Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling

Abstract This research focuses on the uncertainties propagation and their effects on reliability of polymeric nanocomposite (PNC) continuum structures, in the framework of the combined geometry and material optimization. Presented model considers material, structural and modeling uncertainties. The material model covers uncertainties at different length scales (from nano-, micro-, meso- to macro-scale) via a stochastic approach. It considers the length, waviness, agglomeration, orientation and dispersion (all as random variables) of Carbon Nano Tubes (CNTs) within the polymer matrix. To increase the computational efficiency, the expensive-to-evaluate stochastic multi-scale material model has been surrogated by a kriging metamodel. This metamodel-based probabilistic optimization has been adopted in order to find the optimum value of the CNT content as well as the optimum geometry of the component as the objective function while the implicit finite element based design constraint is approximated by the first order reliability method. Uncertain input parameters in our model are the CNT waviness, agglomeration, applied load and FE discretization. Illustrative examples are provided to demonstrate the effectiveness and applicability of the present approach.