华中科技大学学报（自然科学版）2013，Vol.41Issue(8)：101-105,5.
紧支Shepard近似在拓扑优化中的应用研究
Application of compactly supported Shepard approximation in topology optimization
摘要
Abstract
To examine the numerical instabilities in the topology optimization by finite element method,compactly supported radial basis function was employed as the weight function of Shepard method to construct a compactly supported Shepard approximation function.Continuous density field and sensitivity field were established by replacing the original discrete density variables and sensitivity variables with the approximations based on Shepard function.Density approximation and sensitivity approximation methods were thus proposed for topology optimization.Numerical examples show that checkerboard pattern and mesh dependency problems can be solved by the density approximation and sensitivity approximation methods.As the refinement of mesh size increases,the gray scale elements of topology optimization results obtained from the density approximation method increase proportionally.However,the sensitivity approximation method can suppress the grey scale elements effectively.关键词
拓扑优化/数值不稳定性/Shepard近似函数/密度近似/敏度近似Key words
topology optimization/ numerical instabilities/ Shepard approximation function/ density approximation/ sensitivity approximation分类
机械制造引用本文复制引用
杜义贤,付君健,严双桥,陶然..紧支Shepard近似在拓扑优化中的应用研究[J].华中科技大学学报（自然科学版）,2013,41(8):101-105,5.基金项目
国家自然科学基金资助项目(51105229) （51105229）
湖北省自然科学基金资助项目(2010CDB10805) （2010CDB10805）
三峡大学水电机械设备设计与维护湖北省重点实验室开放基金资助项目(2010KJX04). （2010KJX04）
