应用数学和力学2026，Vol.47Issue(9)：1222-1234,13.DOI:10.21656/1000-0887.460154
基于RMB样条的壳结构等几何拓扑优化
Adaptive Isogeometric Topology Optimization of Shell Structures Based on RMB-Splines
摘要
Abstract
An adaptive isogeometric topology optimization algorithm based on RMB-splines(reachable minimal-ly supported b-splines)was proposed to optimize the material distribution problem of shell structures.This al-gorithm 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 analy-sis 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 implementa-tion,the RMB-splines provides stable and efficient numerical support for the optimization process.The projec-tion 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,im-prove computational efficiency,and obtain a clearer and more engineering-feasible topological layout,promis-ing great application potential in the topological optimization of complex structures.关键词
等几何分析/拓扑优化/壳结构/RMB样条Key words
isogeometric analysis/topology optimization/shell structure/RMB-spline分类
数理科学引用本文复制引用
李嘉蔚,李杭川,王选,潘茂东..基于RMB样条的壳结构等几何拓扑优化[J].应用数学和力学,2026,47(9):1222-1234,13.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) （12471359）
航空科学基金(20240009052001) （20240009052001）
