Hierarchical optimization for topology design of multi-material compliant mechanisms

Multi-material topology optimization enables potential design possibilities in the multiphysics and structural designing fields. In this article, a bi-level hierarchical optimization method is introduced to address the multi-material design of compliant mechanisms. The hierarchical optimization develops decomposition approaches allowing the original complex multi-material optimization problem to be reduced to set of low-order single-material optimization sub-problems. The solution of the complex multi-material problem is found as a vector of the single-material sub-problems solutions. All the local sub-problems are solved with the solid isotropic material with penalization method independently, and a stiffness spreading technique is worked out to coordinate components of the global solution of the original problem. Several numerical examples are presented to demonstrate the validity of this method.