Probabilistic multi-scale optimization of hybrid laminated composites

This study presents a hierarchical multi-objective optimization over multiple scales of hybrid laminated composites. The fine-scale optimization problem is treated as a meso-level single-ply representative volume element (RVE) problem or lamina wherein the weave pattern is embedded in a matrix pocket. The weave pattern is the design variable of the first task considering the stochastic effects under uncertainties wherein four uncertain mesoscopic parameters are investigated: yarn spacing, yarn width, yarn height and misalignment in yarn angle. The fine-scale objective functions are to maximize the macroscopic elastic properties of single-ply RVE with periodic boundary conditions and optimize the pattern arrangement using evolutionary algorithm. The fine-scale optimization problem is done for a selected set of uncertainties by utilizing Latin Hypercube Sampling. The coarse-scale optimization problem is presented as the stacking sequence optimization of hybrid fiber-reinforced composite plate with two nonlinear objectives and two design constraints. The coarse-scale optimization goals are to minimize the cost and weight of the laminated plate with constraint on the first fundamental frequency and the buckling load factor. A multi-ply-ed, fiber reinforced and hybrid laminated composites are reconsidered with respect to the optimized macroscopic elastic properties of single-ply RVE in the fine-scale optimization problem. The investigated single-ply RVE is made of alumina oxide-aluminum (Al₂O₃-Al) and silicon carbide-aluminum (SiC-Al) plies to combine the toughness and economical attributes. Ant colony optimization (ACO) is utilized to formulate the Pareto-optimal solutions by optimizing a convex combination of the two nonlinear objectives, weight (W) and cost (C) based on a series of multiplier values (α). Simultaneously, the latter task could be simplified into a single-objective optimizer by employing the concept of weighted sum method. Conclusively, the best hybrid laminated composites based on the series of multiplier values are presented in the coarse-scale optimization problem.