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


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.


Asymptotic Solution Large Parameter Axisymmetric Problem Comparative Equation Ring Shell 
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Radius of curvature in meridional direction of toroidal shell

\(\tilde C_1 \tilde C_2 \)

Arbitrary complex constants


Modulus of elasticity


Horizontal and Vertical forces


Wall thickness


Meridional and circumferential moments per unit length


Meridional and circumferential forces per unit length


Transverse shear force per unit circumferential width

qH, qV

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


Radius of whole toroidal shell


Radius of curvature in the circumferential direction of toroidal shell


r 2 sinφ


Meridional and circumferential strains


Poisson's ratio


Rotation of tangent to meridian


Coordinate defining angular position on meridian of toroidal shell


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


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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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