hard grounding of large sailing...
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HARD GROUNDING OF LARGE SAILING YACHTS
H. Conradi, Hamburg University of Technology, Germany, [email protected]
H. Hoffmeister, DNV GL, Germany, [email protected]
S. Ehlers, Hamburg University of Technology, Germany, [email protected]
Running aground with a sailing yacht can result in significant damage to the structures of a yacht;
particularly at high speeds. The prediction of grounding forces and an associated maximum speed is
therefore an important precaution measure to remain inside the structural design envelope; to obtain
robust structures at predictable grounding scenarios. Since current classification rules do not explicitly
regard the vessel’s speed, an improved method of predicting grounding forces is desired. The aim of
this work is to investigate the forces that act on a sailing yacht during grounding. A nonlinear finite
element analysis of a large sailing yacht is performed, that accounts for plastic deformation of the keel
bulb, elastic deformation of the keel fin and hull as well as hydrostatic restoring forces. The influence
of the yacht’s initial velocity, draft and ballast/displacement ratio is investigated. Furthermore, the
grounding force experienced by a yacht with a crashworthy bulb is examined.
NOMENCLATURE
Symbol Definition Unit
Length between perpendiculars (m)
Draft (m)
Displacement, fully loaded (t)
Density (
Torsional spring stiffness ( )
Pitch Angle (deg)
Initial velocity ( )
Von Mises Stress ( )
Yield Stress ( )
Engineering Stress ( )
True Stress ( )
Engineering Strain ( )
True Strain ( )
Strain Rate ( )
1 INTRODUCTION
Grounding of a sailing yacht can differ significantly from
other vessels, due to the yachts unique geometry. The
keel, in which the ballast of the yacht is concentrated,
extends significantly below the actual draft of the hull.
Modern yachts often feature a “T-keel”, that consists of a
keel fin with a foil shaped cross section and a lead bulb,
attached to the bottom end of the fin. Grounding of a T-
keel yacht is likely is likely to happen as a collision
between bulb and ground. A severe case of grounding is
“horizontal grounding”, in which the bulb hits a rigid
wall, frontally. The collision forces act in the opposite
direction of the vessels forward movement, resulting in
large reaction forces due to inertia and most likely in
damage to keel and hull structure. A worst case of
damage is the total loss of the bulb, resulting in a
dramatic reduction of hull stability.
In grounding, several factors influence the magnitude
of the forces, that act on the keel and hull. The vessel’s
mass and velocity prior to grounding determine its
kinetic energy and impulse. Plastic deformation of the
bulb prolongs the collision time, thus reducing the
maximum force and absorbing kinetic energy. Elastic
deformation of the keel fin and hull structure from the
imposed bending moment result in further reduction of
the maximum force. The yacht’s pitch motion causes
waves, which absorb some energy, while hydrostatic
restoring forces increase the moment acting around the
transverse axis at the keel root.
More recently, initiatives are undertaken to improve
structural predictability and thus to reduce pecuniary
risks associated with grounding. Keel manufacturer
APM-Keels performed a finite-element analysis (FEA)
on a “crash-save bulb”, that relied on slits to reduce its
stiffness. In the simulation, the bulb impacted into a rigid
plate at an initial velocity of 12 m/s. The slits helped to
prolong the collision time between bulb and plate and
reduced the reaction force by 40%, compared to a regular
bulb [1].
References on conventional ship grounding or collision
analysis and consequence assessments can be found, i.e.,
in ICCGS [2]. Extensive research like this is not
available for sailing yachts. An assessment of the
grounding force by estimating the deceleration of the
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yacht has been presented in literature [3]. In their rules
for yachts, classification society DNV GL provides the
following equation to assess the horizontal grounding
loads [4]:
( 1 )
With being the horizontal grounding force,
gravitational acceleration, displacement of fully
loaded vessel and bulb mass. This formula neglects
some aspects that are believed to be influencing the
magnitude of the grounding force, such as initial velocity
and stiffness of the yacht’s structure and bulb. Today,
owners and operators desire a clearer correlation between
boat speed and possible damage. Therefore, the present
research project is initiated by DNV GL to improve
methodologies and refine scantling rules.
It is assumed, that the bulb experiences large
deformations during grounding. Thus, it is deemed that
FE calculations will have to be performed as non-linear
type. To reduce computational effort, some
simplifications are made. It is assumed, that hydrostatic
restoring forces are greater than hydrodynamic forces,
acting on the hull due to the pitch movement of the
yacht. Therefore, hydrostatic pressure will be
implemented into the finite element (FE) simulation,
while dynamic effects are neglected. The elasticity of
keel fin and hull structure determine the overall stiffness
of the system and influence the maximum grounding
force. Based on the assumption that keel fin and hull
structure deform elastically, their stiffness can be
combined as a rotational spring that connects hull and
keel.
2 MODELLING
2.1 LS-DYNA
LS-DYNA is a keyword based, explicit finite element
solver, well suited for simulations that involve large and
plastic deformations. Simulations are performed on the
HPC cluster of the TUHH, using LS-DYNA version
7.1.2.
Meshing has been performed with ANSYS Workbench,
where the use of tetrahedron elements delivered the most
satisfactory results. Tetrahedron elements can experience
volumetric locking, which leads to an overestimated
stiffness, compared to hexahedron elements. To
overcome this, averaged nodal pressure (ANP)
tetrahedrons with four nodes and one integration point
are used. Strains and stresses are calculated as in
standard linear tetrahedrons, with additional averaging of
nodal pressures to reduce volumetric locking [5]. ANP
tetrahedrons are implemented into LS-DYNA as element
type 13 and are described to be well suited for
applications including incompressible material behaviour
of ductile metals with isochoric plastic deformations [6].
Plastic deformation of the bulb will be caused by
compression forces. Since most materials have different
a compressive strength than tensile strength, a material
model is chosen that differentiates between the two. The
material that is implemented as keyword *MAT_124, is
an isotropic elastic-plastic material. Two load curves
and are defined, representing yield stress
versus plastic strain for tension and compression [7]. The
sign of the mean stress is used for differentiation between
the two. A positive mean stress represents tension. Strain
rate effects are regarded by multiplying the stress-strain
curve with a strain rate dependent factor. This factor is
determined using the Cowper-Symonds model, that
calculates the strain rate dependent strengthening of the
material as follows:
( 2 )
In which is the strain rate, and are constants and
is the ratio between dynamic and static stress.
2.2 PROPERTIES OF LEAD-ANTIMONY ALLOYS
Lead’s high density of and
availability, compared to denser materials, make it the
ideal ballast for sailing yachts. Nonetheless, production
yachts often feature cheaper keels of cast steel. Pure Lead
has a low tensile strength of 17 MPa, compared to 400-
550 MPa of common steel. However, the addition of
alloying elements, such as antimony, strengthen the
material significantly. An antimony content of 3.5%
doubles the lead alloy’s tensile strength, whereas 8%
antimony alloys possess three times the strength of soft
lead. Since lead creeps under static load, it has no
definite yield strength. In yacht design, the antimony
content of the keel bulb must be balanced to be large
enough to support the bulbs own weight, while
maximizing the density of the ballast. Generally, more
performance oriented yachts feature lower contents of
antimony. Since the application of lead as a structural
material is rare, few sources about its mechanical
properties are available. While manufacturers provide
ultimate tensile strength and elongation [8], stress-strain
curves, influence of strain rate effects and compressive
strength were found in older publications [9]. Therefore,
material tests were conducted to validate the material
model used in the simulation.
2.2.1 Material Test Setup
Material Tests were performed with lead specimens of
1.5% antimony content. The dimensions of the
specimens were defined to satisfy DIN standards for
tensile [10] and compression tests [11]. Compression
tests were performed with cylindrical specimens,
featuring the same height as their diameter of
. The cylindrical specimens were placed
between two horizontal and parallel bearing surfaces.
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Testing was performed displacement controlled, using
hydraulic cylinders.
Tensile tests were performed with flat specimens
(Figure 2.1), that were fitted in serrated grips. The
dimensions were determined to avoid plastic deformation
within the grip area, by satisfying the following
condition:
( 3 )
With and being the cross-section areas of
gage and grip and and being yield strength and
ultimate strength. Since the yield strength is unknown
and strain rate effects may account for additional
ultimate strength, a ratio of of 0.2 is chosen.
The dimensions of the grip are determined by the testing
machine, which features a width of ,
resulting in a gage width of . The tensile
specimen feature a reduced section of with
a thickness of . The grip has a height of
. The total length of a specimen is
. Specimen were cast in an open, preheated
mould.
Figure 2.1: Flat specimen according to DIN 6892-1
2.2.2 Material Test Results
Tensile tests were performed in the strength laboratory of
the Institute M-10 at Hamburg University of Technology
at a strain displacement of , ruling out
strain rate dependency. The engineering stresses and
strains of individual specimens up to breaking varied
significantly (see Figure 2.2). Several probes failed due
to blowholes, enduring only 1/5 of the expected stress
and 1/10 of the elongation. Other specimens endured
twice the stresses and strains expected from literature
values. Since casting of the specimens took place over an
extended period of time, the molten material might have
segregated. Antimony may have deposited in the upper
part of the melting pot, due to its 40% lower density. The
increased antimony concentration could have resulted in
specimen with higher strength.
Figure 2.2: Tensile test results. Black, dashed curve
represents material curve selected for the FEA.
Based on the observations made above, the tensile test
that matches literature values best was chosen for the
stress-strain curve to be used in the simulation. The curve
has an engineering stress of 24 MPa and reaches an
engineering strain of 15% at breaking. These properties
align well with specifications by manufacturer Vulcan,
who states a tensile strength of 26 MPa at 16%
elongation [8].
Compression tests were performed at different strain
displacements, to evaluate strain rate effects.
Compression tests delivered much more consistent
results and showed a logarithmic influence of strain rate
effects (Figure 2.3). Chosen displacements are
, and .
When compared to the tensile test results, it stands out
that yield strength under compression is more than twice
of that in tension.
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Figure 2.3: Compression test results (previous page).
Black, dashed curve represents material curve selected
for FE. Yield stress versus Displacement (top). Black,
dashed line represents logarithmic trendline.
The significantly higher strength of lead under
compression than in tension, is important to note for the
simulation, since the stiffness of the bulb will be mostly
determined by its compression strength. For the material
curve to be used in the simulation, measured engineering
stresses and strains are converted into true stresses and
strains (see Figure 2.4):
( 4 )
With true strain , engineering strain , true stress
and engineering stress .
Figure 2.4: True stresses and strains. Negative values
represent compression.
The stresses and strains from the material tests were
then converted to be used in LS-DYNA. Discretizing a
geometry results in stiffness changes, based on mesh
resolution and used element type. Therefore, the material
curve obtained by material testing needed to be
calibrated to match the element size and type, that will be
used in the grounding simulation. This was realized by
analysing the material tests in a FEA. The element size of
the simulated specimen was chosen to be as coarse as
possible, since the same element size must be used in the
later grounding simulation. Figure 2.5 explains the
process of aligning the FE material curve with the
stresses and strains obtained by material testing. True
stress-strain curve from the material test is used as input
data for the first iteration of the remodelled material test.
The simulation result is compared to the result of the
actual material tests. The stress-strain curve is then
modified to improve agreement of the FEA and actual
material test results. This process is repeated, until the
simulation result matches the material test result.
Figure 2.5: Procedure of aligning the stress-strain curve
used in FE with the material test
After modifying the stress-strain curve under tension,
the elongation in the FEA reached 87% of the elongation
from the material test, compared to 82% of the
unmodified stress-strain curve. Due to a lack of necking
in the FEA, further accordance with the material test
could not be achieved. Under compression, the
elongation at yield strength was overestimated by 30%
and was reduced to 5%, by modifying the material curve.
In each of the figures below (Figure 2.6), three stress-
strain curves are shown. One resembles the result from
the material tests, the other two are the material curve
used in the last FEA iteration and the respective
simulation result. The stress-strain curve used in the
material definition of the last simulation will be applied
in the grounding simulation.
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Figure 2.6: Comparison of material test result with FE
input and FE output of last iteration for tension (top) and
compression (bottom)
2.2.3 Mesh Refinement Study
To obtain accurate results in the full-scale grounding
simulation, an element size of 5 mm, which also has been
used in the FE material tests, was applied to the bulb. To
reduce the number of elements needed, the mesh
resolution is finest within 500 mm of the contact area. In
greater distance of the contact, the mesh resolution is
gradually reduced (see Figure 2.7). Results of
simulations with element sizes of 5 mm, 10 mm, 20 mm
and 50 mm have been compared. The contact force of the
coarsest mesh is 3% greater, while the keel root force is
the same as in the simulation with 5 mm elements. An
overestimation of 3% is deemed acceptable, compared to
a 98% reduction of elements and the corresponding
increase in performance.
Figure 2.7: Mesh refinement of the bulb
3 GROUNDING SIMULATION
3.1 EXAMPLE OF BALTIC 175 “PINK GIN VI”
The example, chosen for the grounding simulation, is
175 feet (53.9 m) “Pink Gin VI”, that is being built at
Baltic Yachts, in Finland. The Baltic 175 is
representative for a modern super-yacht, that reaches
high speeds, thanks to a comparatively low displacement.
“Pink Gin VI” has a lifting keel that can reduce its draft
from 7 m to 4.5 m. The lifting keel is mounted in a keel
trunk, which extends to the deck. The trunk is supported
by a bulkhead, resulting in a high local stiffness, in the
keel area. It is assumed that the speed and structural
stiffness of the Baltic 175 can result in large loads in case
of grounding, which makes her a good example for this
study.
3.2 FINITE ELEMENT MODEL
The FE model of the Baltic 175 consists of one
deformable and four rigid bodies (Figure 3.1). The front
part of the bulb is defined as plastically deformable,
whereas the remaining part of the bulb, keel fin, hull and
the plate that resembles the obstacle are defined as rigid.
The rigid back of the bulb is simplified as a box. Mass
and inertia is assigned to the hull and keel parts.
Figure 3.1: Part definition for the grounding simulation
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3.2.1 Keel Fin and Hull Stiffness
It is expected that elastic deformation of keel fin and hull
prolongs the contact time during collision and therefore
reduces the peak force. Even though modelled as rigid
bodies, the elastic stiffness of keel fin and hull is
regarded by implementing a rotational spring, that
connects hull and keel. The combined rotational spring
stiffness of hull and keel is:
( 5 )
Hull stiffness is derived from a FE simulation
performed by GURIT, the structural designer of “Pink
Gin VI” [12]. In the simulation, the DNV GL grounding
loads were applied on the bulb tip of the keel, which was
modelled from overly stiff, solid elements. The
simulation also included rig forces in dock condition.
The hull stiffness is derived as deflection per force from
the simulation. Similarly, keel stiffness is derived from
an FE simulation, performed on behalf of APM, who
manufactured the keel [13]. As in the simulation
described above, the grounding force is applied to the
COG of the keel bulb. The keel fin is constrained by
contact elements at the bearings.
3.2.2 Hydrostatic Restoring Forces
Hydrostatic pressure is applied to the hull by using the
keyword *LOAD_SEGMENT_SET. The magnitude of
the pressure is determined by a user defined function,
using the keyword *DEFINE_FUNCTION. The function
calculates the hydrostatic pressure based on the
segment’s z-position and sets it to zero, if the z-position
is greater than zero. This is implemented as follows:
*DEFINE_FUNCTION
$# fid heading
5hpress
$# function
float hpress(float z, float z0)
{
float fac1, refz, rho, grav;
refz = 0.; rho = 1.025e-9; grav = 9810;
fac1 = 1.0;
if(z>refz) fac1 = 0.0;
return fac1*rho*grav*(refz-z);
}
4 RESULTS
Grounding simulations were performed at five different
initial velocities, ranging from to
, or an equivalent of Froude numbers from
to .
Figure 4.1 shows the contact and keel root force
progression for an initial velocity of . The
cross-section at the centreline of the bulb at four different
time-steps is presented below. At the beginning of the
collision, the reaction force of the plate progresses
steeply, up to a peak at (1). The bulb bounces
back from the plate, forcing the keel to rotate backwards,
reducing the contact force to ¼ of the first peak (2). The
stiffness of the torsional spring builds up resistance
against the backward rotation of the keel, which
transmits forces between the keel and the so far
unaffected hull, resulting in the maximum force (3). The
pitch-motion of the yacht rotates the keel back from the
plate, which ends the contact and causes the contact force
to drop to zero (4).
Figure 4.1: Contact force and keel root force progression
(top) and bulb deformation (bottom)
Up to its first peak (1), the force vs. time curve is
identical to that of a simulation excluding the hull.
Whereas the sole keel would rebound from the plate after
the first peak (2), a simulation involving the hull leads
the force vs. time curve to increase, again. Thus, the
second peak (3) in the force progression is a result of the
hull’s inertia. This is reflected in the keel root force,
which is zero during the first peak (1), but rises to its
maximum with the second peak (3).
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4.1 INFLUENCE OF HYDROSTATIC FORCES
Figure 4.2 shows a comparison between a simulation
with implemented hydrostatic forces and a simulation
without. The movement of the yacht over the course of
the collision is displayed above a graph with the contact
force and pitch angle progression. It stands out, that at
(3), when the force reaches its maximum, the
pitch angle is small, at 0.5°. The pitch angle progression
curves of the two simulations separate only when the
force is already declining, rendering the influence of
hydrostatic forces insignificant.
Figure 4.2: Yacht’s movement (top) at four different
time steps and contact force progression on primary axis,
with pitch angle on secondary axis, for a simulation with
and without hydrostatic pressure (bottom)
4.2 INITIAL VELOCITY
Figure 4.3 displays the maximum forces over initial
velocity, that occur over the course of the collision. The
upper curve resembles the maximum contact force,
acting between bulb and obstacle and the lower curve
being the keel root force, acting between keel fin and
hull. The forces increase linearly with initial velocity,
with the keel root force being about 22% lower than the
contact force.
Figure 4.3: Maximum contact force and keel root force
over initial velocity
4.3 ANTIMONY CONTENT IN LEAD ALLOY
Simulations with four different material curves were
performed, representing lead alloys containing 0%, 1.5%,
4% and 8% antimony. The simulations were performed
at an initial velocity of . As expected, higher
amounts of antimony result in greater stiffness and
consequently higher grounding forces. Figure 4.4 shows
the maximum contact and keel root force over the
antimony content. The force increase from pure lead to
an alloy with 8% antimony is 35%, while the ratio
between contact force and keel root remains constant.
Figure 4.4: Maximum Contact force and keel root force
versus antimony content of lead alloy
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4.4 STRUCTURAL STIFFNESS
The effect of the elasticity of keel fin and hull structure
in the keel area is assessed by varying the stiffness of
the rotational spring that connects hull and keel by
factors of 0.5 and 2. Figure 4.5 displays the progression
of the contact forces versus time for an initial velocity of
. A 50% lower stiffness reduces the
grounding force by 17%. A 100% greater stiffness
increases the grounding force by 26%. In both cases, the
keel root force is about 25% smaller than the contact
force.
Figure 4.5: Contact force progression for different
structural stiffness factors.
This shows that a lower structural stiffness prolongs
the collision time effectively and has a similar impact on
the grounding forces as the stiffness of the bulb material.
4.5 DRAFT
The draft of the Baltic 175 is varied by a factor of 0.5
and 1.5. The resulting maximum contact and keel root
force versus draft is shown in Figure 4.6. While the
maximum keel root force decreases uniformly with
greater drafts, the maximum contact force plateaus
between draft factor 1 and 1.5. This is due to a similar
force progression as in Figure 4.5, where the first peak in
the force progression is its maximum.
Figure 4.6: Contact force progression (top) and
maximum contact and keel root force (bottom) for
different drafts
4.6 BALLAST/DISPLACEMENT RATIO
The ratio between ballast and hull mass is varied while
keeping the displacement constant. Figure 4.7 shows the
maximum contact and keel root force over the
ballast/displacement ratio. An increase in
ballast/displacement ratio results in a larger contact force
and smaller keel root force.
Figure 4.7: Maximum contact and keel root force versus
ballast/displacement ratio.
4.7 CRASHWORTHY BULB
There are different concepts to reduce the grounding
force, that generally aim to prolong the collision time
while reducing the maximum force. One concept of keel
manufacturer APM is the implementation of vertical slits
into the bulb, that run longitudinally through the front
part. Those have the advantage of removing little
material from the bulb and therefore conserve its density,
while maintaining section modulus against bending
under own weight.
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For this study, a simulation with five longitudinal slits
has been performed. The slits extend 1.2 m backwards
from the tip of the bulb. The slits are 100 mm apart and
feature a width of 10 mm, reducing the total volume of
the bulb by 0.5%. The simulation has been performed at
an initial velocity of .
Figure 4.8 shows the deformation of the slitted bulb as
well as the force progression versus time. Compared to a
regular bulb, the first force peak is reduced by 22%,
whereas the second force peak is reduced by 12%. The
longitudinal force in the keel root is reduced by 14%,
compared to a regular bulb.
Figure 4.8: Deformation of a crashworthy bulb (left
column) and force progression in contact and keel root,
compared to a conventional bulb (top)
The arrangement of the slits has not been optimized,
thus it is assumed that the reduction in grounding force
can potentially be reduced further. In the present
simulation, the root of the outer webs is significantly
wider than that of the inner ones. Their higher resistance
against bending locks the inner webs, which results in
higher stiffness. Additional slits or a more even spacing
of the existing ones may lead to further reduction in
stiffness and grounding force.
5 CONCLUSIONS
A method of assessing the grounding forces experienced
by a sailing yacht has been successfully demonstrated. A
nonlinear FEA was performed to evaluate the influence
of plastic deformation of the keel bulb, while the
simplified implementation of the yacht’s structural
stiffness as a rotational spring reduced computational
effort. The investigation delivered valuable insights, such
as the negligible influence of hydrostatic restoring forces.
Material tests have shown, that lead features a more than
two times greater yield strength under compression, than
under tension. Further material tests that aim at
compression strength for different lead alloys are
recommended for future research projects.
The DNV GL rules predict a grounding load of 3.2 MN
for the Baltic 175. Based on the research of this paper, it
can be assumed that this force acts on the hull structure
when grounding occurs at a velocity of 4 knots. Since the
Baltic 175 is capable of much higher speeds, the actual
grounding loads might exceed the ones predicted by the
rules.
This paper presents an intermediate result on the
research currently done on horizontal grounding of
sailing yachts. A parametric study, which has not been
concluded at the time of completion of this paper,
investigates the grounding forces of yachts with different
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displacements. The aim is to find a general approach of
assessing horizontal grounding forces on sailing yachts.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the help of Baltic
Yachts, for providing the geometry of the Baltic 175 and
the permission to use the yacht as an example for this
study. The authors also thank Schumacher Metall for
providing specimens for material testing. Further
contributions were made by APM-Keels, who provided
data about crash-save bulbs, GURIT, who provided FEA
results on the Baltic 175 and judel-vrolijk, who
contributed weight calculations.
REFERENCES
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[3] L. Larsson, R. E. Eliasson and M. Orych,
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appendages,” in Rules for Classification - Yachts,
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[12] GURIT, “Baltic 175 Longitudinal Grounding
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AUTHORS BIOGRAPHY
H. Conradi is graduating as M.Sc. in Naval Architecture
and Ocean Engineering from the Hamburg University of
Technology (TUHH). He currently writes his master
thesis on the topic of grounding of sailing yachts at DNV
GL.
S. Ehlers, D.Sc., is a professor for design and analysis of
ships and offshore structures and the head of the institute
for ship structural design and analysis at the Hamburg
University of Technology (TUHH). He is an expert in
consequences assessment for accidental events and
further in the field of material modelling for non-linear
finite element simulations. Furthermore, he is developing
new ice material models to assess the ice-structure
interaction and design methods for ice going vessels. He
is concerned with the overall structural response and
strength of ships subjected to extreme conditions.
Additionally, he combines optimization techniques with
extensive assessment procedures to obtain new concepts.
H. Hoffmeister has been working for Classification
Society DNVGL (former Germanischer Lloyd) since
1993, as graduated Naval Architect. Since, he has been
involved in the assessment of marine structures, yachts
and rigs, developed several standards and guidelines,
amongst which are the GL Guidelines for Structural
Design of Racing Yachts. Thus, his particular field of
expertise is the evaluation of composite structures.
Parallel to his employment at Germanischer Lloyd,
Hasso Hoffmeister was member of the design team of
“United Internet Team Germany” for the Americas Cup
2007 as the team’s rig designer.
The Fourth International Conference on Innovation in High Performance Sailing Yachts, Lorient, France
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