基于节点密度的柔性机构的拓扑优化设计

针对连续体结构拓扑优化中出现的棋盘格式问题提出了一种新的以节点密度作为设计变量的优化方法,从而使设计区域内的密度场函数具有C0连续性。建立了以互能和应变能比值为目标函数的柔性机构拓扑优化数学模型,推导了基于节点密度的柔性机构敏度计算的解析表达式。应用节点密度法对典型算例进行了拓扑优化计算,计算结果表明不需要借助滤波处理,节点密度法就能够得到具有清晰拓扑结构的优化结果,真实地反映了机构的结构细节。

Topology optimization design for compliant mechanisms based on nodal density

A new method using nodal density as design variable of continuum topology optimization was proposed to resolve the checkerboard pattern.This method ensured C0 continuity of density field in a fixed design domain.The mathematical model of topology optimization for compliant mechanisms was established,in which,the ratio of mutual energy to strain energy of the mechanism is regarded as the objective function.The analytical expression of sensitivity based on nodal density for compliant mechanisms was also deduced.The method proposed in the paper was applied in sample problems of topology optimization.The results show that the mechanisms obtained by the nodal density method have clear topology structures which actually reflect the structures of the mechanisms without any filtering schemes.