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Finite element method of a kind of new variational principle

  • Tang Song-hua  (唐松花)
  • Luo Ying-she  (罗迎社)Email author
  • Zhou Zhu-bao  (周筑宝)
  • Wang Zhi-chao  (王智超)
  • Li Qian-mei  (李倩妹)
Article

Abstract

A new variational principle is used to establish more reasonable finite element method, which set no limits to physical equations, that is, appropriate to general situations including elasticity, plasticity and rheology. According to theory of finite element method, tanking the Lagrange multiplier as unknown variables with unit joint stress, the corresponding calculating formula of the finite element method is derived. Through solving the equations about basic unknown variables, all unknown variables such as the strains and stresses in the whole solving area, can be work out. A problem about elastic body and a problem about Maxwell body are given and work out, and the results are both identical with the results in the corresponding literature. So the finite element calculating formula can be used to solve the problem of structure analysis with different stress-strain relations and may offer a new alternative way for some more complex problems, for example, the study on the elasticity-plasticity interface. And the other difference with the finite element calculation of common generalized variational principles is: the Lagrange multipliers are not determined beforehand, but to join in the calculating of finite element to get their physical meaning, the train of thought is more natural and the range for solving is expanded.

Key words

the least work consumption principle variational principle finite element method elasticity plasticity rheology 

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References

  1. [1]
    QIAN Wei-chang. Colloquia of Applied Mathematics and Mechanics[M]. Nanjing: Science and Technology Publication of Jiangsu, 1980. (in Chinese)Google Scholar
  2. [2]
    ZHOU Zhu-bao. The Least Energy Dissipation Principle and Its Application[M]. Beijing: Science Press, 2001. (in Chinese)Google Scholar
  3. [3]
    XIE Yi-quan. The Finite Element Method in Elastic and Plastic Mechanics[M]. Beijing: China Machine Publication, 1981.(in Chinese)Google Scholar
  4. [4]
    LUO Y S, DOHDA K, WANG Z. Experimental solution for viscosity coefficient of solid alloy material[J]. Int J Applied Mechanics and Engineering, 2003, 8(S1): 271–276.Google Scholar
  5. [5]
    East China Irrigation Institute. The Finite Element Method of Elasticity Mechanics Problems[M]. Rev. ed. Shanghai: Irrigation and Electricity Press, 1978. (in Chinese)Google Scholar
  6. [6]
    YNAN Long-wei. Rheological Mechanics[M]. Beijing: Science Press, 1986. (in Chinese)Google Scholar
  7. [7]
    YANG Ting-qing. Viscoelastic Mechanics[M]. Wuhan: Huazhong University of Science and Technology Press, 1990. (in Chinese)Google Scholar
  8. [8]
    ZHAO Zhi-ye, WANG Guo-dong. Modern Plastic Processing Mechanics[M]. Nanjing: Northeast Engineering College Press, 1986. (in Chinese)Google Scholar

Copyright information

© Central South University Press, Sole distributor outside Mainland China: Springer 2007

Authors and Affiliations

  • Tang Song-hua  (唐松花)
    • 1
    • 2
  • Luo Ying-she  (罗迎社)
    • 3
    Email author
  • Zhou Zhu-bao  (周筑宝)
    • 2
  • Wang Zhi-chao  (王智超)
    • 1
  • Li Qian-mei  (李倩妹)
    • 3
  1. 1.Institute of Fundamental Mechanics and Material EngineeringXiangtan UniversityXiangtanChina
  2. 2.School of Civil Engineering and ArchitectureCentral South UniversityChangshaChina
  3. 3.Institute of Rheological Mechanics and Material EngineeringCentral South University of Forestry and TechnologyChangshaChina

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