Keywords: ant colony, multi-objective optimization, dispersed, laminates, biaxial, failure constraints.

The development of the manufacturing and moulding technology for laminated composites, automated tape laying and automated fibre placement machines, are capable nowadays of building laminates with orientation angles different from the conventional ones (0, ±45, 90°) in an easy and reliable way and replacing what is commonly called `black aluminium'. Such laminates, with non-conventional orientations, may lead to a better response.

The possibility of tailoring the stiffness and strength of the laminated composite materials to meet certain application requirements is directly related to optimization. Metaheuristic optimization methods are used because of their capacity to search the whole feasible space, (thus avoiding local optimum convergence), and the capability of dealing with discontinuous problems. The ant colony algorithm is selected to conduct the current work based on the published comparisons, [1] between the ant colony and the other metaheuristic optimization methods.

The idea of using two pheromone systems, working in parallel for the same problem was introduced by Solnon [2] to optimize a car sequencing problem.

The current paper shows the benefits of using orientations ranging from -90° to 90° with a 5° jump for the optimization of 48-layer symmetric and balanced laminated panels based on a two pheromone system ant colony optimization. The first pheromone system is responsible for the selection of the design variables, e.g. the orientation of the plies and the other pheromone system is responsible of the distribution of these orientations inside the laminate.

Two loading conditions are studied, the biaxial compression and the biaxial tension. The biaxial compression loading case is designed to maximize the buckling load such that the maximum value of the failure index can not exceed 1.0. The LaRC03 failure criteria are used to assess the failure. Results show that dispersed laminates can improve the critical buckling load by up to 8%.

The biaxial tensile loading case is solved using two different formulations. The first formulation minimizes the matrix cracking failure index. Results show that the failure index can be decreased by 20% to 100%, with respect to the loading ratio. Since the fiber tension failure index is also important, the second formulation minimizes both the matrix cracking and the fiber tensile failure indices in a multi-objective form. Results show that the fiber tensile failure index can be decreased by more than 40% with this formulation. With respect to both formulations the same constraints are used as in the biaxial compression case.

1

M.W. Bloomfield, J. Enrique Herencia, P.M. Weaver, "Analysis and benchmarking of meta-heuristic techniques for lay-up optimization", Computers and Structures, 88, 272-282, 2010. doi:10.1016/j.compstruc.2009.10.007

2

C. Solnon, "Combining two pheromone structures for solving the car sequencing problem with Ant Colony Optimization", European Journal of Operational Research, 191, 1043-1055, 2008. doi:10.1016/j.ejor.2007.04.037

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