北京航空航天大学学报 ›› 2017, Vol. 43 ›› Issue (3): 432-440.doi: 10.13700/j.bh.1001-5965.2016.0221

• 论文 • 上一篇    下一篇

含局部缝隙与重叠特征的Mindlin板等几何分析

赵罡, 杜孝孝, 王伟   

  1. 北京航空航天大学 机械工程及自动化学院, 北京 100083
  • 收稿日期:2016-03-21 出版日期:2017-03-20 发布日期:2016-06-12
  • 通讯作者: 王伟,E-mail:jrrt@buaa.edu.cn E-mail:jrrt@buaa.edu.cn
  • 作者简介:赵罡,男,博士,教授,博士生导师。主要研究方向:虚拟现实技术、飞行器数字化装配、曲面造型新方法及其在数控加工中应用等。;杜孝孝,男,博士研究生。主要研究方向:CAD/CAE、等几何分析。;王伟,男,博士,讲师。主要研究方向:CAD/CAE、等几何分析、工程结构优化。
  • 基金资助:
    国家自然科学基金(51305016,61572056);2013年北京市支持中央高校共建项目(29201437)

Isogeometric analysis of Mindlin plate with local gap and overlapping feature

ZHAO Gang, DU Xiaoxiao, WANG Wei   

  1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2016-03-21 Online:2017-03-20 Published:2016-06-12

摘要: 等几何分析(IGA)中非均匀有理B样条(NURBS)被同时用作计算机辅助设计(CAD)中的建模工具以及有限元分析(FEA)中的逼近函数。NURBS模型中常见的缝隙和重叠问题使得分析变得困难。基于Mindlin板理论,对含有缝隙与重叠部分的NURBS模型进行等几何分析,采用Nitsche方法处理模型交界面上的非协调问题,并通过标准数值仿真算例的计算结果与解析解对比验证方法的可行性。研究结果表明:基于Nitsche的等几何方法可以用来对含局部缝隙与重叠特征的非协调Mindlin板模型进行分析;NURBS次数越高,等几何分析计算结果越精确,并且收敛速度越快。

关键词: 等几何分析(IGA), Mindlin板, 非协调, Nitsche方法, 缝隙与重叠

Abstract: In the frame of isogeometric analysis (IGA), non-uniform rational B-spline (NURBS) serves as both the description of geometries in computer aided design (CAD) and the shape function in finite element analysis (FEA). The common problems of gap and overlapping in NURBS models increase the difficulty of analysis. Based on Mindlin plate theory, the NURBS plate models with gap and overlapping were analyzed by IGA method. The Nitsche method was employed to solve non-conforming problem along models' interfaces. The simulation results of benchmark problem obtained by IGA method were compared with analytical solutions to verify the validity of the presented method. It is demonstrated that Nitsche based IGA method can be used to analyze non-conforming Mindlin plate models with local gap and overlapping feature. Higher NURBS polynomial degrees will produce more accurate IGA results and faster convergence.

Key words: isogeometric analysis (IGA), Mindlin plate, non-conforming, Nitsche method, gap and overlapping

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