ZHANG Guo-qing, YU Jian-xing. Study of the Equivalent Theorem of Generalized Variational Principles in Elasticity[J]. Applied Mathematics and Mechanics, 2004, 25(3): 313-322.
Citation: ZHANG Guo-qing, YU Jian-xing. Study of the Equivalent Theorem of Generalized Variational Principles in Elasticity[J]. Applied Mathematics and Mechanics, 2004, 25(3): 313-322.

Study of the Equivalent Theorem of Generalized Variational Principles in Elasticity

  • Received Date: 2002-12-16
  • Rev Recd Date: 2003-10-28
  • Publish Date: 2004-03-15
  • The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functionals and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.
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  • [1]
    Hellinger. E.Der allgemeine ansatz der meshanik der kontinua[J].Encyclopadia der Mathematishen Wissenshaten,1914,4(4):602—694.
    [2]
    Reissner, E.On a variational theorem in elasticity[J].Journal of Mathematics and Physics,1950,29(2):90—95.
    [3]
    胡海昌.论弹性体力学与受范性体力学的一般变分原理[J].物理学报,1954,10(3):259.
    [4]
    Washizu K. On the variational principles of elasticity and plasticity[R]. Aeroelastic and Structures Research Laboratory, Massachusettes Institute of Technical Report,25-18.
    [5]
    钱伟长.高阶拉氏乘子法和弹性理论中更一般的广义变分原理[J].应用数学和力学,1983,4(2):137—148.
    [6]
    钱伟长.再论弹性力学中的广义变分原理——就等价定理问题和胡海昌先生商榷[J].力学学报,1983,(4):325.
    [7]
    李灏,陈树坚.断裂理论基础[M].〈应用数学和力学〉讲座丛书.重庆:重庆出版社,1983.
    [8]
    Fletcher D C.Conservation laws in linear elastodynamics[J].Arch Rational Mech Anal,1976,60(2):329.
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