A RBRDO approach based on structural robustness and imposed reliability level

A new approach for the multi-objective optimization of composite structures under the effects of uncertainty in mechanical properties, structural parameters and external loads is proposed, to guarantee higher levels of accuracy exclusively with Evolutionary Algorithms (EA). The concepts of Reliability-Based Robust Design Optimization (RBRDO) are applied. Optimality is defined as the minimization of the structural weight and robustness as the minimization of the determinant of the variance-covariance matrix of the structural responses. Reliability assessment is performed through a mathematical reformulation of the Performance Measure Approach, suitable for EA, where the standard normal uncertainty space was defined in directional coordinates and reduced to the surface of the hypersphere of radius β^a. A binary reliability constraint, that allowed avoiding unnecessary runs of the reliability inner-cycle is defined. The Robust Design Optimization cycle is solved by a multi-objective EA, based on constrained-dominance. Sensitivities of the structural responses, necessary for uncertainty analysis only, are calculated analytically by the Adjoint Variable Method. A numerical example considering a balanced angle-ply laminate shell is presented. Results show an effective convergence of the Pareto-optimal Front (POF). Uncertainty analysis shows that the variability of the critical displacements increases along the POF. For the stresses, variability is stable but of higher values. The incorporation of the reliability constraint prevents the natural decrease of the reliability index, along the POF, to reach levels too close, or inside, of the failure domain. The distribution of the reliability measures along the POF is similar and demonstrates the effects of reliability in the RBRDO procedure.