Risk averse stochastic structural topology optimization

A novel approach for risk-averse structural topology optimization under uncertainties is presented, which takes into account stochastic data of the state equation, specifically random material properties and random forces. For the distribution of material, a phase field approach is employed, which allows for arbitrary topological changes during the iterative optimization. The state equation is assumed to be a high-dimensional PDE parametrized in a (truncated finite) set of random variables. The examined case employs linearized elasticity with a parametric elasticity tensor. For practical purposes, instead of an optimization with respect to the expectation of the involved random fields, the designed structures should in particular be robust with respect to rather unlikely and possibly critical events. For this, as a common risk measure, the Conditional Value at Risk (CVaR), is introduced to the cost functional of the minimization procedure. The proposed method is illustrated with numerical examples based on Monte Carlo sampling for different risk values and compared with the result of the deterministic formulation. It is observed that the resulting shapes dependent on the risk parameter of the functional and can deviate significantly from the deterministic case. (C) 2018 Elsevier B.V. All rights reserved.