A hierarchical genetic algorithm for reliability based design of geometrically non-linear composite structures

Abstract A design optimisation methodology based on structural reliability of beam reinforced composite shell structures with non-linear geometric behaviour is proposed. The formulation involves probabilistic stress, displacement and buckling constraints. The structural integrity is evaluated through the reliability index using a Lind–Hasofer second-order-second-moment approximation method together with the Newton–Raphson iterative procedure and the arc-length method. The random variables are the mechanical properties of the laminates treated as homogeneous orthotropic materials. A new methodology based on an evolutionary strategy searching the global most probable failure point (MPP) for composite structures under non-linear geometric behaviour is proposed. The optimal design performs on a hierarchical genetic algorithm (HGA) based on weight minimisation under prescribed reliability constraints. The design variables are the ply angle, the ply thickness and the geometric variables associated with the cross sections of the stiffeners. To demonstrate the applicability of the proposed developments, optimisation problems are presented.