Robust design optimization with design-dependent random input variables

This paper addresses the dependency of design parameters and random variables within robust design optimization. If the stochastic distributions of random input variables are design-dependent, then this dependency must be included in the gradient, when using gradient-based optimization methods. The paper provides the basic theoretical principles and two approaches for incorporating design-dependent distributions of random variables in robust design optimization: one approach based on Monte Carlo sampling and another based on Taylor series expansions. Both these approaches do not require additional structural analyses (e.g., finite element simulations). Describing the design dependency of input distributions can, however, be a challenging task. Numerical applications to different academic examples are presented, demonstrating the potential of the proposed approaches and several implications that may emerge in the process.