Robust topology optimization of continuum structures using Monte Carlo method and Kriging models

The aim of this paper is to introduce an efficient and accurate new approach called Monte Carlo and Kriging (MCK) to robust topology optimization. The objective is to minimize the expected value of ''compliance'' under concentrated loading uncertainty. The loading uncertainty may occur in magnitude, direction and/or position. The Monte Carlo simulation method and Kriging model are used to evaluate the objective function. To evaluate the expected value of ''compliance'' the probabilistic problem is transformed into a multiple loading deterministic one using of Monte Carlo method but with a reduced evaluations number of simulation model. A small sample obtained with a Latin Hypercube is used to build a Kriging model of the simulation model. This is utilized to estimate the ''compliance'' in those points used by Monte Carlo simulation method. Two problems are solved to demonstrate the efficiency and accuracy of the approach. The examples are solved again using a standard Monte Carlo simulation to check the proposed approach.