Dynamic concurrent topology optimization and design for layer-wise graded structures

Abstract

There are many requirements in engineering fields to improve the structural performance. Thus, the hierarchical structures have attracted lots of attention because of the appealing material efficiency and functionality, e.g., the bearing capacity and interfacial strength from large aerospace structures to small device facilities. However, the dynamic topology optimization design of these structures composed of multiple microstructures remains challenge by the connectivity issue between different microstructures and the extensive computational cost when handling the interval-frequency problem during multiscale concurrent design. In this work, the connectivity model is proposed for improving the manufacturability of hierarchical structure, which includes the connectable layer scheme between different microstructures and the enlarged filter domain. To break the bottleneck of computation cost induced by the simultaneous optimization of macro-microscopic design variables, the combined method of modal superposition and model order reduction is incorporated to efficiently compute the frequency response. Two response vectors are presupposed before decoupling sensitivity analysis. In addition, in order to implicitly ensure the bearing capacity of the structure, the stiffness maximization design is integrated into the response minimization problem when the frequency interval range is high. The layer-wise graded cantilever beam is used as an example to demonstrate the effectiveness and accuracy of proposed method in handling dynamic concurrent topology optimization problem. The manufacturability and systematic performance of hierarchical structures are significantly improved when they simultaneously experience the interval-frequency harmonic and static loads.