A COPULA-FUNCTION-BASED MODEL FOR THE RELIABILITY ANALYSIS OF COMPOSITE STRUCTURES

The failure probability (FP) function, aiming to decouple the nested-loop reliability based design optimization (RBDO) into a single-loop optimization problem, is proposed. The FP function is defined as a failure probability function with respect to the design variables of the random inputs, which can be used to decouple the nested-loop reliability-based design optimization solution into a single-loop optimization problem. In the proposed approach, using the Bayes theorem and copula, a FP function estimation is established for laminated composite structures. The FP function is defined as a product of the conditional copula density and the augmented failure probability, in which the vine copula is employed to decompose the multidimensional conditional copula density into several bivariate copula density functions, and they can be completed by the existing PDF estimation methods.