Optimal design of a thick-walled pipeline cross-section against creep rupture |
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Authors: | Dr in? M Rysz |
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Affiliation: | (1) Institute of Mechanics and Machine Design, Technical University of Cracow, Warszawska 24, PL-31-155 Krakow, Poland |
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Abstract: | Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation
A
cross-sectional area
-
C, ,
creep rupture constants
-
K, n,
C
,
C
creep constants
-
F
dimensionless creep modulus
-
M
bending moment
-
N
axial force
-
a( ),b( )
internal and external radii of the cross-section
-
j
creep modulus
-
p
internal pressure
-
r, ,z
cylindrical coordinates
-
s
r
,s
,s
z
,t
r
dimensionless stresses
-
t
R
time to rupture
-
stress function
- , ( )
dimensionless internal and external radii
-
e
effective strain rate
-
kl
strain rates
-
rate of curvature
-
rate of elongation of the central axis
-
dimensionless radius
-
e
effective stress
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I
maximal principal stress
-
S
Sdobyrev's reduced stress
-
r
,
,
z
,
r
components of the stress tensor
-
measure of material continuity
-
measure of deterioration
With 7 Figures |
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Keywords: | |
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