摘要
现有等几何拓扑优化隐式过滤方法的基函数空间具有非单元一致性的性质,导致每个参数单元的基函数值及其索引均需计算和保存,从而使得过滤所需内存较大和计算耗时较长的问题。针对上述问题,提出了一种基于Bernstein基函数的等几何拓扑优化NURBS高效隐式过滤方法。首先基于Bernstein基函数、Bézier提取算子和B样条基函数的有理形式进行NURBS基函数的等价表达。随后进行NURBS参数化所表达的等几何拓扑优化设计变量场的重映射,进而实现基于Bézier提取矩阵对NURBS控制点传统隐式过滤方法和灵敏度分析的重构。最后,对该NURBS高效隐式过滤方法与传统NURBS过滤方法进行二维和三维数值算例对比。数值结果表明:研究提出的高效隐式过滤方法可以在更短的计算时间和更少的内存占用得到与NURBS隐式过滤方法相同的优化结果和优化过程,实现了传统NURBS隐式过滤方法的等价替换和数据结构的优化。
The basis function space of existing isogeometric topology optimization implicit filtering methods have a common property of the local basis space varying with the knot spans,resulting in the base function values and their indices at the centroid of each parameter cell to be calculated and saved,which makes the current topology optimization computation process suffers from the drawbacks of large memory burden and long computation time.Firstly,the equivalent expression of the NURBS basis functions is expressed by Bernstein basis function and Bézier extraction operator,in the rational form of B-splines.Then,the design field parametrized by the NURBS basis functions is remapped by Bernstein basis functions,which can implement the optimization of calculation process and storage for the data of traditional NURBS implicit filtering methods.Finally,the proposed implicit filtering method based on the Bernstein basis function is compared with the conventional filtering method for two-dimensional and three-dimensional numerical benchmarks.The numerical result shows that:compared with the traditional isogeometric topology optimized NURBS implicit filtering method,as the same number of design grid resolutions and design element orders,the proposed filtering method can obtain identical optimized result and optimization process to the traditional one,with reduced computing time and memory burden,and the traditional NURBS implicit filtering method can be equivalently replaced by the proposed one with optimized data structure.
作者
朱浩然
谢贤达
杨奥迪
王书亭
ZHU Haoran;XIE Xianda;YANG Aodi;WANG Shuting(School of Mechanical Science and Engineering,Huazhong University of Science and Technology,Hubei Wuhan 430074,China)
出处
《机械设计与制造》
北大核心
2026年第2期227-232,共6页
Machinery Design & Manufacture
基金
国家重点研发计划课题资助项目(2020YFB1708300)
中国博士后科学基金面上资助项目(2021M701310)。
