Page 27 - eBook_Proceedings of the International Conference on Digital Manufacturing V2

Collaborative Study on Weight Optimisation of Lubricant Bottles under
Stacking Condition using Finite Element Analysis and Machine Learning

Depending on the value of N=2, the general polynomial form
of Mooney Rivlin 5th parameter strain energy potential model
(Sasso, Palmieri, Chiappini & Amodio, 2008) is described in
Error! Bookmark not defined. :

E = C (I − 3) + C (I − 3) + C (I − 3) +
2
20
1
2
10
1
01
C (I − 3)(I − 3) + C (I − 3) (1)
2
2
02
11
1
1

where C10, C01, C20, C11, and C02 are the material constants
(Sasso, Palmieri, Chiappini & Amodio, 2008). I1 and I2 are the
strain invariants (Muslov et al., 2023) which are functions of the
three principal stress, with λ1, λ2, and λ3 correspond to X, Y and
Z axis principal stretches, respectively (Muslov et al., 2023), as
shown in Equations (2) and (3):

I = λ + λ + λ (2)
2
2
2
1
3
2
1

I = (λ λ ) + (λ λ ) + (λ λ ) (3)
2
2
2
2 3
1 3
2
1 2

Boundary Condition

With the material properties defined, the next step is
preprocessing which includes discretisation and boundary
condition. To evaluate the mechanical behaviour of HDPE based
lubricant can and set up a SOP for calculating the total load
applied to a single can positioned at the lowest layer of stack, a
real-world stacking condition is simulated, as shown in Error!
Reference source not found.. For this purpose, the mass of pellet,
the mass of empty bottles with caps, the mass of fluid inside the
cans, and the mass of cartons themselves were also considered.
Error! Reference source not found. shows that the total load of
60N is applied to a single can positioned at the lowest layer of
stack, while the bottom of can is fixed with the carton’s surface to
replicate realistic constraints. Since the calculated hydrostatic
pressure (0.00163 MPa) is quite small, its effect can also be
neglected.
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