. Two approaches were investigated: Pareto set optimization (PSO), and multi-objective genetic algorithm (MOGA). In PSO, a single objective function is constructed as a weighted sum of multiple objective terms. Multiple weighting sets are evaluated to determine a Pareto set of solutions. MOGA mimics evolutionary principles, where the best design points populate subsequent generations. Instead of weight factors, MOGA uses a domination count that ranks population members. Results showed both methods converged to solutions along the same Pareto front. The PSO method calculated fewer function evaluations, but provided many fewer final data points. At a certain threshold, MOGA provides more solutions with fewer calculations. The PSO method requires more user intervention which may introduce bias, but can largely be run in parallel. In contrast, MOGA generation are evaluated in series. The Pareto front showed the trend of increasing frequency with increasing stress. At the low stress and frequency extreme, the stacking sequence tended toward (45°/90°/45°) with max principal stress located in the inner ply in the hoop direction. At high stress and frequency, the stacking sequences (90°/*/90°) indicated that the middle ply orientation was less significant. A mesh convergence study and dynamic validation experiments gave confidence to the computational model. Future work will include an uncertainty quantification about selected solutions. The final selected solution will be fabricated and experimental validation testing will be conducted.


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