连续体结构的变密度拓扑优化方法研究

为了实现使连续体结构的体积约束和柔顺度最小的拓扑优化及解决采用经典变密度法引起的结构优化结果存在如灰度单元、棋盘格等数值不稳定问题，提出了一种新的拓扑优化方法。首先，采用改进的固体各向同性材料惩罚法作为材料插值方案，建立结构拓扑优化模型；其次，通过引入基于高斯权重函数的敏度过滤法和设计新灰度单元抑制算子来解决数值不稳定问题；最后，借助优化准则法求解优化模型。通过算例分析可知：新策略可以改进拓扑优化方法；新的拓扑优化方法具有收敛速度较快、能更好地获取柔顺度小且拓扑构型好的优化结构和抑制灰度单元产生等优势。研究结果为其他连续体结构的拓扑优化研究提供了新思路。

Research on variable density topology optimization method for continuum structure

In order to achieve the topological optimization of the volume constraint and the minimum compliance of the continuous structure and solve the numerical instability problems, such as gray-scale element and checkerboard grid caused by classical variable density method, a new topology optimization method was proposed. Firstly, the method of improved solid isotropic material with penalization was used as the material interpolation scheme to establish a structural topology optimization model；secondly, the numerical instability problem was solved by introducing sensitivity filtering method based on the Gaussian weight function and designing a new gray-scale element suppression operator; finally, the optimization model was solved by the optimality criterion method. Through example analysis, it could be seen that the new strategy could improve the topology optimization method. The method had the advantages of faster convergence, acquisition of optimized structures with small compliance and good topological configuration and better suppression of gray-scale element generation. The results provide new ideas for the study of topological optimization of other continuum structures.