# Dimensional reduction of probability spaces via Sobol’ indices applied to composite laminates optimal design

## Palavras-chave:

Sobol’ indices, importance analysis, reliability assessment, composites optimal design## Resumo

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.