基于参数化水平集法的约束阻尼结构动力学拓扑优化

Dynamic topology optimization for constrained layer damping structures using parametric level set method

约束阻尼(CLD)结构拓扑优化是轻量化设计下实现振动与噪声控制的有效手段。结合约束阻尼结构的有限元模型,以前两阶模态损耗因子及其加权最大化为目标函数,以参数化水平集函数的扩展系数为设计变量,以约束阻尼材料用量为约束条件,建立了基于参数化水平集法(PLSM)的拓扑优化模型。基于伴随向量法推导了目标函数对设计变量的灵敏度,采用优化准则法更新设计变量。算例结果表明:基于参数化水平集法对约束层阻尼结构进行拓扑优化是可行有效的,且以基板结构应变能分布构建初始构型可提高优化效率。此外进一步讨论了在附加质量保持不变的条件下,约束层材料和阻尼材料厚度变化对约束阻尼材料模态损耗因子和最优构型的影响规律。

Topology optimization of constrained layer damping(CLD)structure is an effective means to control vibration and noise under lightweight design.Combined with the finite element model of constrained layer damping structure,the first and second modal loss factor and its weighted value are defined as the objective functions.The expansion coefficients of the parametric level set function are chosen as the design variables,and the amount of CLD material is employed as the constraint condition.A topology optimization model based on parametric level set method(PLSM)is established.The sensitivity of objective function with respect to design variables is derived based on adjoint vector method and the design variables are updated by using optimization criterion method.Numerical results show that it is feasible and effective for topology optimization of the constrained layer damping structure using parametric level set method.In addition,the optimization efficiency can be improved by the initial configuration based on the strain energy distribution of the substrate structure.Furthermore,considering the additional mass kept unchanged,the influence of the thicknesses of constrained layer material and damping material on the modal loss factor and optimal configurations for constrained damping material is discussed.