FIRST SOUTH EUROPEAN TECHNOLOGICAL MEETING
INTERNATIONAL CONFERENCE
The role of simulation in improving products development process
June 7 through 9, 2000
Principaute de Monaco
Title: The role of finite element technique in ship structural design.
Authors:
R. Dambra, R. Iaccarino, R. Porcari
CETENA - Italian Ship Research Centre
Genova - Italy
Abstract:
The finite element technique was introduced in ship design with a significant delay with respect to
other fields, as for example automotive, aircraft and aerospace industry, since the high degree of
conventionality of the vessels allowed a complete and effective structural scantling based on
experienced and consolidated rules.
In the last years, the development of unconventional vessels and the adoption of light and
advanced materials showed the limitations of the range of validity of the existing rules and gave a
very large impulse to the use of F.E. technique, making it a common and extensively used tool to
design the hull ship structure.
In the present paper a review and a state of the art of application of F.E. method to ship structural
design are reported, by presenting significant examples of analyses relevant to hull beam strength
calculation, collapse of structural components in advanced materials and impact simulations with
fluid-structure interaction.
1. INTRODUCTION
The finite element technique was introduced in ship design with a significant delay with respect to other
fields, as for example automotive, aircraft and aerospace industry, since the high degree of conventionality of
the vessels allowed a complete and effective structural scantling based on experienced and consolidated
rules.
In the last years, the development of unconventional vessels and the adoption of light and advanced
materials showed the limitations of the range of validity of the existing rules and gave a very large impulse to
the use of F.E. technique, making it a extensively used tool for facing a large number of different applications
in ship design.
In this paper some significant examples relevant to the application of F.E. technique to ship structural design
are reported. Examples make reference to global and local strength evaluation, to the collapse of structural
components in advanced materials and to impact simulations with fluid-structure interaction.
As far as the reported examples are concerned, particular emphasis is devoted to the fluid-structure
interaction, which represents one of the most recent numerical application in the field of ship design.
2. LINEAR ANALYSIS
2.1
Global Strength Evaluation
Global strength evaluation, generally means evaluation of the stress levels related to the hull beam
idealisation, considering the main global load effects due to both wave and still water conditions acting on
the hull as:

longitudinal bending moment, both hogging and sagging;

shear force;

torque moment.
Originally, this type of evaluation was simply made by considering the properties of the different transverse
hull sections such as section modulus, shear resisting area and torsion properties (structural capacity), and
comparing them with the global load effects relevant to those sections, i.e. bending moment, shear force end
torque (demand).
According to the computational capability increase, (both hardware and software), the approach adopted to
face this kind of analysis has been continuously refined, as reported:

adopting the shear stress flow distribution theory using a thin walled beam approach. In this case the
improvements mainly regard the evaluation of shear stress distribution within the longitudinally
extended structural elements, belonging to a specific ship cross section;

the adoption of F.E. technique, using a beam idealisation of the ship, (figure 2.1);

using a 3D - F.E. model of a part of the ship, (figure 2.2 - MSC/MARC);

using a 3D - F.E. model representing the whole hull structure, (figure 2.3 - MSC/NASTRAN).
As a matter of facts, the latter way to proceed allows a more complete overview of the structural behaviour of
the hull, and just from initial calculations, the designer can obtain useful information about:

global and local deflection;

stress concentration and structural behaviour in the main structural discontinuities of the hull and
superstructures;

the contribution level of the different decks versus longitudinal bending (especially for passengers
vessels);

the distribution of shear stress in the main structural components of the hull;

the stress level in pillar structural elements.
Fig. 2.1 - Hull beam idealisation
Fig. 2.2 - 3D model of two holds (MARC)
Fig. 2.3 - 3D global hull model of a cruise ship (NASTRAN)
2.2
Local strength evaluation
In ship structural design, the sentence local strength evaluation can be interpreted in two different ways:

the structural analysis of a limited part of the structure subjected to the loads directly applied on it;

the analysis of a limited part of the structure or what happens in a well defined structural detail when
the whole ship structure is subjected to the global load effects.
While the first meaning does not imply any new concept and represents a typical application of F.E.
technique, the second one represents a very ambitious objective, and large efforts are continuously
addressing in setting up of proper procedures to support the user in the substructuring process.
This kind of approach is particularly used for a better evaluation of stress concentration factors to be used
both in strength and/or in fatigue life considerations. A typical mesh refinement, inserted in a global 3D
model is reported in figure 2.4.
Fig. 2.4 - Example of substructuring
2.3
Stress concentration factor for fatigue analysis
From the point of view of fatigue phenomena, the substructuring process can be ideally continued up to
investigating very small parts or structural details. The analysis refers to a stiffened end bracket, as reported
in figure 2.5. In figure 2.6 the detailed model of the stiffened end-bracket is shown (MSC/MARC).
In this context, a further methodology that can offer a great help in local strength evaluation is represented
by adaptive-meshing procedure. This procedure is practically an automatic refinement of the mesh, that can
be guided by the user, and is based on two distinct methods: h-method and p-method.

In the h-method, refinement are obtained by subdividing the original elements. New generated
elements maintain the same polynomial order of the shape functions, (figure 2.7). Nodal links are
automatically generated in order to ensure congruity among old and new nodes.

In the p-method, the refinement of the model is obtained by increasing the polynomial order of the
shape functions of the elements.
So, adaptive method may represent a very useful tool for investigating stress levels in structural details, even
if the following criteria should be used:

starting from a 3D global model of the ship, adaptive meshing should be used after a first refinement
step of the whole model;

the actual geometry of the examined structure should be completely defined in the initial mesh. In
fact, it is not effective to deal with very fine meshes if the geometric shapes and details do not
correspond to the actual structure.
Fig. 2.5 - Stiffened end bracket - structural detail
Fig. 2.6 - Detailed F.E. model of a bracket (MSC/MARC)
Fig. 2.7 - Example of adaptive "h" meshing (MSC/MARC)
3
STATIC NON-LINEAR ANALYSIS
3.1
Collapse of stiffened panel in composite materials
This analysis describes the structural behaviour of a stiffener-shell joint (figure 3.1) under pull-off load,
(figure 3.2). The main objectives for the computational analysis of pull-off loaded stiffened panels are :

to simulate the non-linear structural behaviour up to collapse under pull-off load;

to set up and validate the theoretical analysis procedure, comparing results with experimental ones.
43.14
34.58
12.5 22.08
1 Stiffener table
2 Stiffener top flange
145
2 Stiffener web
85°
12.5
31
.29
2 Stiffener flange
3 Plate
87
23.04
Y
Z
X
272
Fig. 3.1 - Dimensions adopted in the F.E. model
3.2
Fig. 3.2 - Pull-off test description
Finite element model
In order to model the laminated composite plates a plane-strain model has been adopted. The orthotropic
specification of material characteristics allows to simulate the superposition of actual 0°/90° orientated
layers. As far as the modelling of the laminates is concerned, each WR layer has been modelled by two
orthotropic elements having characteristics able to simulate global WR characteristics, while each UD layer
corresponds, obviously, to a single orthotropic element. A general description of a typical 2-D finite element
should require the following constants:
Thickness
t
Young's moduli
E xx , E yy , E zz
Poisson's ratios
 xy ,  yz ,  zx
Shear moduli
G xy , G yz , G zx
Density

Element types from MARC library used for
F.E. calculations are :
- type 11 : 4-node arbitrary quadrilateral;
- type 7 : 3-node arbitrary triangular.
Fig. 3.3 - Section modelled by F.E.
In figure 3.3 the detail of the section as modelled by finite elements is shown. In Table 3.2 the adopted
stacking sequences for laminates identified in figure 3.3 by numbers 1 to 3, is reported. As previously
defined, each unidirectional ply corresponds to one element in the thickness of the section ; hence, in the
table, “number of plies” means “number of elements in the Y direction”.
Table 3.2 - Laminates properties
Laminate
number
1
2
3
Description
Stiffener table
Stiffener web
and flanges
Plate
Total thickness
[mm]
22.08
Number and type
of layers
24 UD 600 g/m2
Thickness per layer
[mm]
UD = 0.92
Number of
U.D. plies
24 UD 90° th = 0.92
12.50
13 WR 800 g/m2
WR = 0.96
23.04
24 WR 800 g/m2
WR = 0.96
13 UD 0° th = 0.48
13 UD 90° th = 0.48
24 UD 0° th = 0.48
24 UD 90° th = 0.48
The total number of nodes and elements are respectively 12424 and 12086, in figure 3.4 the mesh and
some particulars are shown.
Fig. 3.4 - Particulars of F.E. mesh.
3.3
Failure criteria and control
During the incremental calculation the following failure criteria have been adopted:

Azzi-Tsai criteria/failure index (f.i.) has been adopted for the “woven rovings” layers, (via MARC
user subroutine);

maximum stress and maximum strain for unidirectional layers;
maximum stress for filled material.

In addition, the MARC user subroutine (UACTIVE) has been used, to deactivate those elements in which the
100% of failure index is reached at all integration points.
3.4
Results
Results in terms of tangential stress, at two different calculation increments, are reported in the figure 3.5.
Increment 10
Increment 14
Fig. 3.5 - Tangential stress
In figure 3.6 the load displacement curve is reported, while the results obtained by the use of UACTIVE user
subroutine are shown in the next figure 3.7, in terms of deactivated elements, at different calculation
increments.
Fig. 3.6 - Load displacement curve
Increment 11
Increment 12
Increment 13
Increment 14
Fig. 3.7 - Deactivated elements (via UACTIVE user subroutine)
4
4.1
TRANSIENT DYNAMIC ANALYSES
Drop test simulation
Large impulse loads are experienced by a body during impact with water. This is often designated as
slamming. Both fore and bottom parts of a ship are exposed to slamming, as well as the deck between the
two hulls of a catamaran or a surface effect ship. Slamming loads can lead to structural damage as well as
induce whipping. Current trend to produce innovative, lighter and faster ships, increases the probability of
slamming and, in addition, lighter structures are more prone to slamming damage than conventional
structures. Both aspects ask for a better understanding and treatment of slamming loads and, in general,
conventional analyses are not able to provide good descriptions or exhaustive models for this kind of
phenomena.
The study of hydrodynamic impact between ship panels and a free water surface is traditionally dealt with
analytical methods and experiments, these latter being preferably carried out under controlled conditions
(drop tests). Direct calculations, even on medium sized hardware platforms, are nowadays feasible in terms
of time efficiency, by means of suitable finite element codes for transient analysis that include structure-fluid
interaction algorithms. This implies that an additional tool for accurate structural analysis can be available to
the naval architect in the near future.
The analyses were addressed to the study of flat ship panels impacting the calm water surface at prescribed
falling velocities. Analytical methods for wedge bodies break down when the impact angle approaches 0°
degrees. For grazing angles of incidence, a crucial role is played by the air entrapped between the structure
bottom and the water surface, which is responsible for a reduction of the impact loads amplitude
(cushioning), an increasing of the impulse rise-time and the creation of an air/water mixture at the interface
(coalescence). The flexibility of the falling body is responsible for a lowering of the impact load too. The finite
element simulation of the above problem needs a multi-fluid (water & air) approach for the fluid domain, the
modelling of the structural properties of the plate, equations of state for the fluids, a fluid-structure coupling
algorithm.
4.2
Numerical simulation strategy
MSC/DYTRAN is the code chosen to numerically simulate the impacts. In our analyses, the Lagrangian
solver is used for the structure modelling while the Eulerian method is applied to the fluid domain. The
General Coupling is adopted for the interaction of the structural/Lagrangian with the fluid/Eulerian mesh. The
General Coupling uses a coupling surface working as a boundary for the flow of the Eulerian material which,
in its turn, causes forces to act on the surface causing distortion of the Lagrangian mesh. As often the
Eulerian mesh is aligned with the basic co-ordinate system, the Fast Coupling Algorithm can be activated,
reaching a much higher computation efficiency. The most suitable among the models available in
MSC.Dytran can be used to model the yielding of the panel, which likely occurs in typical conditions.
A gamma law equation of state is adopted for the air (the pressure is a function of density, specific internal
energy and ratio of specific heats), and a polynomial equation of state is adopted for the water (the pressure
is a function of relative volume and specific internal energy). Typical impact configurations provide that the
plate falls from assigned quotes on the free surface; to save computation time, it’s not necessary to run the
simulation during all the period before the plate reaches the water. Nevertheless, as an appreciable deviation
from the atmospheric value in the air layer between plate and water takes place after the gap is reduced to
about 5% of the half breadth of the plate, such an elevation of the plate above the water must exist at the
beginning.
4.3
Example of calculation
The test body was a panel clamped on a box. The outer dimensions of the plate, including a 160 mm
support, were 2.270 m x 1.820 m. The dimensions of the unsupported span of the panel were 1.950 m x
1.500 m. Two stiffeners were applied at a spacing of 0.650 m. The panel thickness was 6 mm, stiffeners
were 140 mm x 8 mm. Panel material was Steel, having the following properties:
E = Young modulus = 210 Gpa
Y = Yield stress = 250 MPa
 = density = 8000 kg/m3
 = 0.3
The estimated total mass of the body (panel & supporting box) resulted 1200 kg. As far as fluids (air and
water) are concerned, the following properties were assumed:
Water
Air
Density (kg/m 3)
1000
1.293
Bulk modulus (GPa)
2.18
-
Ratio spec. heats
1.004
1.402
The atmospheric pressure value was assumed 0.1013 MPa and the gravity acceleration 9.81 m/s 2.
The impact configuration with the panel impacting the calm water surface at 0° degree, and an initial height
of free drop of 1.5 m, have been selected to be presented here in the following.
The structure was modelled using 2868 elements, and 2806 grid points. In particular, for the flexible panel,
900 quadrilateral (CQUAD4) elements were used; the stiffeners were modelled with 120 CQUAD4 and 60
rod (CROD) elements. The support and the box were modelled with 1788 CQUAD4 elements with rigid
properties. Isotropic elasto-perfectly plastic behaviour was assigned to the panel. A view of the modelled
impacting plate is shown in figure 4.1 (box not visible).
Fig. 4.1 - Impacting plate modelling
Fig. 4.2 - Lagrangian and Eulerian (half) mesh
The fluid domain was 5.0 m x 5.0 m x 3.0 m, with rigid walls. It was sub-divided into 43200 solid (CHEXA)
elements, with 47027 grid points. The upper 17280 elements (0.5 m height) were initially assigned to the air
domain, while the lower 25920 elements (2.5 m height) were assigned to the water domain. A view of half of
the fluid domain is visible in figure 4.2, together with the panel.
The adopted equations of state for water and air respectively were stated as below (p = pressure ;  =
density, E = spec. int. energy,  = ratio of spec. heats):
Water
Air
(   0)
p  a1  a 2  2  a3  3  (b0  b1  b2  2 )  0 E w
p  (  1)  a Ea
(   0)
p  a1  (b0  b1 )  0 Ew
   0w
 w
Ea  196
 0w
kJ
kg
J
kg
a1  2.18 GPa ; a2  8.43 GPa ; a3  8.01 GPa
b0  0.493; b1  1.39 ; b2  0.00
E w  205
The rigid body vertical motion of the whole box was monitored on a grid point of the rigid support; the result
in terms of velocity and acceleration is shown in figure 4.3 (different units used to super-impose the graphs).
In figure 4.4 distributions of the effective (Von Mises) stresses on the deformed panel are shown at t = 11
ms (at reaching of maximum values) on the three integration layers. Integration sub-layer 1 is the upper one,
layer 2 the middle one. During all the simulation time the yield stress is exceeded by the Von Mises stress
value on layer 1 only.
Monohull Steel panel - 0° deg - 1.5 m
Rigid frame motion
900
800
Velocity (cm/s)
700
600
Acceleration (m/s2)
500
a/v
400
300
200
100
0
-100
-200
-300
0.000
0.005
0.010
0.015
0.020
0.025
0.030
t(s)
Fig. 4.3 - Rigid body motion
Layer 1
Layer 2
Layer 3
Fig. 4.4 - Effective stress distributions (units : Pa)
The distributions of the pressure load on the impacting surface were recorded at intervals of 1 ms. Four plots
of pressure on the deformed panel, corresponding to t = 5, 10, 15 and 20 ms of simulation respectively, are
shown in figure 4.5.
t=5 ms
t=10 ms
t=15 ms
t=20 ms
Fig. 4.5 - Pressure distributions (units : Pa)
The pressure distribution plots indicate that initially higher values of pressure take place around the more
rigid areas (stiffeners and support), with lower values under the more flexible plates; afterwards maximum
pressure values are reached at the centre of the deformed plates between stiffeners. To deeper investigate
this point, an additional calculation was performed assigning rigid properties to the panel. The comparison in
terms of pressure loads for the point at the centre of the panel is shown in figure 4.6 below.
Monohull Steel panel - 0° deg - 1.5 m
Pressure loads - PANEL CENTRE
0.55
0.50
0.45
Flexible
0.40
0.35
Rigid
p (MPa)
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
0.000
0.005
0.010
0.015
0.020
0.025
0.030
t (s)
Fig. 4.6 - Pressure loads at panel centre– flexible/rigid comparison
The comparison seems to indicate that:



a first peak in the load impulse of the flexible case exists which corresponds to the peak of the rigid
panel case, but with amplitude attenuated by the upwards local motion of the panel (pressure release);
the second peak in the load pulse of the flexible case is due to the downward motion of the panel portion
between stiffeners, after the first inversion of the motion; this second peak is not present in the rigid
case;
the above points seem confirmed by the comparison flexible/rigid at a point located closer to a stiffener:
the effects of flexibility discussed above are reduced both on the first and on the second peak, figure 4.7
below.
Monohull Steel panel - 0° deg - 1.5 m
Pressure loads - POINT 22
0.55
0.50
0.45
Flexible
0.40
0.35
Rigid
p (MPa)
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
0.000
0.005
0.010
0.015
0.020
0.025
0.030
t (s)
Fig. 4.7 - Pressure load close to stiffener – flexible/rigid comparison
The selection of results shown above illustrates well the typical capability of a numerical approach both in
producing a large amount of information and in allowing to go deeper in the physical mechanisms of
phenomena.
Preliminary results from comparisons between our numerical predictions and experimental tests, performed,
within the Brite-Euram project SEAWORTH (BE-97-4469) sponsored by the EU, by the project partner TNO,
showed interesting agreement; an example is shown in figure 4.8 below for the pressure load.
Exper. / Numer. comparison - Point 22
h = 1.5 m -  = 0° deg
Pan. #3 - Test #22 - Point 22
4.0E+05
3.5E+05
TNO (experimental)
3.0E+05
CET (numerical)
2.5E+05
p (Pa)
2.0E+05
1.5E+05
1.0E+05
5.0E+04
0.0E+00
-5.0E+04
-1.0E+05
2.07
2.08
2.09
2.1
2.11
2.12
2.13
t (s)
Fig. 4.8 - Numerical/experimental comparison
2.14
2.15