A generalized approach for robust topology optimization using the first-order second-moment method for arbitrary response functions

The paper presents a rigorous formulation of adjoint systems to be solved for a robust design optimization using the first-order second-moment method. This formulation allows to apply the method for any objective function, which is demonstrated by considering deformation at certain point and maximum stress as objectives subjected to random material stiffness and geometry, respectively. The presented approach requires the solution of at most three additional adjoint systems per uncertain system response, when compared to the deterministic case. Hence, the number of adjoint systems to be solved is independent of the number of random variables. This comes at the expense of accuracy, since the objective functions are assumed to be linear with respect to random parameters. However, the application to two standard cases and the validation with Monte Carlo simulations show that the approach is still able to find robust designs.

Automated summary

The paper introduces a rigorous formulation of adjoint systems for robust design optimization. The presented approach allows for the optimization of any objective function by considering deformation and maximum stress as objectives subjected to random material stiffness and geometry. The method requires solving at most three additional adjoint systems per uncertain system response, regardless of the number of random variables. Despite the assumption of linearity with respect to random parameters, the approach is able to find robust designs according to the validation with Monte Carlo simulations.