On the orthogonal similarity transformation (OST)-based sensitivity analysis method for robust topology optimization under loading uncertainty: a mathematical proof and its extension

The main purpose of this work is to provide a mathematical proof of our previously proposed orthogonal similarity transformation (OST)-based sensitivity analysis method (Zhao et al. Struct Multidisc Optim 50(3):517–522 2014a, Comput Methods Appl Mech Engrg 273:204–218 c); the proof is designed to show the method’s computational effectiveness. Theoretical study of computational efficiency for both robust topology optimization and robust concurrent topology optimization problems shows the necessity of the OST-based sensitivity analysis method for practical problems. Numerical studies were conducted to demonstrate the computational accuracy of the OST-based sensitivity analysis method and its efficiency over the conventional method. The research leads us to conclude that the OST-based sensitivity analysis method can bring considerable computational savings when used for large-scale robust topology optimization problems, as well as robust concurrent topology optimization problems.