Applied Mathematics and Mechanics

, Volume 6, Issue 5, pp 417–430 | Cite as

New solutions of Novozhilov's equation of toroidal shells

  • Dong Ming-de


New solutions are obtained for Novozhilov's equation of toroidal shells having general slenderness ratio 0<a<1 (a=a/R). In contrast to the results by continued fraction technique, the exponents and expansion coefficients of our series solutions are all closed and explicit. The series satisfies shell equation identically. Convergence proof is also demonstrated.

Explicit expressions for boundary effect and monodromy indices are also given. Finally, we discuss the possibility of applying the present method to solve the fundamental system of equations for elastic shells with rotational symmetry.


Mathematical Modeling Industrial Mathematic Expansion Coefficient Explicit Expression Present Method 
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  1. [1]
    Novozhilov, V. V.,Theory of Thin Shells, GESL (1951). (in Russian)Google Scholar
  2. [2]
    Chien, W. Z., S. L. Zheng, General solutions of axial symmetrical ring shells,Applied Mathematics and Mechanics,1, 3 (1980). 287–300. (and literature cited)Google Scholar
  3. [3]
    Chien, W. Z., S. L. Zheng, Calculations for semi-circular are type corrugated tube-applications of general solutions of ring shell equation,Applied Mathematics and Mechanics,2, 1 (1981), 97–111.Google Scholar
  4. [4]
    Dong Ming-de,Poincare's Problem of Irregular Integrals. (Lecture Notes, to be published)Google Scholar
  5. [5](a)
    Dong Ming-de, Non-perturbative solutions of Bloch-Mathieu Hamiltonian system,Physics Letters,97A, 7 (1983), 275–279.Google Scholar
  6. [5](b)
    — The problem of secular terms: Non-perturbative analysis of Hill-Bloch system,ibid.98A, 4, Oct. (1983), 156–160.Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1985

Authors and Affiliations

  • Dong Ming-de
    • 1
  1. 1.Institute of Theoretical PhysicsAcademia SinicaBeijing

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