Abstract

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.

Abstract

In this paper a robust topology optimization algorithm for linear elastic structures in unilateral contact is presented. The deformation of the linear elastic structure is constrained by support structures that are modeled with the help of Signorini's contact conditions. The contact conditions in turn are enforced with the augmented Lagrangian approach. Doing so, the robust optimization considers uncertainties at the support such as manufacturing tolerances and its local friction behavior. Due to high numerical costs in robust optimization, the firstorder second-moment approach is used to approximate the mean and variance of the objective. This approximation results in minimal additional costs to approximate the mean, the variance and their gradients. Consequentially, a gradient-based optimization algorithm can be used to minimize a weighted sum of both. The results show that the presented approach indeed improves the robustness with respect to uncertain contact conditions compared to a deterministic optimization.