Examples

Optimisation: Car body

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Suppose you wish to develop a derivative car off the back of an existing model.  Specifically, you wish to bring to market a convertible derivative of an hatchback base model.  Such a vehicle programme should be cheap, employing as much as possible the principle of platform sharing, i.e. common parts, options and supply chains.

 

The old chestnut is that chopping the roof off a car has serious structural consequences.  So, as well as developing and packaging the convertible roof system you also need to reinforce the car body to recover the handling, NVH and crashworthiness qualities of the hardtop hatchback.

 

Using optimisation, this study looks at recovering one fundamental characteristic related to handling; body torsional stiffness.  The principles involved are extendable to multiple criteria.

The study first evaluates the torsional stiffness of the hatchback variant as the baseline.

 

The torsional stiffness of a car is predominantly due to its body-in-white (BIW).  Therefore, the baseline analysis includes the BIW, but also includes the front windscreen and rear quarter windows in the structure.  However, the analysis does not include the doors, tailgate or bonnet.  The torsional stiffness for the baseline structure as described is found to be 2039 Nm/deg, which compares well to existing data.

Removing the roof from behind the windscreen, the upper B and C pillars and rear quarter windows, all together a mere 20kg of structure, reduces the torsional stiffness to 275 Nm/deg, or 13% of the baseline value and firmly in 'jalopy' territory.

Three optimisation analyses are conducted, each with the single criterion of increasing torsional stiffness in a mass efficient manner back up to 2039Nm/deg by:

  1. Panel thickness changes (increase only)

  2. Localised reinforcement of any panel

  3. Localised reinforcement of select panels

 

This study targets feasibility and preliminary design to demonstrate the basic principles involved.  As such the optimisations only consider changing panel thickness; locally or for the whole panel.  In reality, local panel thickness changes could not be manufactured with existing production line technology, but the thickness changes do indicate where reinforcing doublers or stiffeners can be located, or reductions in spotweld pitch or changes to laser welding can be made. Significant global panel thickness changes are probably infeasible and are presented for hypothetical consideration only.

Design data infographics test: Car BIW initial design - material properties and geometry
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The first two optimisation strategies bookend a range of solutions to the torsional stiffness problem in the 'hacked' structure.  Also, where there is package space, additional load paths can be added and similarly optimised, after all additional BIW structure will be required for safety requirements such as roll-over protection etc.

 

The plots in the gallery below show panel thickness of the structure affected by Optimisation Strategy 1 compared against baseline, and also the localised reinforcement from Optimisation Strategy 2:

Baseline panel thicknesses
Baseline panel thicknesses

Original panel thicknesses (only showing panels affected by via Optimisation Strategy 1)

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Optimisation Strategy 1
Optimisation Strategy 1

Optimisation by changing panel thickness (affected panels shown)

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Optimisation Strategy 2
Optimisation Strategy 2

Optimisation via localised stiffening

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Baseline panel thicknesses
Baseline panel thicknesses

Original panel thicknesses (only showing panels affected by via Optimisation Strategy 1)

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Similarly, the plots in the next gallery show optimised panel thicknesses for the panels subject to Optimisation Strategy 3, these being the floor pan, firewall and suspension tower structure:

Optimisation Strategy 3
Optimisation Strategy 3

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Optimisation Strategy 3
Optimisation Strategy 3

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Optimisation Strategy 3
Optimisation Strategy 3

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Optimisation Strategy 3
Optimisation Strategy 3

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As mentioned, the target of optimisation was 2039Nm/deg torsional stiffness for minimal mass increase.  Mass increases over baseline for the three optimisation strategies are:

  1. 91kg (Optimal panel thickness increases)

  2. 17kg (Localised reinforcement of any panel)

  3. 101kg (Localised reinforcement of a select subset of panels)

So, as is obvious, Optimisation Strategy 2 is the most mass efficient strategy, due to only making changes where most effective.  But, understanding the trends in this study are important for pragmatic decision-making.  The results tell us the following:

  • A strategy of localised reinforcement similar to Optimisation Strategy 2 will save approximately the mass of an adult compared to the strategy of panel thickness changes of Optimisation Strategy 1.  Note: Significant panel thickness increases are prohibitively expensive or even impossible to manufacture.

  • A strategy of localised reinforcement to a select subset of panels, as considered by option 3, may lead to large increases in mass if the panel subset does not include all panels with localised high strain energy density.

  • If geometry changes are considered acceptable then the geometry can be similarly optimised within user-specified limits.  The geometry change principle includes shape optimisation of additional structure such as struts, channels and subframes.

 

Optimisation analyses are not only pivotal in fine-tuning a structure but can also provide cost benefit analyses with crucial clear options at any stage of a programme.