Risk averse stochastic structural topology optimization

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.