广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (1): 15-21.

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弹性力学问题Locking-free有限元离散系统的两水平方法

张红梅1, 肖映雄2, 欧阳媛3   

  1. 1.湖南工业大学理学院,湖南株洲412007;
    2.湘潭大学土木工程与力学学院,湖南湘潭411105;
    3.湖南华菱涟源钢铁有限公司,湖南娄底417009
  • 收稿日期:2012-01-09 出版日期:2012-01-20 发布日期:2018-12-03
  • 通讯作者: 肖映雄(1970—),男(苗族),湖南城步人,湘潭大学教授,博士。E-mail:xyx610xyx@yahoo.com.cn
  • 基金资助:
    国家自然科学基金资助项目(10972191);湖南省教育厅一般项目(11C0411)

A Two-Level Method for Locking-free Finite Element Discretizationin Linear Elasticity

ZHANG Hong-mei1, XIAO Ying-xiong2, OUYANG Yuan3   

  1. 1.School of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China;
    2.College of Civil Engineering and Mechanics,Xiangtan University,XiangtanHunan 411105,China;
    3.Hunan Valin Lianyuan Iron and Steel Company Limited,Loudi Hunan 417009,China
  • Received:2012-01-09 Online:2012-01-20 Published:2018-12-03

摘要： 高次协调元能有效克服弹性力学问题的闭锁(Locking)现象,称这种单元为无闭锁(Locking-free)有限元,但它与线性元相比,往往需要更多的计算机存储单元,具有更高的计算复杂性。针对弹性力学问题Locking-free(四次)有限元离散系统的求解,本文通过分析四次有限元与二次有限元空间之间的关系,并利用有限元基函数的特殊性质,如紧支集性,建立一种以二次有限元(P2)为粗水平空间的两水平方法;然后,利用减缩积分方案,以P2/P0元作为四次元空间的粗水平空间,并结合有效的磨光算子,为Locking-free有限元离散系统设计具有更好计算效率和鲁棒性的求解方法。数值实验结果验证了算法的有效性。

关键词: 弹性力学问题, 高次元, 闭锁现象, 两水平法, 减缩积分

Abstract: Higher-order conforming finite elements can effectively overcome the poisson-Locking in linear elasticity,which is call and Locking-free finite elements.But when compared with the linear element,it often requiresmore computer storage and has a higher computational complexity.For the Locking-free(quartic) finite element discretization in linear elasticity,a general two-level method is proposed by analyzing the relationship between the quadraticfinite element space and the quartic finite element space and by taking advantage of the special nature of the finite element's basi functions,such as compactly supported.First,the quadratic element is chosen as the coarse level space.Second,by combining the selective reduced integration and some efficient smoothers,then,obtain the two-level method is obtained in which the element is chosen as the coarse level space for the Locking-free finite element discretization with better robustness and high efficiency.The numerical results show the efficiency of the resulting method.

Key words: elasticity problem, higher-order finite element, locking phenomenon, two-level method, selective reduced integration

中图分类号: 

  • O343
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