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The axial symmetrical problems ofa/r 2>1 toroidal shells with constant thickness

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Abstract

In this paper, the uniformly valid asymptotic solutions for the complex equation of the axial symmetrical problems of a/,r2>0 toroidal shells with constant thickness in bending theory are given.

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Abbreviations

a :

Radius of curvature of the meridional direction

\(\tilde C_1 ,\tilde C_2 \) :

Arbitrary complex constants

E :

Modulus of elaslicity

H,V :

Horizontal and vertical forces per unit circumferential width

h :

Wall thickness of the toroidal shell

M φ, Mθ :

Meridional and circumferential moments per unit length

N φ, Nθ :

Meridional and circumferential forces per unit length

Q φ :

Transverse shear force per unit circumferential width

q H, qV :

Components of external loading forces per unit middle surface area

R :

Radius of whole toroidal shell

r :

r=r 2 sinφ

r 2 :

Radius of curvature of the circumferential direction

M ϕ,Mθ :

Meridional and circumferential strains

ϑ:

Rotation of tangent to meridian

ν:

Poisson's ratio

ϕ:

Co-ordinate defining angular position on meridian of toroidal shell

ϕ0 :

Value of ϕ atr=0

V *,r*,ϕ* :

Values ofV,r, φ at upper edge of toroidal shell, respectively

References

  1. Chang, W., The state of stress in toroidal and similar shells with Azimental rings under torsionally symmetrically stress,Science Report of National Tsing Hua University,5 (A), (1949), 289–349. (in Chinese)

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  2. Chien, W.Z., Equations of symmetrical ring shells in complex quantities and their general solutions for slender ring shells,Journal of Qinghua University,19 (1979), 27–47. (in Chinese)

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  3. Clark, R.A., On the theory of thin elastic toroidal shells,J. Math. Phys.,29 (1950), 146–179.

    MATH  Google Scholar 

  4. Novozhilov, V.V.,The Theory of Thin Shells, Groningen, The Netherlands (1959). (in Russian)

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Authors and Affiliations

  1. Tianjin General Paint Factory, Tianjin

    Chen Guo-dong

Authors
  1. Chen Guo-dong
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Communicated by Chien Wei-zang

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Guo-dong, C. The axial symmetrical problems ofa/r 2>1 toroidal shells with constant thickness. Appl Math Mech 9, 597–602 (1988). https://doi.org/10.1007/BF02465415

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  • DOI: https://doi.org/10.1007/BF02465415

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