An efficient online successive reanalysis method for dynamic topology optimization

In this study, an efficient reanalysis strategy for dynamic topology optimization is proposed. Compared with other related studies, an online successive dynamic reanalysis method and a Proper Orthogonal Decomposition (POD)-based approximate dynamic displacement strategy are integrated. In the dynamic reanalysis, the storage of the stiffness matrix decomposition can be avoided, and the reduced basis vectors should be successively updated according to the structural state in each iteration. Thus, the bottleneck of the combined approximation method for large-scale dynamic topology optimization can be overcome. Sequentially, POD is applied to obtain the approximate dynamic displacement, in which the Proper Orthogonal Mode (POM) of the displacement field is applied to obtain the approximate equivalent static loads of the Equivalent Static Load (ESL) method. Compared to the exact equivalent static loads at all the time intervals, the number of equivalent static loads is significantly reduced. Finally, the 2D and 3D test results indicate that the proposed method has remarkable speed-up effect under the premise of small relative error, support the strength of the proposed strategy.