An efficient decoupled sensitivity analysis method for multiscale concurrent topology optimization problems

The conventional coupled sensitivity analysis method for concurrent topology optimization problems is computationally expensive for microscale design variables. This study thus proposes an efficient decoupled sensitivity analysis method for concurrent topology optimization based on the chain differentiation rule. Two numerical studies are performed to demonstrate the effectiveness of the decoupled sensitivity analysis method for concurrent topology optimization problems with single or multiple porous materials. It can be concluded from the results that the decoupled method is computationally much more efficient than the coupled method, while they are mathematically equivalent. The outstanding merits of the decoupled method are two-fold: (1) computational efficiency of sensitivity analysis with respect to the microscale design variables; and (2) applicability to concurrent topology optimization problems with single or multiple porous materials as well as with composite microstructure and multi-phase materials.