Concurrent Topology Optimization of Multi-Scale Composite Structures Subjected to Dynamic Loads in the Time Domain

Abstract

This paper presents a concurrent topology optimization of multi-scale composite structures subjected to general time-dependent loads for minimizing dynamic compliance. A three-field density-based method is adopted to implement the concurrent topological design, with macroscopic effective properties of the microstructure evaluated through energy-based homogenization method (EBHM). Transient response is obtained from the two-scale finite element analysis with the HHT-α approach as an implicit time integration procedure. Design sensitivities are formulated employing the adjoint variable method (AVM) based on two main philosophies: “discretize-then-differentiate” and “differentiate-then-discretize” approaches, respectively. The method of moving asymptotes is adopted to update the design variables at two scales. Several benchmark examples are presented to demonstrate that the “discretize-then-differentiate” AVM attains consistent sensitivities in an inherent manner such that the resulting optimal topology is more efficient when compared with the “differentiate-then-discretize” AVM. Moreover, the potential of the proposed method for concurrent dynamic topology optimization problems under general time-dependent loads is also highlighted.