基于改进准则法的复合壳阻尼结构拓扑减振动力学优化

针对复合壳阻尼结构的拓扑减振优化问题，以约束阻尼层的有限单元为设计变量，采用体积比、模态频率和振型为优化约束条件，构建以多模态权重系数的结构模态损耗因子数值关系为优化目标函数的拓扑减振优化模型。为了拓展优化目标灵敏度具有不局限于某一变密度法插值模型的形式，推导了数值表达式的一般函数式。动力学优化中优化目标灵敏度正、负数集共存，使得非凸性的目标函数设计变量出现负值或优化函数寻优于局部极值点。为此，推导出复合壳阻尼结构的全域灵敏度改进优化准则法迭代格，以确保每次迭代域均为全域设计变量集。结合有限单元法编程实现了复合壳阻尼结构改进准则法，并对复合壳结构进行拓扑减振优化分析。结果表明：在敷设体积减为全覆盖的50%时，复合壳结构的模态损耗因子增减偏差为10%，具有提升减振的轻量化设计目的；各阶目标函数和拓扑构型所需的迭代次数少，中间密度区域较小，多阶优于单阶模态优化函数，易于获得全域寻优的有效减振。

Topology optimization of composite shell damping structures based on improved optimal criteria method

Aiming at the damped composite shell structure in topology vibration reduction optimization, a topology vibration reduction optimization model is constructed by taking the finite element of the damped layer as the design variable and the volume ratio, modal frequency and mode shape as the optimization constraintshe model of the structure modal loss factor is designed with the multi-modal weight coefficient as the optimization objective function. The form of the interpolation model limit to a variable density method, the general function of the sensitivity of the optimized objective is derived. Due to existence of the positive and negative sets of this sensitivity, the design variables of the non-convex objective function has negative values or optimal solution of this optimization function is the local extremum. With the improved global sensitivity optimization criterion, the iteration method for composite shell damping structures is derived, ensur that each iteration is a set of global design variables. Based on the finite element method, the improved criterion programming is written, and the optimal analysis of topological vibration reduction is carried out on the damped composite shell structure. The results indicate that hen the volume of constrained damping layer is reduced to 50% of the total coverage, the mode loss factor of the shell structure is increased or decreased by 10%, which has the purpose of lightweight design to improve the vibration reduction The number of iterations required by each order objective function and topology configuration is small, the middle density area is smaller, and the multi-order is better than the single-order modal optimization function, which is easy to obtain the effective vibration reduction of global optimization.