Optimal design of laminates orientation in a composite material by genetics algorithm and simulated annealing

Abstract

The present work sets out the evaluation of composite laminates through optimization objective functions. Genetic Algorithms (GA), as well as Simulated Annealing (SA), were performed to determine the optimal ply orientations of a fiber-reinforced polymer laminate for three given load cases: (1) in-plane loads, (2) combined moments, and (3) in-plane loads and combined moments. It searches the optimal orientation layup, which fulfills at the same time both the maximum strain criterion and the Tsai–Wu failure criterion. Construction of an objective function based on the strains and the stresses involves a minimization process to deformations and a maximization of the safety factor. For the first load case, the initial solution is [±45/0/90/±45]s, and the best solution is [(45/135)2/452]s. For the second load case, [–45/45/45/–45/0/90]s is the initial layup sequence, then, the best solution obtained is [(45/–45)2/452]s, where plies at 0° and 90° are not necessary even when axial loads are applied. For the third study case, the original layup sequence is [0/45/–45/45/0/90]s; meanwhile, the best solution calculated is [21/24/145/140/45/49]s. An interesting observation is that each pair of layers has a 5° gap. The simulations show that the qualitative results from the GA are better than the SA, but with a significantly higher computational cost. These computational tools are expected to be used as a reference guide for an optimal fiber configuration concerning the common orientations used when composite laminates are designed for a structural application.