Robust topology optimization of structures under loading uncertainty

A new efficient and accurate approach to robust structural topology optimization is developed in this work. The objective is to minimize the expected compliance of structures under loading uncertainty. The new approach is akin to a deterministic multiple load case problem where the load cases and weights are derived by numerical methods. Efficient and accurate methods to compute expected compliance and its derivatives are developed for both concentrated and distributed uncertain loads. The Monte Carlo method and matrix decomposition are employed for concentrated loads, and the Karhunen-Loeve expansion and its orthogonal properties of random variables are used for distributed loads. Numerical examples using the modified solid isotropic material with penalization approach are provided to demonstrate the accuracy and efficiency of the proposed approach.