ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

oth deformations resulting from the shell bending and membrane effect and Hertzian
contact deformation must be considered.
The proposed analytical model can be applied for both fluid filled shells and empty
shells. In fact the fluid bulk modulus has no effect on the obtained response. Also the
total impact response and the start of transient pressure are not a function of fluid bulk
modulus.
By increasing the velocity of shell the maximum transferred force and the maximum
deformation increases, and the impact duration decreases. In a constant velocity by
increasing the attack angle, the maximum transferred force and maximum
deformation decease and the impact duration increases. The increase of positive
radius of curvature results in a decrease force. Also increasing the ratio of negative
radius of curvature increases the value of force. This means that a negative radius of
curvature (concave shell) is more dangerous than a positive radius of curvature
(convex shell).
α
Vsh
Equation
FEM
Error
Equation
FEM
Error
Equation
FEM
Error
0
Xmax Tp Fmax∆
0.706 1.43 10789
0.655 1.38 11407
7% 3% 5%
0.924 1.41 14588
0.875 1.39 14841
5% 1% 1.7%
1.14 1.389 18420
1.095 1.39 18853
4% 0.07% 2%
15
Xmax Tp Fmax∆
0.638 1.43 10400
0.633 1.39 11094
7% 2% 6%
0.894 1.4 14072
0.847 1.39 15095
5% 0.7% 7%
1.1 1.39 17767
1.06 1.39 18621
3.7% 0% 4.8%
30
Xmax Tp Fmax∆
0.617 1.44 9272.5
0.56 1.39 10600
10% 3% 14%
0.807 1.42 12547
0.76 1.39 13467.9
6% 2% 7%
0.995 1.399 15848.6
0.957 1.39 16827
4% 0.6% 6%
Table 1: The results for different cases of collision between head and stationary elastic torus shape object
6. REFERENCES
45
Xmax Tp Fmax∆
0.512 1.46 7490.8
0.457 1.385 8509.8
12% 5% 13%
0.669 1.43 10141.7
0.61 1.39 11874
9% 3% 17%
0.823 1.41 12818.7
0.777 1.39 14465.8
6% 1% 12%
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