Abstract
In this paper, the uniformly valid asymptotic solutions for the axial symmetrical edge problems of thin-walled shells of revolution in bending are given.
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Abbreviations
- \(\tilde A_1 ,\tilde A_2 ,\tilde C_1 \cdot \cdot \cdot \tilde C_4 \) :
-
Complex constants
- B 1...B 4, ϕ, ϕ1 :
-
Real constants
- E :
-
Modulus of elasticity
- H, V :
-
Horizontal and vertical forces
- h :
-
Wall thickness of shell
- M ϕ,M θ :
-
Meridional and circumferential moments
- N ϕ,N θ :
-
Meridional and circumferential forces
- Q ϕ :
-
Transverse shear force
- r :
-
r=r 2sinϕ
- r 1 :
-
Radius of curvature of the meridional direction
- r 2 :
-
Radius of curvature of the circumferential direction
- s :
-
Merdional length is measured from a datum mark on the meridian of shell
- U :
-
U=r 2 Q ϕ
- δ:
-
Horizontal displacement
- ε:
-
Rotation of tangent to meridian
- μ:
-
Poisson't ratio
- ϕ:
-
Angle between a normal to shell and its axis of revolution
- r *,V *,s * :
-
Values ofr. V. s at upper edge of shell. respectively
- r 2*,s * :
-
Values ofr 2,s at lower edge of shell, respectively
- (...)0 :
-
Values of the (...) at some edge of shells or other
References
Timoshenko, S. and S. Woinwskly-Krieger,Theory of Plates and Shells, 2nd ed, New York (1959).
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Communicated by Chine Wei-zang
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Guo-dong, C. The axial symmetrical edge problems for thin-walled shells of revolution. Appl Math Mech 7, 1005–1016 (1986). https://doi.org/10.1007/BF01907603
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DOI: https://doi.org/10.1007/BF01907603