AD ALTA
JOURNAL OF INTERDISCIPLINARY RESEARCH
where:
λ
t max
maximum specific strain energy,
λ
D
maximum allowable strain energy.
Dangerous condition occurs in the specific strain energy for
changing the shape:
=
1+
3
2
,
(2)
where:
poisson ratio,
Young's modulus,
maximum allowed stress.
Whichever is:
=
1+
3
(
1
2
+
2
2
+
3
2
−
1
.
2
−
1
.
3
−
2
.
3
), (3)
where:
1
first principal stress,
2
second principal stress,
3
third principal stress.
Parameters
1,2,3
are principal stresses in each direction.
Substituting relations (2) and (3) to (1) and by adjusting receive
strength condition according HMH hypothesis for the spatial
state of stress:
=�
1
2
+
2
2
+
3
2
−
1
.
2
−
1
.
3
−
2
.
3
≤
, (4)
where:
reduced stress according HMH hypothesis.
For planar state of stress is valid relation:
=�
1
2
+
2
2
−
1
.
2
≤
.
(5)
For planar state of stress given by the normal and shear stresses
τ:
=√
2
+3
2
≤
,
(6)
where:
τ
shear stress.
Using HMH strength hypothesis, it is possible to calculate the
reduced stress without the knowledge of the principal normal
stresses. The reduced stress can be directly calculated for a given
state of stress by 6 independent components of the stress:
=
√2
2
.��
−
�
2
+�
−
�
2
+(
−
)
2
+6.�
2
+
2
+
2
�≤
, (7)
where:
normal stress in directions X,
normal stress in directions Y,
normal stress in directions Z,
shear stress in directions X,
shear stress in directions Y,
shear stress in directions Z.
The maximum allowed stress can be seen from relation:
=
,
(8)
where:
yield strength for the material,
safety factor (for the chosen material mostly
determined by relevant standard),
maximum allowed stress.
In the case of LNG tanks, which are the subject of this paper,
safety factor is determined by IMO standard. This standard
prescribes a safety factor
=1.5 for all load cases specified in
this standard (Lisowski et al, 2010).
Computational models of vessels were made based on
ideological proposals, where individual dimensions were chosen.
Models were modified so that the all parts that do not affect the
stress have been removed from ideological models. For stress
analysis, it has not been take into account the strength of
insulation. Its impact was specified as the mass on the inner shell
(Stopka et al, 2016).
5.1 Loading
Maximum allowed working pressure of tanks is prescribed up to
10 bar it was prescribed on inner shell. Vacuum between shells
was prescribed like pressure of the value 130 MPa on the
internally sides of shell and atmospheric pressure of value
101,325 kPa prescribed on external side of outer shell. Portable
tanks and their fastenings should be capable of withstanding
separately applied forces, based on:
1.
twice the total mass acting in the direction of travel of the
tank simultaneous with the weight of the tank;
2.
the total mass acting horizontally at right angles to the
direction of travel of the tank (where the direction of travel
is not clearly determined, the total mass should be used)
simultaneous with the weight of the tank;
3.
the total mass acting vertically upwards;
4.
twice the total mass acting vertically downwards.
Impact of LNG was included in the computation by the
hydrostatic pressure as follows according to standard four load
cases (Figure 2).
Figure 2 Hydrostatic pressure for all load-cases (Source: authors)
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