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On second order asymptotic solutions of axial symmetrical problems ofr>0 thin uniform circular toroidal shells with a large parametera 2/R0h

  • Chen Guo-dong
Article
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Abstract

According to the classical shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a2/R0h. In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions.

Keywords

Asymptotic Solution Large Parameter Axisymmetric Problem Comparative Equation Ring Shell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

a

Radius of curvature in meridional direction of toroidal shell

\(\tilde C_1 \tilde C_2 \)

Arbitrary complex constants

E

Modulus of elasticity

H,V

Horizontal and Vertical forces

h

Wall thickness

Mφ,M0

Meridional and circumferential moments per unit length

Nφ,N0

Meridional and circumferential forces per unit length

Qφ

Transverse shear force per unit circumferential width

qH, qV

components of external loading forces per unit middle surface area of toroidal shell

R0

Radius of whole toroidal shell

r2

Radius of curvature in the circumferential direction of toroidal shell

r

r 2 sinφ

Nφ,Mθ

Meridional and circumferential strains

ν

Poisson's ratio

ϑ

Rotation of tangent to meridian

φ

Coordinate defining angular position on meridian of toroidal shell

V*,r#,ψ*

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

References

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Copyright information

© SUT 1988

Authors and Affiliations

  • Chen Guo-dong
    • 1
  1. 1.Tianjin General Paint FactoryTiajin

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