Stability Study on US-FE-LSPIM QUAD4 Element Based onNummerical inf-sup Condition
[1]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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Journal of Zhengzhou University (Engineering Science)[ISSN
1671-6833/CN
41-1339/T] Volume:
33
Number of periods:
2012 04
Page number:
36-40
Column:
Public date:
2012-07-10
- Title:
- Stability Study on US-FE-LSPIM QUAD4 Element Based onNummerical inf-sup Condition
- Keywords:
- US-FE-LSPIM QUAD4 element; consistency requirement; stability requirement; inf-sup condition
- CLC:
- O343.1
- DOI:
- 10.3969/j.issn.1671-6833.2012.04.009
- 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.
- References:
- -
- Similar References:
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Last Update:
1900-01-01