[1]贾程,陈卉卉..基于数值inf-sup条件的US-FE-LSPIM四边形单元稳定性研究[J].郑州大学学报(工学版),2012,33(04):36-40.[doi:10.3969/j.issn.1671-6833.2012.04.009]
　JIA Cheng,CHEN Huihui.Stability Study on US-FE-LSPIM QUAD4 Element Based onNummerical inf-sup Condition[J].Journal of Zhengzhou University (Engineering Science),2012,33(04):36-40.[doi:10.3969/j.issn.1671-6833.2012.04.009]
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基于数值inf-sup条件的US-FE-LSPIM四边形单元稳定性研究()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
33
期数:
2012年04期
页码:
36-40
栏目:
出版日期:
2012-07-10

文章信息/Info

Title:
Stability Study on US-FE-LSPIM QUAD4 Element Based onNummerical inf-sup Condition
作者:
贾程; 陈卉卉.
盐城工学院土木工程学院,江苏盐城,224051, 盐城工学院土木工程学院,江苏盐城,224051
Author(s):
JIA Cheng; CHEN Huihui
School of Civil Engineering, Yancheng Institute of Technology, Yancheng 224051 , China
关键词:
US-FE-LSPIM四边形单元;  一致性要求;  稳定性要求;  inf-sup条件
Keywords:
US-FE-LSPIM QUAD4 element;  consistency requirement;  stability requirement;  inf-sup condition
分类号:
O343.1
DOI:
10.3969/j.issn.1671-6833.2012.04.009
摘要:
US-FE-LSPIM四边形单元由传统的四节点等参元形函数集和FE-LSPIM四边形单元形函数集分别作为检验函数和试函数而构成.传统的四节点等参元形函数集用于满足单元间和单元内位移连续性要求;FE-LSPIM四边形单元形函数集用于满足位移完备性要求.该单元能方便地施加整段长度的位移边界条件.它具有计算精度高、对网格畸变不敏感的优点,满足数值收敛的一致性要求.进一步研究该单元数值收敛的稳定性.由于通过解析的方法验证单元是否满足inf-sup条件较为困难,利用数值的方法,推导出了该单元数值化的inf-sup条件表达式,检验该单元是否满足inf-sup条件.典型算例表明,该单元能通过数值inf-sup检验,满足稳定性要求,为检验单元的稳定性提供一种简便途径.
Abstract:
US-FE-SPIM QUAD4 element is constructed by using classical QUAD4 element isoparametric shapefunctions sets and FE-LSPiM QUAD4 element shape functions sets as test functions and the trial functions re-spectively. The former is used for requirements of intra-element and inter-element continuity in displacementfield, and the latter is for requirements of completeness in displacement field. US-FE-SPIM QUAD4 elementeould easily fulfil exaet essential boundary condition along the entire length of the edge. This element has goodprecision and insensitivity to mesh distortion, and satisfies the consistency requirement. Further studies on sta.bility of US-FE-SPIM QUAD4 element for convergence are made in this paper. Because an analytical proof ofwhether the inf-sup condition is satisfied by a specific element is difficult, in this paper, the formulation of nu-merical inf-sup condition for this element is derived and whether the inf-sup condition is satisfied for this ele.ment is tested by the numerical method. Numerical examples show that US-FE-SPIM QUAD4 element couldpass numerical inf-sup testing, satisfying the stability requirement. And this paper offers a simple way to testelement stability.
更新日期/Last Update: 1900-01-01