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Applied Mathematics and Mechanics

, Volume 11, Issue 9, pp 895–900 | Cite as

Momental solution of spherical shells with variably nonlinear section under normal pressure

  • Jia Nai-wen
Article
  • 13 Downloads

Abstract

In this paper, spherical shell with variably nonlinear section that is widely used in engineering and its equation of the section,δ=δ0(1+βφ)2), is analysed to momental problem. The Euler solutions of internal forces are obtained under normal pressure.

Key words

nonlinear Euler equation variable thickness 

Nomenclature

Nφ,Nθ

Radial and troidal axial force per unit length in middle surface of the shell.

Mφ,Mθ

Radial and toroidal bending moment per unit length in middle surface of the shell.

Qφ

Radial shear of crossing per unit length in middle surface of the shell.

qφ,n

Component of distributed load along radial and toroidal and normal direction in middle surface of the shell.

v, w

Radial and normal component of displacement of middle surface of the shell.

r1,r2

Radial of curvature along radial and toroidal direction in the middle surface of the shell.

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References

  1. [1]
    Yang Yao-qian,TheTheory of Thin Shells, Railroad Publishing House (1981), 181–185. (in Chinese)Google Scholar
  2. [2]
    Jia Nai-wen, Progressing step by step and intergrating calculation of overcritical deformation of spherical shellow shells,Applied Mathematics and Mechanics,8, 2 (1987), 155–166.Google Scholar
  3. [3]
    Jia Nai-wen, Design of spherical construct with varying thickness,Special Structures, 26 (1989).Google Scholar
  4. [4]
    Xu Zhi-lun,The Elastic Mechanics (Volume II),Publishing House (1980), 229. (in Chinese)Google Scholar
  5. [5]
    Wang Shen-xing, Axisymmetric spherical shell with variable wall thick,Applied Mathematics and Mechanics,9, 2 (1988), 199–205.Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1990

Authors and Affiliations

  • Jia Nai-wen
    • 1
  1. 1.South China University of TechnologyGuangzhou

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