MATHEMATICAL ENGINEERING TECHNICAL REPORTS An Implicit Formulation of Robust Structural Optimization under Load Uncertainties

This paper discusses an implicit reformulation of the MPEC (mathematical program with complementarity constraints) problem in order to solve a robust structural optimization with a non-probabilistic uncertainty model of the static load. We first show the relation among the robust constraint satisfaction, worst scenario detection, and robust structural optimization, and derive the MPEC formulation of the robust structural optimization. Since MPEC does not satisfy a standard constraint qualification, we propose a reformulation based on the smoothed Fischer–Burmeister function, in which the smoothing parameter is treated as an independent variable. Numerical examples of robust truss design are presented in order to demonstrate that the presented formulation can be solved by using a standard nonlinear programming approach without any difficulty.