改进的抑制灰度单元的拓扑优化方法

An Improved Topology Optimization Method for Suppressing Gray Elements

固体各向同性材料惩罚法或材料属性有理近似法所得拓扑优化结构中存在大量灰度单元,且现有Heaviside投影函数存在频繁调用密度矩阵的问题,进而导致计算效率较低.针对此问题提出了一种基于改进Heaviside投影函数的抑制灰度单元的拓扑优化方法,首先,建立以结构柔度最小化为设计目标的拓扑优化模型;然后,通过固体各向同性材料惩罚法或材料属性有理近似法计算杨氏模量;最后,通过Heaviside投影函数抑制灰度单元,并由优化准则法求解拓扑优化问题.数值模拟结果表明,文中2个Heaviside投影函数能够稳定和有效地抑制灰度单元,且二者分别对固体各向同性材料惩罚法和材料属性有理近似法所得结构的清晰度和刚度的改进效果比较明显.

The topology optimization structure obtained by the SIMP(solid isotropic material with penaliza-tion)method or RAMP(rational approximation of material properties)method has a large number of gray ele-ments,and the existing Heaviside function has the problem of calling the density matrix frequently,so the computational efficiency is relatively low.Aiming at this problem,an improved topology optimization method for suppressing gray elements is proposed in this paper.Firstly,a topology optimization model with minimizing the structural compliance as design objective is established;then,the Young's modulus is calculated by the SIMP method or RAMP method;finally,gray element is suppressed by the Heaviside projection function,and the topology optimization problem is solved by the OC(optimality criteria)method.The numerical simulation results show that:the two Heaviside projection functions proposed in this paper can suppress gray elements stably and effectively,and they can notably improve the definition and stiffness of the structure obtained by the SIMP method and RAMP method respectively.