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Applied Mathematics and Mechanics

, Volume 17, Issue 8, pp 795–804 | Cite as

A group of isoparametric elements suitable for St. Venant's torsion of a bar with cracks

  • Fan Xiuchang
  • Wu Yueming
Article
  • 12 Downloads

Abstract

In this paper, we shall give a group of new isoparametric elements suitable for St. Venant's torsion of a bar with vertical cracks. These elements are eight-point isoparametric element, quarter eight-point isoparametric element and eight-point isoparametric transition element. Among these elements, the second and the third elements possess the singularity of order r-1/2at crack tip. Using these elements, we have completed the calculations of St. Venant's torsion for a cylinder with a radial vertical crack. The calculated results show that the isoparametric elements given by this paper have ideal accuracy, good convergence, high speed of convergence, low freedom and little computational time, and so they can be widely applied to practice.

Key words

singular finite element transition finite element fracture mechanics St. Venant's torsion 

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References

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    ChaiChengwen, Arbitrary high order singular strain element for calculating the K I of St. Venant's torsion, J. Solid Mechanics, 1 (1983), 92–99. (in Chinese)Google Scholar
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    ChienWeizang, Generalized Variational Principles, Knowledge Publishing House, Shanghai, China (1985), (in Chinese)Google Scholar
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    FanXiuchang, Using generalized variational principles to resolve the St. Venant's torsional bar with a crack, Applied Mathematics and Mechanics (English Ed.), 10, 2 (1989), 189–196.Google Scholar
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    R. S.Barsoum, Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements, Int. J. Num. Mech. Engng., 11 (1977), 85–97.Google Scholar
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    C.Manu, Quadratic isoparametric elements as transition element, Engng. Frach. Mech., 24, 4 (1986), 509–512.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Fan Xiuchang
    • 1
  • Wu Yueming
    • 2
  1. 1.Tianjin Institute of TechnologyTianjinP. R. China
  2. 2.Tianjin Financial and Economical UniversityTianjinP. R. China

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