Semi-intrusive approach for stiffness and strength topology optimization under uncertainty

A semi-intrusive approach for robust design optimization is presented. The stochastic moments of the objective function and constraints are estimated using a Taylor series-based approach, which requires derivatives with respect to design variables, random variables as well as mixed derivatives. The required derivatives with respect to design variables are determined using the intrusive adjoint method available in commercial software. The partial derivatives with respect to random parameters as well as the mixed second derivatives are approximated non-intrusively using finite differences. The presented approach provides a semi-intrusive procedure for robust design optimization at reasonable computational cost while allowing an arbitrary choice of random parameters. The approach is implemented as an add-on for commercial software. The method and its limitations are demonstrated by academic test cases and industrial applications.