Applied Mathematics and Mechanics

, Volume 13, Issue 12, pp 1077–1080 | Cite as

Hamiltonian system and simpletic geometry in mechanics of composite materials (II) —Plane stress problem

  • Zhong Wan-xie
  • Ouyang Hua-jiang


Fundamental theory presented in Part (I)[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix; then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress problems on rectangular area.

Key words

anisotropy linear theory of elasticity Hamiltonian matrix analytical solution semi-analytical solution/simpletic geometry 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Zhong, W.X., Method of separation of variables and Hamiltonian system,Comput. Struct. Mech. Appl.,8, 3 (1991). (in Chinese)Google Scholar
  2. [2]
    Zhong, W.X., Plane elasticity problem in strip domain and Hamiltonian system,J. Dalian Univ. of Tech.,31, 4 (1991). (in Chinese)MATHGoogle Scholar
  3. [3]
    Arnold, V.I.,Mathematical Methods of Classical Mechanics, Springer-Verlag, New York Inc. (1978).Google Scholar
  4. [4]
    Lehnichikii, S.G., Anisotropic Plates, translated by Hu Hai-chang Science Press, Beijing (1963).Google Scholar
  5. [5]
    Xu, Z.L.,Elastic Mechanics, People's Education Press, Beijing (1979). (in Chinese)Google Scholar
  6. [6]
    Qin, M.Z., Simpletic geometry and computational Hamiltonian mechanics,Mechanics and Practice,12, 6 (1990). (in Chinese)Google Scholar
  7. [7]
    Zhong, W. x. and Zhong, X. x., Computational structural mechanics, optimal control and semi-analytical method for PDE,Computer and Structures,37, 6 (1990).MATHCrossRefGoogle Scholar
  8. [8]
    Zhong Wan-xie and Ouyang Hua-jiang, Hamiltonian system and simpletic geometry in mechanics of composite materials (I)—Fundamental theory,Appl. Math. and Mech. (English Ed.),13, 11 (1992).MATHGoogle Scholar

Copyright information

© Shanghai University of Technology (SUT) 1992

Authors and Affiliations

  • Zhong Wan-xie
    • 1
  • Ouyang Hua-jiang
    • 1
  1. 1.Dalian University of TechnologyDalian

Personalised recommendations