适用于等几何分析退化光滑插值曲面片构造

doi:10.3969/j.issn.0253-2778.2020.03.011

中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (3): 335-342.DOI: 10.3969/j.issn.0253-2778.2020.03.011

适用于等几何分析退化光滑插值曲面片构造

王旭辉，燕明叶，吴梦

1.合肥工业大学数学学院, 安徽合肥 230061；2.南京审计大学统计与数学学院, 江苏南京 210000

收稿日期:2019-12-05 修回日期:2020-01-12 接受日期:2020-01-12 出版日期:2020-03-31 发布日期:2020-01-12
通讯作者: 吴梦
作者简介:王旭辉, 男, 1980年生，博士/教授, 研究方向:计算几何、等几何分析. E-mail: xhw@hfut.edu.cn
基金资助:
国家自然科学基金(61772167,11601114); 安徽省自然科学基金会(1608085QA14)资助.

Suitable for the construction of degenerate smooth interpolated surfaces patches in isogeometric analysis

WANG Xuhui, YAN Mingye, WU Meng

1.School of Mathematics, Hefei University of Technology, Hefei 230061, China; 2.School of Statistics and Mathematics, Nanjing Audit University, Nanjing 210000, China

Received:2019-12-05 Revised:2020-01-12 Accepted:2020-01-12 Online:2020-03-31 Published:2020-01-12

摘要/Abstract

摘要： 不同于经典几何造型领域构造退化光滑曲面片, 以等几何分析为背景, 构造基于等几何分析中奇异H正则参数化下的插值算子. 首先基于奇异参数化介绍了H正则性定义, 其次引入了D-patch和插值算子的定义, 最后验证了插值型曲面的G光滑性, 并给出数值算例.

关键词: 等几何分析, D-patch, 插值算子, H正则性

Abstract: Different from constructing the degenerate smooth surface patches in the field of classical geometric modeling, the paper constructs an interpolation operator based on the singular H regularity parameterization in the isogeometric analysis. First, the definition of H regularity is introduced based on singular parameterization. Then, the definition of D-patch and interpolation operator is discussed. Finally, the Gsmoothness of the interpolation surface is verified and numerical examples are given.

Key words: isogeometric analysis, D-patch, interpolation operator, Hregularity

中图分类号:

TP391.41

王旭辉，燕明叶，吴梦. 适用于等几何分析退化光滑插值曲面片构造[J]. 中国科学技术大学学报, 2020, 50(3): 335-342.

WANG Xuhui, YAN Mingye, WU Meng. Suitable for the construction of degenerate smooth interpolated surfaces patches in isogeometric analysis[J]. Journal of University of Science and Technology of China, 2020, 50(3): 335-342.

参考文献

［1］
CRISFIELD MA. Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics[M]. London: John Wiley & Sons, Inc. 1997.
[2] 高曙明, 何发智. 异构CAD系统集成技术综述[J].计算机辅助设计与图形学学报, 2009, 21(5): 561-568.
GAO S M, HE F Z. A survey of heterogeneous CAD system integration[J]. Journal of Computer Aided Design & Computer Graphics, 2009, 21(5): 561-568.
[3] HUGHES T J R, COTTRELL J A, BAZILEVS Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39-41): 4135-4195.
[4] 张汉杰, 王东东, 轩军厂. 薄梁板结构NURBS几何精确有限元分析[J]. 力学季刊, 2010, 31(4): 469-477.
ZHANG H J, WANG D D, XUAN J C. Non-uniform rational B spline-based isogeometric finite element analysis of thin beams and plates[J]. Chinese Quarterly of Mechanics, 2010, 31(4): 469-477.
[5] 许华强. 面向等几何分析的样条参数体生成方法研究[D].杭州: 杭州电子科技大学, 2012.
[6] BAZILEVS Y，BEIRAO D V L, COTTRELL J A, et al. Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes[J]. Mathematical Models and Methods in Applied Science, 2006, 16(7): 1031-1090.
[7] 徐岗，李新，黄章进，等. 面向等几何分析的几何计算[J]. 计算机辅助设计与图形学学报,2015, 27(4): 570-581.
XU G, LI X, HUANG Z J, et al. Geometric computing for isogeometric analysis[J]. Journal of Computer Aided Design & Computer Graphics, 2015, 27(4): 570-581.
[8] 吴紫俊，黄正东，左兵权，等. 等几何分析研究概述[J]. 机械工程学报,2015, 51(5): 114-129.
WU Z J, HUANG Z D, ZUO B Q, et al. Perspectives on isogeometric analysis[J]. Journal of Mechanical Engineering, 2015, 51(5): 114-129.
[9] COHEN E, MARTIN T, KIRBY R M , et al. Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(5-8): 334-356.
[10] XU G, MOURRAIN B, RGIS D, et al. Parameterization of computational domain in isogeometric analysis: Methods and comparison[J]. Computer Methods in Applied Mechanics & Engineering, 2011, 200(23-24): 2021-2031.
[11] XU G, LI M, MOURRAIN B, et al. Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 328: 175-200.
[12] DED L, QUARTERONI A. Isogeometric analysis for second order partial differential equations on surfaces[J]. Computer Methods in Applied Mechanics & Engineering, 2015, 284: 807-834.
[13] LU J. Circular element: Isogeometric elements of smooth boundary[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(30-32): 2391-2402.
[14] MARTIN T, COHEN E, KIRBY R M. Volumetric parameterization and trivariate B-spline fitting using harmonic functions[J]. Computer Aided Geometric Design, 2009, 26: 648-664.
[15] WANG D, XUAN J. An improved NURBS-based isogeometric analysis with enhanced treatment of essential boundary conditions[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37-40): 2425-2436.
[16] WU M , WANG Y , MOURRAIN B , et al. Convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis[J]. Computer Aided Geometric Design, 2017, 52-53:170-189.
[17] TAKACS T. Construction of smooth isogeometric function spaces on singularly parameterized domains[J]. Curves and Surfaces, 2014, 9213: 433-451.
[18] NGUYEN T, PETERS J. Refinable C spline elements for irregular quad layout[J]. Computer Aided Geometric Design. 2016, 43: 123-130.
[19] TOSHNIWAL D, SPELEERS H, Hiemstra R.R, et al. Multi-degree smooth polar splines: A framework for geometric modeling and isogeometric analysis[J]. Computer Methods in Applied Mechanics & Engineering, 2017, 316: 1005-1061.
[20] TAKACS T. Approximation properties of isogeometric function spaces on singularly parameterized domains[J].Mathematics, 2015:arXiv:1507.08095v1.
[21] WU M, MOURRAIN B, GALLIGO A, et al. Hermite type spline spaces over rectangular meshes with complex topological structures[J]. Communications in Computational Physics, 2017, 21(03): 835-866.
[22] JEONG J W, OH H S, KANG S, et al. Mapping techniques for isogeometric analysis of elliptic boundary value problems containing singularities[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 254: 334-352.
[23] OH HS, KIM H, JEONG J W. Enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and/or corners[J]. International Journal for Numerical Methods in Engineering, 2014, 97(3): 149-180.
[24] WU M, MOURRAIN B, GALLIGO A, et al.H-parameterizations of complex planar physical domains in isogeometric analysis[J].Computer Methods in Applied Mechanics and Engineering, 2017, 318: 296-318.
[25] WU M, WANG X H. A H-integrability condition of surfaces with singular parametrizations in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 332: 136-156.
[26] HEBEY E. Sobolev Spaces on Riemannian Manifolds[M]. Berlin: Springer, 1996: 1635.
[27] 施法中. 计算机辅助几何设计与非均匀有理B样条[M].北京: 高等教育出版社, 2013: 217-258.
[28] TAKACS T, JTTLER B. Existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis[J]. Computer Methods in Applied Mechanics & Engineering, 2011, 200(49-52): 3568-3582.
[29] REIF U. A refineable space of smooth spline surfaces of arbitrary topological genus[J]. Journal of Approximation Theory, 1997, 90(2): 174-199.

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适用于等几何分析退化光滑插值曲面片构造

Suitable for the construction of degenerate smooth interpolated surfaces patches in isogeometric analysis

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