基于RMB样条的壳结构等几何拓扑优化

李嘉蔚; 李杭川; 王选; 潘茂东

doi:10.21656/1000-0887.460154

基于RMB样条的壳结构等几何拓扑优化

doi: 10.21656/1000-0887.460154

1. 南京航空航天大学数学学院，南京 211106;
2. 合肥工业大学土木与水利工程学院，合肥 230009

基金项目:

国家重点研发计划青年科学家项目（2024YFA1016300；2022YFB3302900）；国家自然科学基金面上项目（12471359）；航空科学基金（20240009052001）

详细信息

作者简介:
李嘉蔚（2001—），女，硕士(E-mail: sukiyakiawei@163.com)；潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).

通讯作者:
潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).

中图分类号: O29
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- 文章访问数: 103
- HTML全文浏览量: 28
- PDF下载量: 10
- 被引次数: 0
出版历程
- 收稿日期: 2025-08-27
- 修回日期: 2025-12-09
- 网络出版日期: 2026-09-24
- 刊出日期: 2026-09-01

Adaptive Isogeometric Topology Optimization of Shell Structures Based on RMB-Splines

1. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.R. China;
2. College of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R. China

Funds:

The National Science Foundation of China(12471359)

摘要

摘要: 提出了一种基于RMB样条（reachable minimally supported B-splines）的自适应等几何拓扑优化（isogeometric topology optimization, ITO）算法，针对壳结构的材料分布问题进行优化.该算法结合SIMP变密度模型插值材料密度，采用新型局部加细样条RMB样条（reachable minimally supported B-splines）精确描述位移场和密度场，利用其局部线性无关性、最小支撑性和高效的局部细化能力，实现了分析域与设计域的统一.制定依据密度分布变化自动选择细化区域的自适应网格加细策略，使得RMB网格沿材料边界进行局部细化，在保证优化精度的基础上有效降低整体自由度.数值实现中，RMB样条为优化过程提供了稳定而高效的数值支持，引入投影函数进行密度过滤以平滑材料分布，并结合MMA算法求解优化问题.通过多个壳结构的数值算例验证表明，与B样条方法相比，该方法可显著减少基函数个数，提升计算效率并获得更清晰、更具工程可实现性的拓扑布局，展现了其在复杂结构拓扑优化中的巨大应用潜力.
- 等几何分析 /
- 拓扑优化 /
- 壳结构 /
- RMB样条
Abstract: An adaptive isogeometric topology optimization algorithm based on RMB-splines (reachable minimally supported b-splines) was proposed to optimize the material distribution problem of shell structures. This algorithm combines the SIMP model to interpolate material density, and uses a new type of local refinement spline RMB-splines to represent the displacement field and density field. By taking advantages of its local linear independence, minimum support, and efficient local refinement ability, it achieves the unification of the analysis domain and the design domain. An adaptive mesh refinement strategy was constructed to identify refinement regions from the density distribution and to refine the mesh locally along material boundaries. This effectively reduces the overall degree of freedom while ensuring the optimization accuracy. In the numerical implementation, the RMB-splines provides stable and efficient numerical support for the optimization process. The projection function was introduced for density filtering to smooth the material distribution, and the MMA algorithm was used to solve the optimization problem. The numerical examples of multiple shell structures show that, compared with the B-spline method, this method can significantly reduce the number of basis functions, improve computational efficiency, and obtain a clearer and more engineering-feasible topological layout, promising great application potential in the topological optimization of complex structures.
- isogeometric analysis /
- topology optimization /
- shell structure /
- RMB-spline

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参考文献(25)

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基于RMB样条的壳结构等几何拓扑优化

doi: 10.21656/1000-0887.460154

作者简介:
李嘉蔚（2001—），女，硕士(E-mail: sukiyakiawei@163.com)；潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).

通讯作者:
潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).

计量

Adaptive Isogeometric Topology Optimization of Shell Structures Based on RMB-Splines

计量

目录

留言板

基于RMB样条的壳结构等几何拓扑优化

doi: 10.21656/1000-0887.460154

作者简介: 李嘉蔚（2001—），女，硕士(E-mail: sukiyakiawei@163.com)；潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).

通讯作者: 潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).

计量

出版历程

Adaptive Isogeometric Topology Optimization of Shell Structures Based on RMB-Splines

计量

出版历程

目录

作者简介:
李嘉蔚（2001—），女，硕士(E-mail: sukiyakiawei@163.com)；潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).

通讯作者:
潘茂东（1990—），男，教授，博士生导师(通信作者. E-mail: maodong@nuaa.edu.cn).