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Hamiltonian system and the Saint Venant problem in elasticity

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Abstract

The traditional semi-inverse solution method of the Saint Venant problem, which is described in the Euclidian space under the Lagrange system formulation, is updated to be solved in the symplectic space under the conservative Hamiltonian system. It is proved in the present paper that all the Saint Venant solutions can be obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix.

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References

  1. B. Saint, Venant, Memoire sur la torsion des prismes, Paris Memoires des Savants etrangers, 14 (1956), 233–560.

    Google Scholar 

  2. S. Timoshenko and J. N. Goodier, Theory of Elasticity, third ed., N. Y. McGraw-Hill Book Co., (1970).

  3. I. S. Sokolnikoff, Mathematical Theory of Elasticity, 2nd ed., N. Y. McGraw-Hill Book Co., (1956).

  4. W. Z., Chien and K. Y., Yie, Theory of Elasticity, Science Press, Beijing (1956) (in Chinese)

    Google Scholar 

  5. W. X., Zhong and X. X., Zhong, Computational structural mechanics, optimal control and semi-analytical method in PDE, Computers and Structures, 37, 6 (1990), 993–1004.

    Google Scholar 

  6. W. X., Zhong, Computational structural mechanics and optimal control, Dalian University of Technology Press, Dalian (1993). (in Chinese)

    Google Scholar 

  7. W. X., Zhong, Plane elastic problem in strip domain and the Hamiltonian system, J. Dalian Univ. of Tech., 31, 4 (1991), 327–384. (in Chinese)

    Google Scholar 

  8. W. X., Zhong, On the reciprocal theorem and adjoint simpletic orthogonal relation, ACTA Mech. Sinica, 24, 4 (1992), 432–437. (in Chinese)

    Google Scholar 

  9. W. X. Chien, Eighty autobiography (1993). (in Chinese)

  10. Th.von, Karman and W. Z., Chien, Torsion with variable twist, J. Aeronautical Science, 13 (1946), 503–510.

    Google Scholar 

  11. W. Z., Chien, H. S., Lin, H. C., Hu and X. Y., Yie, Torsion Theory of Elastic Cylinder, Science Press, Beijing (1956). (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Research Institute of Engineering Mechanics, Dalian University of Technology, 116023, Dalian, P. R. China

    Zhong Wanxie, Xu Xinsheng & Zhang Hongwu

Authors
  1. Zhong Wanxie
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  2. Xu Xinsheng
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  3. Zhang Hongwu
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Project supported by the National Natural Science Foundation of China

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Wanxie, Z., Xinsheng, X. & Hongwu, Z. Hamiltonian system and the Saint Venant problem in elasticity. Appl Math Mech 17, 827–836 (1996). https://doi.org/10.1007/BF00127182

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  • DOI: https://doi.org/10.1007/BF00127182

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