Carbon fibre monocoque for a LMP3 racecar

THE 4th STUDENT SYMPOSIUM ON MECHANICAL AND MANUFACTURING ENGINEERING
Carbon fibre monocoque for a LMP3 racecar
J. Thomsen, M. Nør, N. Laue
Department of Mechanical and Manufacturing Engineering, Aalborg University
Fibigerstraede 16, DK-9220 Aalborg East, Denmark
Email: [email protected], [email protected], [email protected]
Web page: http://www.mechman.m-tech.aau.dk/
Abstract
In this project a monocoque is designed for a LMP3 racecar. The key points of the regulations for such a racecar
is presented. Small scale models in wooden sticks and cardboard are used to get a preliminary idea of the design
concept and composite layup. Material charts are used to find the best suited materials for a monocoque made of a
sandwich composite, based on shear strength and shear modulus for the core and compression strength and Young’s
modulus for the face sheets. A preliminary optimisation is done for the sandwich structure near the pickup points to
achieve an idea of the optimal size of the sandwich. A shell model analysis is performed to find a light weight design
of the monocoque that can sustain the loads both during driving and a potential crash. A detailed solid model analysis
is performed for a pickup point on the side of the nose. This is done to find a design that gives a low deflection and
to ensure that it can withstand the loads introduced in the pickup points. Intuitive design optimisation is done with
the objective to maximise the torsional stiffness to weight ratio and to ensure it can withstand a frontal impact.
Keywords: Finite element analysis, Composite materials, Light weight construction, Load modelling, Concept
development, Optimisation, Material selection
1. Introducion
This article concerns the design of a carbon fibre
monocoque for a LMP3 racecar. The monocoque is one
of the possibilities to make the chassis, that carries the
load. The objective of this project is to design such a
carbon fibre monocoque as light and strong as possible,
and this article describes the process in doing so. The
main focus is design of the monocoque with the roll
cage and pickup points. One of the main areas of focus
is to design the side of the monocoque in such a way
that it can withstand the loads while minimising the
deflection. If further explanations of the theory and
modelling in this article is needed, attention is directed
to the supplementary report to this article [1].
•
Measures restricting heights are taken relative to a
reference surface coinciding with the bottom of the
monocoque with a minimum rectangular area 800 mm
longitudinally and 900 mm across.
The regulations include templates which must be able to
fit inside the monocoque. These templates are collected
in figure 1 and give minimum dimensions of the cabin
part of the monocoque.
2. LMP3 regulations and templates
In this section the limitations setup by the regulations
[2] will be described. The LMP3 regulations limits
the design of the monocoque by giving restrictions on
several dimensions. The outer restricted dimensions of
the racecar are:
•
•
•
•
Rear overhang length: maximum 750 mm
Fig. 1 Left: Templates ensuring space for seats and door
access. Right: templates ensuring space for seats, driver’s
head and driver’s visibility.
Overall length: maximum 4650 mm
Overall width including bodywork: maximum 1900
mm and minimum 1800 mm
Height: Bodywork maximum 985 mm
Front overhang length: maximum 1000 mm
Template 1 ensures that the sides of the open part of
the monocoque are at least 500 mm high, because the
sides delimiting it may not be lower than the template.
Template 2, placed on the top face of template 1 in
1
figure 1, must be able to be inserted through each side
of the doors laterally until the templates are separated
300 mm symmetrically around the longitudinal plane
while the lower surface of the template are held parallel
with the reference surface. Template 3 ensures space
for the driver’s head and combined with template 2 it
ensures that the driver’s helmet can be removed without
bending the neck or spinal column. Template 4 and 5
define the driver’s view through the front windscreen
and side windows.
that stiffening of the bottom is needed, because the big
cross has a tendency to buckle. In the models, the sticks
lying in the diagonals carry the torsional loads while the
longitudinal sticks carry the impact load. From this, it is
indicated that the layup should mainly consist of ±45◦
and 0◦ layers along the longitudinal axis of the car.
The regulations state that two boxes giving space for
the legs and feet should be placed symmetrically around
the longitudinal centre plane and be 370 mm high and
330 mm wide and the upper edge of the footbox must
be 520 mm above the reference surface. The length is
restricted by the distance from the foremost position of
the driver’s feet to the vertical projection of the steering
wheel centre.
A rollover structure is mandatory and must consist
of a front and rear structure symmetrical around the
longitudinal plane of the car with dimensions specified
by the regulations.
Fig. 2 Small scale models made of wooden sticks and
cardboard. Top left: front model. Top right: middle model.
Bottom: cardboard monocoque.
3. Small scale models
The desing process started by building small scale
models. In this section the outcome will be described.
Small scale models with the scale 1:10 in wooden sticks
and cardboard are made to obtain experience of how
loads are carried through a chassis like structure. In
figure 2 the final stick models can be seen. Two have
been made; one for the front monocoque and one for
the middle.
The cardboard model can be seen in the bottom of figure
2. From this model it was noted that the addition of
side pods increase the torsional stiffness, which can be
increased further by closing the ends of the side pods.
The cardboard model’s sheets have a tendency to buckle
when exposed to a torsional load, and this has to be
taken into account in the design of the monocoque.
4. Basic concept of the monocoque
The basic concept of the monocoque is limited by the
regulations and by the demand from Aquila Racing Cars
saying that two persons should be able to be seated
in the car. Anthropometric data of a 95th percentile
European person is used to ensure that most people will
be able to fit in the car. These dimensions can be seen
in table I together with figure 3.
The monocoque should have high torsional stiffness and
high strength along the longitudinal plane of the car.
High torsional stiffness is wanted because the handling
gets less predictable the more the monocoque flexes.
Furthermore, a monocoque that flexes from larger strain,
is more prone to fatigue, and as the twisting motion
is not practical to dampen, a high stiffness is wanted
[3]. A high strength along the longitudinal axis is
wanted in consideration of a frontal crash. The torsional
load is added to the monocoque at the front and it is
fixed at the rear. The torsional stiffness is achieved by
triangulating the structure wherever possible. The rear
face of the front model is left open to leave room
for the driver’s legs. The middle model can not be
triangulated as simple as the front monocoque because
the templates and regulations delimits how the structure
can be composed. It is observed from the middle model
Based on the regulations, anthropometric data and
suspension geometry a basic concept was created. This
can be seen from above in figure 4. The length of the
monocoque including the drivetrain is defined from the
regulations as the maximum allowable length minus the
length reserved for front and rear overhang, resulting in
2900 mm from the front to the rear axle. From the 2900
mm the length of the drivetrain is subtracted. The engine
required by the regulations is a Nissan V8 Nismo V50,
but it has not been possible to find dimensions of this.
2
Instead dimensions of a Nissan V8 VH45DE engine,
which is similar to the V50 engine, have been found
to 890x740x725 mm (LxWxH) [4]. The length of the
gearbox is approximated based on a picture in which
the engine and gearbox both appear [5]. From this the
length of the gearbox is estimated to 1000 mm of which
350 mm is in front of the rear axle. Therefore 1350 mm
lengthwise in total is reserved for the drivetrain from the
rear centre axle up to the monocoque.
Number
9
11
14
16
17
19
21
22
Description of measurement
Sitting height
Shoulder height
Thigh clearance
Elbow to elbow breadth
Sholder breadth
Hip breadth
Abdominal depth
Knee height
The width of the monocoque in the front is chosen as
800 mm in order to ensure that the wheels are able to
turn 30◦ and at the same time ensuring enough space
for the footbox in the front.
The seats are placed asymmetrically around the longitudinal centre axis to make sure that there is sufficient
space for the driver’s feet. If they were not placed
asymmetrically the driver’s legs would intersect with
the nose necessitating the driver’s position to be angled
to the longitudinal axis. The passenger’s leg room will
be compromised but this will be of less concern as he
is not operating any controls. From the driver’s seat
cushion to the longitudinal centreline there is a free
distance of 45 mm giving room for a 80 mm wide beam
leaving some room to tolerances. The rollover structure
is placed as shown in figure 4 fulfilling the regulations.
The monocoque has a 270 mm front overhang such that
an acceptable suspension geometry can be obtained.
95th percentile
985
695
170
540
485
440
350
602
Tab. I 95th percentile body measures of the European
population. The numbers in the first column refer to the areas
shown in figure 3. Column three contains the measurements,
stated in [mm]. The measures are obtained from [6].
Fig. 4 The basic design concept seen from above. The red
boxes indicate seats
Fig. 3 Measurements which table I refers to. [6]
The outer width of the monocoque is determined by the
demand of having two persons seated inside. The size
of the seats are based on a RECARO Pro Racer SPA
[7] where a person of dimensions from table I fits in.
The seat is 860 mm high and has a width at shoulder
height of 575 mm and a width at the seat cushion of
455 mm. Even though the back of the seat is lower than
the sitting height given in table I the driver is still able
to fit because the seat is curving.
A smooth transition of the bottom of the monocoque
to the front overhang is implemented such that the
overhang is at least 50 mm above the reference surface
as required from the regulations. The length of the
monocoque will be 1820 mm including the 270 mm
front overhang. The height of the monocoque sides
delimiting template 1 are 500 mm high. The top of the
nose is 550 mm high to make space for the footbox
including the wall thickness of the monocoque. The
bottom of the nose is at a height of 120 mm. The wall
thickness of the entire monocoque for the preliminary
design is set to 30 mm.
A central lengthwise hollow beam will be placed in the
middle of the monocoque to increase the longitudinal
stiffness. To ensure space for two seats and some
additional space for the beam in the middle, the
monocoque is given a width of 1400 mm at it widest.
The side pots added to the small scale models are not
included in the basic concept, because the leftover space
3
is wanted for side mounted radiators. Aerodynamics
play an important role, and if the space is taken by
side pots it is not possible to make the air flow to the
rear wing and rear diffuser.
along the member. Force and moment equilibrium is
carried out on the points connecting the suspension to
the upright (figure 5 left) to find the loads transferred
to the pickup points. This is done by setting up the the
linear system of equations for the suspension:
5. Load situations for the monocoque
The monocoque will carry the components of the car
and transfer loads. The loads will primarily arise as
dynamic loads from driving and the load applied during
a crash. The loads during driving will be a mixture of
acceleration, braking and cornering. Bump loadings will
also have an effect on these. Data for friction coefficients
is obtained from the Tyre Test Consortium [8], [9]
for a Hoosier 20.5x7.0-13 tyre which is the tyre used
on the Formula Student racecar at Aalborg University
(AAU). This tyre is smaller than those on the LMP3,
but since tyre data is expensive to obtain it will be used
as an approximation. The data is examined for lateral
and longitudinal loads and give a peek longitudinal
coefficient of friction of approximately 2.3 and a lateral
coefficient of 2.2. The downforce is estimated from
aerodynamic data for a LMP2 racecar at 320 km/h
giving a load of 13300 N [10].
B
Upper Front
Ax = b
(1)
For the three force equilibrium equations A contains
direction vectors describing the direction of each rod
in the suspension, x contains the unknown forces and
b contains the external forces. For the three moment
equilibrium equations A contains vectors from the cross
product of the direction vectors with the external load, x
contains the unknown moments and b contains external
applied torques around the point where the pushrod and
lower wishbone are connected (point A). The force and
moment equilibrium is done with the steering wheel
pointing straight and an assumption of 50/50 weight
distribution front/rear and no weight transfer.
Combined load cases arise in the suspension members
when the car is accelerating, braking and cornering.
As seen in figure 5 right, the friction of the tyre is
not independent on whether the load is longitudinal
or lateral. The loads from driving in the suspension
members can be seen in figure 6. The highest single
load experienced by a suspension member is seen at 10◦
which is primarily braking with a little turning resulting
in 14600 N. Due to the assumptions taken and without
bumps taken into account a factor of safety of two is
applied, such that the maximum load used is 29200 N.
Longitudinal load
Upper Rear
C
Lateral load
Tie Rod
1.5
× 104 Size of forces at different points on friction ellipse
Upper rear
Upper front
Pullrod
Lower rear
Lower front
Steering arm
Lower Front
1
A
Force [N]
Pushrod
Lower Rear
0.5
0
-0.5
Fig. 5 Left: Illustration of the upright and the six rods
connecting it to the monocoque. The pushrod connects to a
spring and damper, the tie rod connects to the steering rack,
and the four remaining wishbone ends are attached to pickup
points on the chassis. The hub which the rim is mounted
onto, will be connected to the circular hole in the upright.
Right: Friction ellipse describing the friction between tyre
and road at a combination of longitudinal load (acceleration
and braking) and lateral load (cornering).
Fig. 6 Plot of the load along each of the suspension
members. The angle represents as; 0◦ is pure braking, 90◦
is pure cornering, 180◦ is pure acceleration and 270◦ is pure
cornering.
A pushrod suspension system will be used to transfer
the loads from the wheels to the monocoque, and if
designed properly all members in the suspension will
be in tension/compression meaning that the force acts
The load arising during a crash is estimated from the
regulations for a Formula 1 car [11] as no source is
available for LMP3. The Formula 1 regulations state that
240 kN will be applied from four crash tubes impacting
-1
-1.5
0
45
90 135 180 225 270 315 360
Angle
4
a steel plate mounted on the front of the car. No damage
of the survival cell is allowed during this crash. The 240
kN will be converted to an equivalent load for the LMP3
racecar by assuming the same acceleration for both cars
and applying Newton’s second law will give:
FLM P =
collecting all the material ratios for Young’s modulus
in one vector and normalizing it:
$
%
1/3
1/3
1/3
1/3
E2
E3
E1
En
ER =
...
ρ1
ρ2
ρ3
ρn
FF 1
240 kN
900 kg ≈ 308 kN
mLM P =
mF 1
702 kg
ER,norm =
ER
kER k
where mF 1 and mLM P is the mass of the Formula 1
and LMP3 racecar respectively. To this force a factor
of safety of 1.2 is added to make sure that potential
imperfections of the material is taken into account such
that the total crash load is 370 kN.
The same is done for the strength ratios resulting in the
vector σR,norm . The first entry in each of the normalized
vectors corresponds to the first material, the second
entry to the second material and so forth. The two
vectors are added together:
6. Material selection
The monocoque is constructed using a composite sandwich structure due to high stiffness/strength to weight
ratios as well as high energy absorption. The regulations
state that it must be a carbon fibre monocoque and therefore the face sheets of the sandwich will be as such. The
carbon fibre can be made with different kinds of resins.
The resins investigated here are; Bismaleimide (BMI),
Cyanate, Epoxy and Polyetheretherketone (PEEK). Data
for these types of carbon fibre reinforced polymers
(CFRP) are obtained from the software ESAComp’s
database, where data from several different manufacturers are available. The applicability of the material
will be based on Young’s modulus in the fibre direction
and compressive strength, both relative to the density
of the CFRP. The compression strength is chosen due
to the crash load being the strength limiting factor. The
tensile strength is not considered because the torsional
load from the wheels is too low to be concerned relative
to the tensile strength.
Λ = ER,norm + σR,norm
The resulting value of each entry of Λ corresponds to
a specific material and can be compared to the values
for the other materials. The material with the highest
value is the most suitable material. This material is
the epoxy CFRP HexPly 8552 UD IM10. The face
sheet material of the central lengthwise beam which
increases the crash strength will only be evaluated on
its compressive strength. The material with the highest
σ 1/2 /ρ is the BMI CFRP Umeco HTM556 UD HTS.
The material for the core will be evaluated based on its
shear strength and shear modulus, as the core is mainly
loaded in shear. The compressive strength of the core
is also important, but shear strength turned out to be
the governing parameter. Three different core types are
evaluated: foams, honeycombs and balsa. The foams
consist of PMI and PVC, while the honeycombs can
be made of aluminium, aramid and fibreglass. They are
evaluated by their specific shear strength and specific
shear modulus in the through the thickness direction in
the plane with the lowest value. The material with the
highest combined specific shear modulus and specific
shear strength is sought and found in the same manner as
for the face sheet, where the specific shear strength and
modulus are equally weighted. In doing so the optimal
core material is found to be 5052 Rigicell Aluminium
hexagonal honeycomb 1/8-2-.003-STD. This core has a
very low flexibility and is not suitable for all the parts of
the monocoque that have curvatures. Instead the optimal
flexible core is sought and found to be 5056 Aluminium
Flex-Core® 5056F80-0.0014 honeycomb. The Rigicell
core will however still be useful in plane areas where a
stronger core is needed.
Young’s modulus of the CFRP will be evaluated by the
cubic root of its stiffness to density ratio defined by the
following equation for a:
v=
E 1/3
ρ
The material giving the highest value of v will have
the lowest mass at a specific displacement of a plate
in bending [12]. In the same manner the compressive
strength to density ratio is evaluated for a plate in
bending from [12]:
v=
σ 1/2
ρ
A compromise between the two ratios will be made.
Each parameter is equally weighted. This is done by
5
7. Shape of the nose side
The shape of the nose side will be evaluated to find
the shape that gives the lowest deflection of the pickup
points. The four different shapes that will be evaluated
can be seen in figure 7.
along the longitudinal axis of the monocoque, where
each sheet has seven CFRP layers:
[0◦ , ±45◦ , ±45◦ , ±45◦ , core, ±45◦ , ±45◦ , ±45◦ , 0◦ ]
The sandwich is modelled with SOLSH190 elements,
while the adhesive and aluminium is modelled with
SOLID186 elements. The results of the analysis can be
seen in table III. The lowest displacement is achieved
Shape
Plane side
Inclined plane side
Convex side
Concave side
Tab. III The displacement for the four different shapes
Fig. 7 The four different shape options for the front
monocoque side. From the left they are: Plane side, inclined
plane side, convex side and concave side. The aluminium
plate and the adhesive is shown in purple.
from the concave side. The boundary conditions used
in the analysis are not fully representative, because the
actual boundary conditions will neither be fixed nor
simply supported. The actual load will not be distributed
over such a big area, and the aluminium plate adds
additional stiffness. Therefore, the results can only be
used to indicate which shape results in the lowest
displacement.
The four shapes are modeled in ANSYS Mechanical
APDL as a solid model. All of the models consist of
the side of the monocoque, an epoxy adhesive and a
aluminium plate which acts as the pickup point. The
model is fixed on the top and bottom surface and
the load is distributed over the aluminium plate. The
dimensions of the model is; height of 429 mm, length of
500 mm and thickness of 30 mm. The adhesive between
the aluminium plate and sandwich is 143 mm high,
500 mm long and 0.25 mm thick. The used material
properties can be seen in table II.
Aluminium
(7075-T6)
E 71.7·109 Pa
ν 0.33
Kg
ρ 2810 m
3
Epoxy
E 4.0·109 Pa
ν 0.30
Kg
ρ 1400 m
3
Carbon-epoxy
(AS/3501 - UD)
E1
125·109 Pa
E2
8.0·109 Pa
E3
8.0·109 Pa
ν12
0.30
ν23
0.49
ν13
0.30
G12 5.0·109 Pa
G23 4.0·109 Pa
G13 5.0·109 Pa
Kg
ρ
1550 m
3
Total displacement
0.946 mm
0.575 mm
0.684 mm
0.538 mm
To evaluate the four different shapes further, some
modifications are done to the modelling. Instead of
having one big aluminium plate simulating the pickup
point, a smaller aluminium plate with the pickup point
on top as another aluminium block is used instead,
see figure 8. The dimension of the aluminium plate is
40x40x5 mm and the block on top is 20x20x5 mm in
height, length and thickness. The adhesive between the
blocks is still 0.25 mm.
Aluminium honeycomb
(5056F80-0.002)
E1
E2
E3
2.14·109 Pa
ν12
0.5
ν23
ν13
G12 G23 1.65·108 Pa
G13 5.03·108 Pa
Kg
ρ
104 m
3
Tab. II Material properties for the used materials in the
analysis. The data for aluminium, epoxy and carbon epoxy are
obtained from [13]. The aluminium honeycomb is a Hexcel®
5056 Aluminium Flex-Core® 5056F80-0.002 honeycomb,
where the data is obtained from the ESAComp database. This
is not the same core as selected in the section 6, but since
this analysis is only used to determine which shape gives the
lowest deflection the core type is not important as long as the
same core is used for all the shapes.
Fig. 8 Model of the further developed pickup point with
mesh. To the right a close up view of the pickup point is
seen.
The layup, materials and elements are the same as
for the previous model. The load is split into two
components, such that a pressure of 5050 N is applied
on one of the sides of the pickup point, while 12200 N
is applied on top of the pickup point. The result, seen
in table IV shows that the concave side still has the
lowest displacement. However, the inclined plane side
The layup of the face sheets are oriented in the following
angles to obtain high torsional stiffness and stiffness
6
and Ef and that d ≈ c. The equivalent shear rigidity is
given by [15]:
only differs with 0.039 mm and it has a simpler shape
than the concave side. Therefore the inclined plane side
is the chosen design for the side of the nose.
Shape
Plane side
Inclined plane side
Convex side
Concave side
(AG)eq = b h Gc ≈ b c Gc
where the height h ≈ c for thin face sheets. (EI)eq and
(AG)eq is inserted into equation (3):
Total displacement
1.729 mm
1.282 mm
1.466 mm
1.243 mm
PL
2 P L3
(4)
+
2
B1 Ef b t c
B2 b c G c
This equation constraints the mass for a given deflection
and load condition. With the previously defined materials the optimisation from here is straight forward;
equation (4) is solved for t which is inserted into
equation (2). This is then derived with respect to c and
set equal to zero. This is solved for c, and can then be
substituted back into equation (4) and solved for t. The
optimisation is done based on the values in table V. The
dimensions for the panel are corresponding to those used
for the plane side shape in the previous section. Young’s
modulus for the face sheet is found from the 10% rule in
tension/compression using a 0◦ , ±45◦ , 90◦ layup. This
approximates the face sheet’s quasi-isotropic modulus in
the xy-plane [16]. The maximum allowable deflection
is based on the change in camber angle. When setting
up camber angles the usual measuring precision is 0.1◦ .
In order to create a change in camber of 0.05◦ with the
selected suspension geometry, it requires an out of plane
displacement of one of the pickup points of 0.29 mm.
The load is as defined in section 5. The optimisation
δ=
Tab. IV The displacement for the four different shapes with
the modified finite element model.
8. Preliminary optimisation of the sandwich structure
Optimisation will be done on the sandwich structure to
determine the optimum core and face sheet thickness in
the area around a pickup point, where the load case is
well defined. The area is considered as a fixed beam
with a central load as seen in figure 9.
P
t
z
c
y
x
d=c+t
t
L
Fig. 9 Load situation for the composite sandwich near the
pickup points.
Material properties
HexPly 8552 UD IM10
Rigicell Aluminium
1/8-2-.003-STD
Sandwich panel parameters
The sandwich is optimised based on obtaining the
minimum mass for a fixed displacement. The mass of
the sandwich is given by:
m = 2 ρf b L t + ρc b L c
(2)
Maximum deflection and load
This is the objective function, and it is subjected to a
stiffness constraint based on the deflection of the beam.
This contains two parts, one for deflection from bending
and one from shear [14]:
P L3
PL
δ = δb + δs =
+
B1 (EI)eq
B2 (AG)eq
Load situation
Clamped beam with central load
copt = 72 mm
ρf
1570 kg/m3
ρc
192 kg/m3
L
429 mm
δmax
0.29 mm
B1
192
topt = 1.3 mm
Ef
57.5 GPa
Gc
0.52 GPa
b
500 mm
P
29.2 kN
B2
4
Tab. V Material properties, dimension parameters and constants depending on load situation. The mechanical properties
are achieved from the ESAComp database and the load
constants are achieved from [14].
(3)
where B1 and B2 are constants dependent on where
the load is applied and how the beam is supported. The
equivalent flexural rigidity is given by [14]:
resulted in an optimal core thickness of 72 mm and
face sheet thickness of 1.3 mm. The optimisation does
not take the aluminium block on top of the sandwich
into account and the actual boundary conditions which
does not correspond to a beam fixed in both ends.
Therefore this optimisation merely gives an idea about
the preliminary thickness of the core and face sheet and
shows that the preliminary 30 mm sandwich thickness
should be increased.
Ef b t3 Ec b c3 Ef b t d2
Ef b t c 2
+
+
≈
6
12
2
2
where Ef and Ec is Young’s modulus for face sheet and
core respectively. The equation is approximated from
the assumption that t and Ec is small compared to c
(EI)eq =
7
9. Finite element analysis of the monocoque
A finite element analysis (FEA) is set up to be able
to see whether the monocoque can handle the loads
from driving and the frontal impact without failing.
Furthermore, the torsional stiffness of the monocoque
will be evaluated through this analysis. In the analysis
the driving load is applied to the upright, which
then transfers the load to the monocoque through the
suspension. The monocoque is fixed on a aluminium
block added to the rear bulkhead simulating the fixation
of the motor on the monocoque. During the frontal
impact test the load is applied to the front as described
in section 5. The model is made as a surface model.
Therefore the FEA uses shell elements based on first
order shear deformation theory and Reissner-Mindlin
plate theory. The roll over structure and suspension is
modelled with beam elements. The aspect ratios of the
mesh can be seen in figure 10.
The layup of the CFRP face sheets in the model is made
such that a high torsional stiffness and high strength
along the longitudinal axis of the car is obtained.
Because the crash load is the biggest load, a lot of
layers oriented in 0◦ are needed. To obtain a high
torsional stiffness layers in ±45◦ and ±30◦ are also
needed. However, not all regions of the monocoque are
experiencing the same type and intensity of loading and
therefore a uniform layup will not be used to improve
stiffness to weight ratio. The face sheet material was
selected in section 6 and will be used for all the layups.
The cores are made of Rigicell in plane areas, while
Flex-Core® is used on all curved sections due to its
higher formability. The core thickness varies, with a
thicker core in regions needing a higher moment of
inertia or regions with high out of plane loads. The
transitions between the cores are placed in locations
with low curvature. At the top rear rounding a PVC
foam core (Divinycell HCP 100;FC-/400) is used instead
of the honeycomb. This is due to large shear stresses at
a curved region where stronger aluminum honeycomb
is not formable enough and balsa is not strong enough.
Fig. 10 Aspect ratio for the elements used. The vast majority
have an aspect ratio of less than 2, and the worst elements
are in non critical areas.
Whether the model can sustain the loads is evaluated
based on different failure criteria. These are; Tsai-Wu,
Puck, max stress and max strain. They are evaluated for
each layer of the face sheet by ANSYS. Core failure is
evaluated based on whether the core fail due to shear
stresses or wrinkling of the face sheets occur.
Fig. 11 The highest inverse reserve factors for every element
in the monocoque.
In figure 12 the layup thickness can be seen. Hereof
it is seen that the rear bulkhead, connection areas near
the rollover structure and the front of the monocoque
are reinforced such that they can carry the applied load.
Contrarily, the bottom of the monocoque has a thinner
core and fewer reinforcement plies as much of the
frontal impact loading is carried by the central beam..
A plot of the worst inverse reserve ratio for every
element can be seen in figure 11. An upper limit of
0.8 was designed for, and is approached near load
introductions. Some areas show low values, but more
material is not removed as these areas play an important
role for displacement of pickup points and torsional
stiffness.
8
through the suspension tubes, with realistic spherical
bearing locations. The moment arising from the force
couple is then divided by angle measured at the uprights
in order to obtain the torsional stiffness.
A submodel of a pickup point has been done in ANSYS
Mechanical APDL as a solid model. This submodel
loads the forces on the boundaries from the shell model.
The pickup points are connected to the monocoque with
both an epoxy adhesive and M6 bolts as seen in figure
14.
Fig. 12 Layup thickness of the face sheets on the monocoque.
The rollover structure has an influence on the torsional
stiffness, and a compromise between the weight and
stiffness needs to be found. A parametric study was set
up in ANSYS where the tubes’ outer radius was set
to six different values varying from 10 to 35 mm. In
figure 13 the result from the parametric study on the
final monocoque design can be seen. In the end a 50x2
mm tube was used, as it provides a good compromise
between weight, stiffness, strength, and packaging.
Torsional stiffness (Nm/deg)
9
4
Torsional
stiffness as a function of mass
× 10
Fig. 14 The solid model of the area around one of the pickup
points.
8
The load from the suspension to the pickup point is
applied to the cube as a surface load. The elements in
the submodel are SOLID186. Near the pickup points the
face sheet is reinforced with carbon fibre plies lying in
0◦ , ±45◦ and 90◦ with eight layers in total. From the
results of the model it is seen that it can withstand the
loads introduced in the pickup point. When analysing
the nose side it is fulfilling the maximum stress failure
criterion and the maximum value was found in the
honeycomb with a value of 0.8. Furthermore, it is seen
that the bolt connection can withstand the load situation
the pickup point is exposed to.
7
Ro=35
Ro=30
Ro=25
Ro=20
Ro=15
Ro=10
6
5
4
55
60
65
70
75
80
85
Mass (kg)
Fig. 13 Torsional stiffness of the final monocoque with
six different outer radii. Wall thickness is varied from 1.0
mm to 2.5 mm in increments of 0.5 mm, with increasing
thickness showing higher stiffness and mass. Many of these
configurations result in templates being violated and/or the
monocoque failing under frontal impact.
10. Conclusion
A carbon fibre monocoque conforming to LMP3
regulations has been designed. It is based on a sandwich
structure consisting of CFRP face sheets and an
aluminium honeycomb core and a tubular steel rollover
structure. The final monocoque weighs 69.2 kg and
has a torsional stiffness of 75500 Nm/deg. This is
achieved by the use of a finite element analysis, where
a complete shell model of the monocoque has been
Torsional stiffness can be measured in a variety of
different ways, that can have a big impact on its
value. Here, torsional stifness is found by fixing the
monocoque at the engine mounting and applying a
force couple to the front uprights. These are connected
9
created. Different rollover structure configurations and
cross sections have been examined and a compromise
between stiffness and weight was selected. Furthermore,
a pickup point has been selected for detailed modelling
which is used to find both the form that minimise
deformation and assures that the side of the nose
withstand the loads introduced at the pickup point.
In the simulations the material choice is based on a
material selection maximising stiffness to weight ratio.
A baseline for face sheet and core thickness has been
determined based on a specific deflection for a relevant
load case. The load situations used in the simulations
are found by designing a suspension geometry and
examining tyre test data. Furthermore, a frontal impact
test has been defined by adapting a Formula 1 test
standard.
[6]
[7]
[8]
[9]
[10]
[11]
10.1 Further work
The places where local reinforcements have been made,
further studies should be done and mounting points
from other auxiliary components. This is particularly
at the pickup points, roll cage mounting points and
the engine to bulkhead interface. Optimisation based on
either shape or topology could also be done to further
improve the stiffness to weight ratio. Further design
for manufacturing should be done before realising this
design.
[12]
[13]
[14]
[15]
Acknowledgement
The authors of this work gratefully acknowledge
Sintex for sponsoring the 4th MechMan symposium.
[16]
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