Civil Engineering Reference
In-Depth Information
analysis is focused on membrane structures having a history of external loadings,
the surface should be based on data measured after adequate iterative loadings.
The model proposed by Day (
1986
) is one of the
first attempts to avoid the
constraining assumptions of plane stress. His approach was used for the design of
the Schlumberger Research Centre and is based on strain mean and difference
functions (Eqs.
4.5
4.10
).
-
r
x
þ r
y
r
a
¼
ð
4
:
5
Þ
2
e
x
þ e
y
e
a
¼
ð
4
:
6
Þ
2
r
y
r
x
T
¼
ð
4
:
7
Þ
2
e
x
þ e
y
g
¼
ð
4
:
8
Þ
2
f
1
f
2
g
r
a
¼
eðÞþ
ðÞ
ð
4
:
9
Þ
f
3
f
4
g
T
¼
eðÞþ
ðÞ
ð
4
:
10
Þ
where
˃
x
warp stress
˃
y
fill stress
˃
a
mean stress
ʵ
x
warp strain
ʵ
y
fill strain
ʵ
a
mean strain
T
stress difference
g
strain difference and
f
1
to f
4
are functions that are to be determined using test data. The work of
Gosling and Bridgens demonstrated that:
Whilst providing a good correlation with the test data upon which they are based, [
…
]
surface plot of the function show that they do not provide stable interpolation between the
tested stress state (Gosling and Bridgens
2008
).
The model utilised for describing the material behaviour plays a fundamental role
in the accuracy of the numerical calculation generally adopted in the design of
membrane structure by means of specialised software. The work of (Galliot and
Luchsinger
2009
,
2010
) aims to reduce the computation time to be used in engi-
neering by means of a simple non-linear material model which describes the yarn-
parallel behaviour of PVC-coated polyester fabrics subjected to biaxial tension.
