面向所有节点等效静态载荷的模态叠加法的结构动态响应优化

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

针对瞬态动力学分析复杂性和等效静态载荷转化的不确定性,提出基于模态叠加的所有节点等效静态载荷法,并将其应用到动态响应优化.首先从模态叠加的原理出发,分析动态响应与各模态的关系;然后根据等效静态载荷法的原理给出利用模态响应的所有节点等效静态载荷的计算表达式;最后提出关键时间点集的所有节点等效静态载荷方法,采用谱元离散插值且微分获得了时间关键点,并与邻近的GLL(Gauss-Lobatto-Legendre)点组成关键时间点集.应用文中方法对124杆桁架结构进行动态响应尺寸优化和18杆桁架结构进行尺寸与形状混合优化设计的结果表明,该方法是可行和有效的.

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 of124bar truss structures and the hybrid size and shape optimization of18bar truss structures were used to show the feasibility and effectiveness of the proposed method.