Dimensional reduction of probability spaces via Sobol’ indices applied to composite laminates optimal design
Palavras-chave:
Sobol’ indices, importance analysis, reliability assessment, composites optimal designResumo
It is proposed the application of Sobol’ indices as importance measures for the dimensionality reduction of probability spaces, in probabilistic reliability assessment. The indices are computed approximately using a local approximation of the response functionals, via an adjoint method. As a numerical example, it is considered the Reliability-based Robust Design Optimization (RBRDO) of a composite shell structure. The problem is defined as the bi-objective minimization problem of the total weight and the determinant of the variance-covariance matrix of the structural response functionals, subject to a deterministic displacement constraint and a probabilistic stress constraint. The goal is to study how the dimensionality reduction in reliability assessment affects the RBRDO of
composite laminate structures. The results show that, from a total of 16 random mechanical properties, only 5 to 8 are important, while explaining at least 99.7% of the uncertainty. It is achieved a drastic reduction in computing times between 2 to 12 times faster, in reliability assessment, and 2 times faster in the overall RBDO of composite laminate structures.
