Structure Dynamic Response Optimization under Equivalent Static Loads of Each Node Based on Mode Superposition

According to the complexity of the transient dynamic analysis and the uncertainty of equivalent static load, the equivalent static load method（ESLM） of each node based on mode superposition was put forward, which was applied to the dynamics response optimization. Firstly, the relationship between the dynamic response and each mode was analyzed based on the principle of mode superposition. Then, the principle of equivalent static load method was analyzed in detail, and the calculation formula of equivalent static load（ESL） of each node using modal response was determined. Lastly, ESLM of each node in the critical point set was proposed, and the time critical points were obtained by using the spectral element discrete interpolation and the differential is equal to zero, which the critical time point sets are composed of the adjacent GLL（Gauss-Lobatto-Legendre） points. The dynamic response size optimization of 124 bar truss structures and the hybrid size and shape optimization of 18 bar truss structures were used to show the feasibility and effectiveness of the proposed method.