Torsional boundary layer effects in shells of revolution undergoing large axisymmetric deformation |
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Authors: | F -C Su L A Taber |
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Affiliation: | (1) Institute of Biomedical Engineering, National Cheng Kung University, 70101 Tainan, Tainan ROC;(2) Department of Mechanical Engineering, University of Rochester, 14627 Rochester, New York, USA |
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Abstract: | Numerical and asymptotic solutions are developed to the equations governing large torsional, axisymmetric deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.List of symbols Latin symbols
a
General dependent variable
-
a
(mn)
Terms of the asymptotic expansion of a(x)
-
b
Characteristic length
-
c
Scalar curvature components in the normal direction
-
c
, c
,
, c
Cosine of
, respectively
-
C
Material constant with units of a Young's modulus
-
e
i
Deformed local orthonormal basis associated with ( , s, n) (x
1, x
2, x
3) coordinates
-
Undeformed cylindrical coordinate basis
-
Intermediate coordinate basis
-
g
Shear correction factor
-
H
Horizontal stress resultants
-
l
1
Strain invariant
-
k
![agr](/content/m6q6306202164m84/xxlarge945.gif)
Scalar curvature components
-
L
Undeformed cylinder length
-
M
![agr](/content/m6q6306202164m84/xxlarge945.gif)
Moment resultants
-
M
r, M
![agr](/content/m6q6306202164m84/xxlarge945.gif) , M
z
Moment resultant components in the basis
-
N
![agr](/content/m6q6306202164m84/xxlarge945.gif)
Membrane stress resultants
-
p
Internal pressure
-
p
H, p
v
Horizontal and vertical surface loads, respectively
-
p
i
Thickness-averaged surface tractions
-
Q
Transverse shear stress resultants
-
, r
Radial coordinate prior to, after deformation
-
R
Undeformed cylinder radius
-
, s
Meridional coordinate prior to, after deformation
-
s
, s
x,
, s
Sine of
, respectively
-
, S
Reference surface prior to, after deformation
-
S
1, S
2
Shear stress resultants parallel to the reference surface
-
S
3
Average transverse normal stress resultant
-
t
Und formed shell thickness
-
T
Axial torque
-
V
Vertical stress resultants
-
w
Two-dimensional strain-energy density function
-
w
n
Terms in expansion for w
-
W
Three-dimensional strain-energy density function
-
x
Undeformed axial coordinate in cylinder
-
, z
Axial coordinate prior to, after deformation |
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Keywords: | |
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