Structural optimization under uncertainties considering reduced-order modeling

This paper focus on the development of a optimization tool in which uncertainties are taken into account to obtain robust and reliable designs. The robustness measures considered here are the expected value and standard deviation of the function involved in the optimization problem. To calculate such quantities, we employ two non-intrusives uncertainty propagation analysis techniques that exploit deterministic computer models: Monte Carlo (MC) method and Probabilistic Collocation Method (PCM). When using these robustness measures combined, the search of optimal design appears as a robust multiobjective optimization (RMO) problem. Reliable design address uncertainties to restrict the probability of failure of structures. These are computed through reliability analysis techniques which are here computed by both MC and FORM methods. The insertion of reliability constraints into the RMO problem formulation turns the formulation for the robust and reliability design optimization (RDO) problem. As both, statistics calculations and the reliability analysis could be very costly, especially when using the MC method, approximation techniques based on reduced-order modeling (ROM) approach are also incorporated in our procedure via proper orthogonal decomposition (POD) method. For fast outputs considering structural nonlinear behavior. Optimization studies will be conducted for trusses problems considering different loads level, exploring the material plasticity.