采用改进导重法的拓扑结构灰度单元过滤技术

针对二分法计算拉格朗日乘子时收敛速度较慢的问题, 提出了拉格朗日乘子计算方法, 应用于优化准则(OC)法和导重(GW)法2种密度更新方法, 并与二分法进行了对比。建立体积约束下柔度最小的拓扑优化模型；通过固体各向同性材料惩罚(SIMP)法或材料属性有理近似(RAMP)法计算单元的弹性模量；通过所提方法计算拉格朗日乘子, 并通过导重法更新单元密度；通过Heaviside投影函数减少灰度单元的数量。计算结果表明:虽然所提方法对有限元分析次数并没有显著改进, 但计算拉格朗日乘子所用CPU时间少于二分法, 且密度更新次数降低至50%以下；在2个数值算例中, 采用SIMP模型时, 导重法所得结构柔度比OC法更小, 能够得到刚度更高的结构。 

Gray element filtering technology of topology structure based on improved guide-weight method

Aiming at the problem of slow convergence speed when calculating Lagrange multiplier by bisection method, the proposed Lagrange multiplier calculation method is applied to the optimal criteria (OC) method and the guide-weight (GW) method to update the density, and the results of the proposed method are compared with the bisection method. The topology optimization model with the smallest compliance under the volume constraint is established. The elastic modulus of element density is calculated by the solid isotropic material with penalization (SIMP) or rational approximation of material properties (RAMP) method. The multiplier is calculated by the proposed method in this paper, and the element density is updated by the GW method. The number of gray element is reduced by the Heaviside projection function. The computational results show that: the proposed method does not significantly reduce the number of finite element analysis, but the CPU time used by the proposed method to calculate the Lagrange multiplier is less than that of the bisection method, and the number of density updates is reduced to less than 50% than before. In addition, in the two numerical examples, when SIMP model is adopted, the structure obtained by the GW method has smaller compliance than the OC method.