摘要
在变密度法拓扑优化结果中,灰度单元及锯齿形边界难以转化为计算机辅助设计(CAD)模型,针对这一问题,提出了一种基于变密度拓扑优化构型的光滑边界提取(重构)方法。首先,使用变密度法得到的伪密度值,在设计域中构造了一个非均匀有理B样条(NURBS)拟合曲面;然后,构造了一种二分法迭代格式,以确定满足体积约束的“零水平集”位置,并运用VBA编写了迭代程序;最后,以水平集方法中的“零水平集”作为结构边界,构成了CAD模型,实现了光滑边界的提取。研究结果表明:采用光滑边界提取方法,降低了变密度拓扑优化过程中的要求(需要减少灰度单元),消除了结果中的锯齿形边界,实现了变密度法优化构型到CAD模型的快速转换;通过3个数值算例得到的拓扑优化模型体积分数误差小于1%,边界光滑、结构性能良好,表明了光滑边界提取方法的有效性和通用性。
Aiming at the problem that it was difficult for the gray elements and zigzag boundaries in the result of density-based topology optimization method to convert the topology optimization result into the computer-aided design(CAD)model and significantly hinder its engineering application,a new method of boundary smooth reconstruction was proposed for variable density topology optimization result.First,the pseudo density values obtained by the density-based method were used to construct a non-uniform rational B-spline(NURBS)surface in the design domain.Then,a bisection iteration algorithm was constructed to determine the position of the"zero level set"surface,so as to ensure that the transformed model met the volume constraint,and the Visual Basic Application(VBA)was employed to compile the iterative program.Finally,the"zero level set"in the level set method was applied as the structure boundary to construct the CAD model and achieve the smooth boundary extraction.The results of the study show that the proposed method reduces the requirement of reducing gray elements for density-based topology optimization,eliminates the zigzag boundary,and realizes the fast conversion from the optimized configuration to the CAD model.The volume fraction error of the topology optimization model obtained by the three numerical studies is less than 1%,the boundary is smooth and the structural performance is good,which shows the validity and versatility of the method.
作者
陈昊怿
吴晓明
CHEN Hao-yi;WU Xiao-ming(School of Aerospace Engineering,Xiamen University,Xiamen 361102,China)
出处
《机电工程》
CAS
北大核心
2023年第6期883-889,共7页
Journal of Mechanical & Electrical Engineering
基金
国家自然科学基金资助项目(52075462)。
关键词
拓扑优化
光滑边界重构方法
边界识别
计算机辅助设计
非均匀有理B样条
topology optimization
boundary smooth reconstruction
boundary detection
computer-aided design(CAD)
non-uniform rational B-splines(NURBS)
