Topology Optimization Under Uncertainty by Using the New Collocation Method

In this paper, a robust topology optimization method presents that insensitive to the uncertainty in geometry. Geometric uncertainty can be introduced in the manufacturing variability. This uncertainty can be modeled as a random field. A memory-less transformation of random fields used to random variation modeling. The Adaptive Sparse Grid Collocation (ASGC) method combined with the geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using the adaptive sparse grid method. The method is demonstrated in the design of a minimum compliance Messerschmitt-Bolkow-Blohm (MBB) and cantilever beam as benchmark problems.