基于基础结构法的柔顺机构动力学拓扑优化

DYNAMIC TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS USING THE GROUND STRUCTURE APPROACH

提出一种新的在简谐激励作用下,基于基础结构法的柔顺机构动力学拓扑优化方法。框架单元能够包含弯曲模式,因此采用它的集合表示设计域。以动力放大系数最大化与应变能的最小化加权函数为目标,满足在动态条件下柔顺机构具有足够柔度和刚度;并且规一化目标函数避免不同性质目标函数的量级差异。目标函数的敏度采用伴随矩阵法求解,用移动近似算法对优化问题进行迭代求解。通过数值算例对不同外激励频率和不同输出刚度的拓扑优化结构进行分析讨论。结果表明,该方法在柔顺机构动力学拓扑优化设计中是正确的和有效的。

A new dynamic topology optimization method of compliant mechanisms using the ground structure approach under harmonic excitation is presented.Frame elements are chosen to represent the design domain because they are capable of capturing the bending modes.The multi-objective function is developed by the maximum dynamic magnification factor and the minimum strain energy to design a mechanism which meets both stiffness and flexibility requirements under harmonic excitation,respectively.The objective function is normalized to eliminate magnitude difference of the objectives.The sensitivities of the objective functions are computed by the adjoint method,the optimization problem is solved using the method of moving asymptotes（MMA）.Some numerical examples with different driving frequency and different output spring stiffness are presented to illustrate the effect of driving frequency and damping factor.The results are shown to demonstrate the validity to the proposed method.