同几何分析研究进展

葛建立; 杨国来; 吕加

doi:10.6052/1000-0992-12-040

同几何分析研究进展

doi: 10.6052/1000-0992-12-040

1 南京理工大学机械工程学院, 南京 210094
2 Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, USA

基金项目: 国家自然科学基金项目(11172139) 和南京理工大学科技发展基金项目(XKF09065) 资助

详细信息

作者简介:
葛建立, 1980 年生, 男, 博士, 硕士生导师. 一直从事计算固体力学、结构设计、非线性动态有限元方面的科研和教学工作, 参与过多项国家级和省部级项目, 主持"973" 专题1 项, 获得军队科技进步三等奖1 项, 在国内外核心期刊及学术会议上发表学术论文二十多篇, 十多篇被EI、ISTP 等收录. 参与出版专著1 部, 申请国防专利4 项. 为武器系统与工程专业课群国家级教学团队成员.

通讯作者:
葛建立

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出版历程
- 收稿日期: 2012-03-21
- 修回日期: 2012-07-24
- 刊出日期: 2012-11-25

Advances in isogeometric analysis

GE Jianli^{1
, ,},
YANG Guolai¹,
LU Jia²

1 School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
2 Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, USA

Funds: The project was supported by the National Natural Science Foundation of China(11172139) and the Science and Technology Development Fund of NUST(XKF09065).

More Information

Corresponding author: GE Jianli

摘要

摘要:
同几何分析(isogeometric analysis) 是当前工程分析的一种发展趋势, 有可能对计算机辅助工程(CAE) 产生重大影响. 同几何分析的思想是采用计算机辅助设计(CAD) 的几何语言, 如NURBS(non-uniform rational B-spline) 几何替代拉格朗日插值作为分析计算的基础. 这种看似简单的几何语言变化, 消除了困扰CAE 多年的瓶颈问题, 开启了一条紧密联系分析、设计和优化的新途径. 本文论述了同几何分析的产生背景、理论、优点及其在各个领域的应用. 系统总结了同几何分析在NURBS, T 样条基函数构建, 非结构化网格构建, 有效积分方法, 曲面修剪技术, 网格细化等基础理论方面的进展, 以及在板壳问题、大变形问题、流固耦合、结构优化、接触问题、生物力学、温度场和电磁场等领域的应用, 展示了同几何分析相对于标准多项式插值有限元法的优势.
- 同几何分析, 有限元法, 非均匀有理B 样条, T 样条, 结构优化, 接触问题
Abstract:
Isogeometric analysis (IGA) is a current trend in engineering analysis that is likely to leave a significantly impact on Computer-Aided Engineering (CAE). The basic idea of IGA is to utilize CAD geometry to facilitate analysis. This seemingly simple change of geometric language eliminates many bottle-neck issues that plagued CAE for years, and opens a pathway for a tighter integration of design, analysis, and optimization. In this review paper, the background, theory, advantages, and applications of isogeometric analysis are discussed. Topics of algorithmic development, including NURBS bases, T-spline bases, unstructured meshes, efficient quadrature methods, trimmed surface technologies, refinements and so on are reviewed. Recent advances of IGA in shell problems, large deformation, fluid-structure interaction, structural optimization, contact problems, biomechanics, thermal analysis, and electromagnetics are also summarized.
- isogeometric analysis, finite element method, NURBS, T-spline, structural optimization, contact problem

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