Reliability-based design optimization and uncertainty quantification for optimal conditions of composite structures with non-linear behavior

An approach to reliability-based design (RBDO) of beam reinforced composite structures with non-linear geometric behavior is proposed. A unified approach following both buckling and first-ply failure (FPF) is used to verify the integrity of beam reinforced shallow shell laminated structures. A new RBDO methodology using a genetic algorithm and a hierarchical decomposition searches the global most probable failure point (MPP). For the reliability analysis, the random parameters are the mechanical properties of laminates. Simultaneously the optimal design based on weight minimization under prescribed reliability and buckling constraints is searched through this hierarchical genetic algorithm (HGA). The design variables are the ply angle, the ply thickness, the height and the width of the cross sections of the stiffeners. Numerical results show the capabilities of the proposed approach using the MPP search inner loop integrated in a HGA scheme. Based on a sensitivity methodology the uncertainty for the optimal solution obtained from HGA is analyzed. In the neighborhood of critical buckling values of the structural response the asymptotic behavior of uncertainty propagation is observed. The influence of uncertainties from random parameters and design variables are studied on critical load factor and critical displacement. The variability of these structural response functions are measured by their coefficients of variation and Sobol indices. The most important influences for uncertainty propagation are obtained from ply angle of shell laminates and from longitudinal elastic modulus group.