1. Principal Roll Structure Design Using Non-Linear Implicit
Optimisation in Radioss
David Mylett, Dr. Simon Gardner
Force India Formula One Team Ltd.
Dadford Road, Silverstone, Northamptonshire, NN12 8TJ, UK
dave.mylett@forceindiaf1.com
simon.gardner@forceindif1.com
Abstract
Driver safety is the most important aspect to consider in the design of any Formula One car,
especially in the event of a rollover. The design of the principal roll structure for a Formula
One car is strictly governed by a number of FIA regulations, and most importantly, must
satisfy a static load test as described in Article 17.2 of the FIA 2011 Formula One Technical
regulations:
FIA 17.2: Principal roll structure test:
A load equivalent to 50kN laterally, 60kN longitudinally in a rearward direction and 90kN
vertically, must be applied to the top of the structure through a rigid flat pad which is 200mm
in diameter and perpendicular to the loading axis.
The primary objective of this study is to show how Non-Linear Implicit Optimisation using
RADIOSS can be employed in the detailed design of a principal roll structure. As part of this
study the targets listed below must be met.
FIA compliance
Lightweight
Ease of manufacture
Compressed design time
Keywords: Topology Optimisation, Geometric Non-Linear, Implicit, Free Shape.
1.0 Introduction
The high safety standards within Formula One (F1) have become one of the sports many
trademarks. Over the 61 year history the governing body the FIA have strived to improve
the safety afforded to the drivers and are constantly looking at ways to further improve the
safety to all involved within F1.
One of the first and most important safety features introduced into the sport in 1961 was the
addition of the principal roll over bar. Since then, the teams have pushed the boundaries of
design to ensure the principal roll structure is as light as possible, with minimal influence on
aerodynamic performance, whilst providing the best protection for the driver in the event of
a roll over.
In order to ensure the principal roll structure provides the best protection to the driver, the
FIA outlines a number of strict regulations governing the design and minimum strength
requirements for the structure. These are outlined in FIA technical regulations [1] article
15.2 Roll Structures, and article 17 Roll Structure Testing, with the main regulation
concerning the strength of the roll structure outlined below:
© Altair Engineering 2011 1

2. 17.2: Principal roll structure test :
A load equivalent to 50kN laterally, 60kN longitudinally in a rearward direction and 90kN vertically, must be
applied to the top of the structure through a rigid flat pad which is 200mm in diameter and perpendicular to the
loading axis.
17.1.3: Under the load, deformation must be less than 50mm, measured along the loading axis and any
structural failure limited to 100mm below the top of the rollover structure when measured vertically.
Force India F1 Team employs CAE tools in order to meet these minimum structural
requirements and ensure minimum mass whilst adhering to the aerodynamic constraints.
Optimisation software such as OptiStruct are used during the design & development
process to assist in reducing the number of design iterations and time taken to design a
lightweight and robust component.
This paper will show the processes involved with designing a principal roll structure for a
Formula One car and provide an overview of the new non-linear optimisation capability
within Altair HyperWorks 11.
2.0 Background
Since the mid 80s the principal roll structure has also acted as the air intake for the engine,
either as a separate metallic component with an aerodynamic shroud, or as an integral
carbon structure incorporated directly into the chassis laminate.
As with most areas of a Formula One car the maximum air intake area is governed by
regulation and over the past few years the design of intakes have varied considerably
between the teams (see Figure 1). It is normally the role of the aerodynamics department to
define the external shape of the principal roll structure, and it is then up to the structural
analysts and design teams to design the primary load bearing structure which will be
contained within this volume.
Figure 1: Typical Formula One Air Intake Designs
Due to the high location of the principal roll structure (highest point on a Formula One Car);
it is paramount to ensure the mass is at a minimum. Mass this high up on the car can have
a significant effect on the centre of gravity and as a consequence has a negative effect on
the handling of the car. As roll structures can weigh anywhere from 1-3kg a significant
amount of mass can be saved within one component.
© Altair Engineering 2011 Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss Bulk 2

3. 3.0 Optimisation Process
Typically the design process for a principal roll structure would be performed in 2 discrete
stages:
1. A linear topology optimisation would be performed using the aerodynamic shape as a
design volume, with constraints such as mass, compliance and stress being among the
most important design considerations.
2. A manual iterative non-linear analysis is performed, initially based on the results from
the topology optimisation. Here the non-linearity of the problem can be exploited to
further reduce the mass of the structure.
This second phase of the design process however can be very time consuming, as the
linear model has to be converted into a non-linear model (either OptiStruct Non-linear or
Radioss Block implicit/explicit) and analysed iteration by iteration until the desired non-linear
targets are achieved.
New to HyperWorks 11.0 is the ability to perform a non-linear optimisation from within
OptiStruct. The method allows optimisation of models containing material & geometric non-
linearity as well as contact using either an implicit or explicit solution sequences.
The non-linear optimisation process within OptiStruct v11 uses the following process:
Solve non-linear analysis
Calculate equivalent static loading (ESL) conditions; approximate the non-linear
solution using linear analysis
Optimisation using ESL
Convergence check & loop
The method uses a dual loop optimisation process as shown in Figure 2.
Figure 2: Dual Loop Optimisation Process
© Altair Engineering 2011 Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss Bulk 3

4. This offers a very efficient technique for optimisation of non-linear events as it only requires
a small number of non-linear simulations. The design is optimised for loads which are
recalculated after every iteration of the outer loop.
The method can be used for concept design optimisation (topology, free-sizing and
topography) as well as design fine tuning optimisation (size, shape free-shape).
4.0 Topology Optimisation
Figure 3 shows the initial aerodynamic shape used to encapsulate the principal roll
structure. This aero surface provides the initial design space used to define the topology
optimisation domain with the loads applied as per the FIA regulation 15.2.2 & 17.2. The
optimum material distribution within the design space is calculated using topology
optimisation.
Figure 3: Aerodynamic Surface
Topology optimisation is performed with symmetry & manufacturing constraints to ensure a
manufacturable solution is obtained whilst maintaining an acceptable linear stress limit and
objective to minimise mass. From this initial optimisation study, OptiStruct was able to
reduce the mass of the original model by over 70%, Figure 4.
Initial Design Domain Optimised Topology Results Initial Detailed Design
Figure 4: Topology Optimisation Process & Results
Once the initial topology results have been detailed into a manufacturable solution, a linear
check analysis is performed and the results of this can be seen in Figure 5.
© Altair Engineering 2011 Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss Bulk 4

5. Combined Max. Von-Mises Stress Critical Load-case
Values less than 1 < y
Figure 5: Initial Detailed Design Results
As can be seen from the results above, the rationalisation from the topology results has left
areas where the stress levels are at unacceptable levels. Furthermore the critical load-case
plot clearly shows that the second load-case (Reversed FIA Load: proven by calculation) is
the primary load-case to consider for the design of the structure.
This is where the traditional second phase iterative non-linear analysis is performed to
ensure the stress levels are within the material limits, and to assess areas where
reinforcement is required or areas where excess material can be removed.
5.0 Non-Linear Shape Optimisation Definition & Results
The results from the initial detailed design show there are areas within the structure that are
below the yield of the material and so can be further optimised to reduce mass. There are
also areas within the structure that are in the elastic-plastic region of the material, but as the
primary analysis is performed using a linear solver, the true magnitude of this stress is not
known.
The normal design procedure would dictate that a set of iterative non-linear analyses would
need to be performed in order to further reduce the mass of the part. This can be a complex
and time consuming process, however, this can now be automated with the combination of
geometric non-linear free shape optimisation.
Free-shape optimisation moves the nodes on the outer surface of the structure, and the
mesh is altered to meet specific pre-defined objectives and constraints. The main
advantage of this type of optimisation is that the user is relieved of having to define many
shape perturbations, and the movement of the outer boundary is automatically determined
by the solver during the optimisation. During free shape optimisation the normal directions
of the outer elements change with the change in shape of the structure, thus for each
iteration, the design grids move along the updated normals.
In order to limit the total amount of deformation of the free-shape design region, the
maximum shrinkage and growth limits can be included within the Free Shape optimisation
along with mesh smoothing parameters to help avoid mesh distortion. Another useful
boundary condition to consider during free-shape optimisation is the use of a boundary
mesh. In this case the aerodynamic defined surfaces can be used to constrain the growth
and shrinkage in the design domain.
After the free-shape optimisation was set-up, material non-linearity data was added by
including a material stress-strain curve. The geometric non-linear analysis type was
selected for the load-case type to allow for large displacements.
© Altair Engineering 2011 Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss Bulk 5

6. Geometric non-linear analysis is automatically controlled within the software code and the
Bulk Data input is directly translated into Block format input without any user intervention.
The Starter and Engine are then executed with the results brought back into the Bulk data
output module to export the different output formats.
This ability to run geometric non-linear analysis directly from the OptiStruct bulk data means
the free-shape optimisation is able to utilise this automatic conversion. This allows non-
linear materials and geometry to be optimised directly from one source file.
In the case of this free-shape optimisation, the initial 2 sub-cases within the OptiStruct bulk
data are solved as a non-linear analysis (RADIOSS implicit). The equivalent static loads are
calculated to mimic the non-linear results, and then an OptiStruct Linear optimisation is
performed, with the process looped until the optimisation converges on a solution.
Figure 6 shows the result output from the geometric non-linear free-shape optimisation.
Here the free-shape optimisation has been set up to include full material non-linearity with
stress constraints within the design domain allowed to go above the yield of the material
(but below UTS). A minimal mass objective was set whilst also observing maximum
displacement constraints.
Optimisation Loop 1 Optimisation Loop 2 Optimisation Loop 3
Optimisation Loop 4 Optimisation Loop 5
Figure 6: Free-Shape Optimisation Results
This 2nd stage optimisation was able to further reduce the mass of the part by over 16%,
whilst still meeting the FIA test requirements. During this optimisation process the optimiser
ran 5x non-linear loops, with each linear optimisation converging in less than 8 iterations.
The total time taken for such an analysis was in the order of ~4hours running in core
memory on an Intel Core i7 CPU.
The results obtained from the Free Shape optimisation can be immediately re-surfaced in
CAD and a much higher confidence in the structural integrity of the part passing first time is
achieved.
© Altair Engineering 2011 Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss Bulk 6

7. 6.0 Discussion of Results
Figure 7 below shows the analysis results for the final optimised shape, and compares the
results from a geometric non-linear analysis to those generated from a traditional linear
analysis.
Final Shape: Non-Linear Analysis Results Final Shape: Linear Analysis Results
Von-Mises Stress (Combined Max. Results)
Displacement (Combined Max. Results)
Figure 7: Comparison of results for Non-Linear & Linear Analysis
The results from the linear analysis show the displacement has been underestimated by
~3.4% and in critical areas of the roll structure the stress has been over predicted by ~7-
15%. This would normally lead to the addition of more mass to reduce the stress in the
areas of the model which are above the stress limit.
7.0 Conclusions
The new geometric non-linear and free-shape optimisation capability within HyperWorks
11.0 has enabled Force India F1 team to significantly improve the design of the primary roll
structure.
The final design was able to reduce mass, pass all FIA regulation criteria, and significantly
reduce the time taken to design the primary roll structure for the car.
© Altair Engineering 2011 Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss Bulk 7

8. 8.0 References
[1] FIA Formula One Technical Regulations (2010)
[2] Altair Radioss 11.0
FIA TECHNICAL REGULTAIONS:
15.2 Roll structures:
15.2.1 All cars must have two roll structures which are designed to help prevent injury to the driver in the event of the car
becoming inverted.
The principal structure must be at least 940mm above the reference plane at a point 30mm behind the cockpit entry template.
The second structure must be in front of the steering wheel but no more than 250mm forward of the top of the steering wheel
rim in any position.
The two roll structures must be of sufficient height to ensure the driver's helmet and his steering wheel are at least 70mm and
50mm respectively below a line drawn between their highest points at all times.
15.2.2 The principal structure must pass a static load test details of which may be found in Article 17.2. Furthermore, each
team must supply detailed calculations which clearly show that it is capable of withstanding the same load when the
longitudinal component is applied in a forward direction.
15.2.3 The second structure must pass a static load test details of which may be found in Article 17.3.
15.2.4 Both roll structures must have minimum structural cross sections of 10000mm², in vertical projection, across a
horizontal plane 50mm below the their highest points.
ARTICLE 17 : ROLL STRUCTURE TESTING
17.1 Conditions applicable to both roll structure tests:
17.1.1 Rubber 3mm thick may be used between the load pads and the roll structure.
17.1.2 Both peak loads must be applied in less than three minutes and be maintained for 10 seconds.
17.1.3 Under the load, deformation must be less than 50mm, measured along the loading axis and any structural failure limited
to 100mm below the top of the rollover structure when measured vertically.
17.1.4 Any significant modification introduced into any of the structures tested shall require that part to pass a further test.
17.2 Principal roll structure:
A load equivalent to 50kN laterally, 60kN longitudinally in a rearward direction and 90kN vertically, must be applied to the top
of the structure through a rigid flat pad which is 200mm in diameter and perpendicular to the loading axis.
During the test, the roll structure must be attached to the survival cell which is supported on its underside on a flat plate, fixed
to it through its engine mounting points and wedged laterally by any of the static load test pads described in Article 18.2
© Altair Engineering 2011 Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss Bulk 8