Introduction to finite element analysis
Introduction to finite element analysis

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Introduction to finite element analysis

Step 4 – Modelling issues and assumptions

For both the boundary condition restraints and load input points we can expect some localised high stresses. We’re not interested in these though. As long as the loads and reaction forces are fed into the structure, the main part - the bit we’re interested in - will be modelled and behave close to the real thing.

For this component Steps 1, 2 and 3 are relatively easy, even easier than for the wheel hub.

Considering modelling issues and assumptions, the tub is large, of a complex shape, and made of a material which is clearly not isotropic. It is ‘orthotropic’.

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Transcript: Video 9

Lewis Butler
The material properties that we use for the chassis are ordinarily linear again, but the data source for that is slightly different because it’s a bit more of a complex problem and there are many more different types of material. They’re obviously not isotropic. They’re all 2D orthotropic layers which come up to build a 2D orthotropic panel.
And all these have different stiffnesses depending on where they are in the car and how many layers of which material we use. So the constitutive model we use is different to that of an isotropic material. And we tend to use manufacturer’s data for that.
The material properties within the chassis are slightly different. So most of the components in each of the layers is a 2D orthotropic material. So that was a different subset within the model when you apply them. And each of the layers-- because they can be orientated differently to one another – allows you to build up different stiffnesses in different directions. And that makes it more complex, both from getting a hold of the data we require, and also actually validating that against tests. So it’s a little more complicated than isotropic material.
This is the input method that we use in this software for actually representing the material stack with all the different plies. If you see the spreadsheet here, in this case, there are nine different layers. Within that, you specify the thickness of each one and the orientation of each one. And there’s also a core material as well, which, again, is represented using a different kind of constitutive model.
And the clever bit, if you like, is it goes and works out the stiffness of that and the strength of each of those plies individually when you actually apply loads to them. For the load case we’re considering for the chassis, which was a torsion test, which is to try and measure the stiffness of the car under a pure torque. We basically use the suspension components, which you can see is the yellow, the yellow sticks on the screen here. And they’re represented using extremely simplified versions of what is really on the car.
But they still obviously apply the forces in the right positions under the chassis. And from that, the loads are carried in in the correct manner. And we try and do a verification test using this very same loading method.
And we also only mesh half of the car, essentially because any asymmetry is fairly minimal in its impact on the overall results. And it saves an awful lot of time for both simplification of the CAD model and also just construction of the model itself. And also many of the load cases are applicable to just a half car, so we tend to only run half the model to save on computing time.
The constraint case we have here is a little more complicated than just symmetry. It doesn’t really represent doing the same thing on both sides, which is what symmetry ordinarily is. It’s actually trying to make the model do the opposite on one side to the other for a vertical load case. So it constrains, out of the six degrees of freedom-- if you count one, two, three for the translational degrees of freedom, and four, five, and six for the rotational ones, this actually constrains one, three, and five. So in effect, it tries to represent anti-symmetry, which is a little complicated to explain in words, but I can show you in the model later on with the display shape.
What it actually means and what it allows and disallows in terms of rotations and displacements at the centre line. It comes out within maybe 2% or 3% of what is known to be the case with a full model. For the load case that we’re considering here, the torsion test, essentially the load is simply a vertical force applied at the contact patch here. And as you can see from there, the load travels up through my representative wheel which is effectively just there for measuring displacement. It’s not applying the load to the suspension members.
Again, these are just representative components, which are very stiff to make sure that the only variable within the model in terms of stiffness comes from the chassis itself, the main body, so that year on year we get good comparison between the effect of that component only within the system. The constraints, at the rear end of the car, are simply the engine mounts, which we showed a little bit earlier on, across the road, on the real component, and you can see there they are just constrained in all three displacement degrees of freedom.
Any calculations that are made on those for strength are done using hand calculations rather than the FE model, so local stresses are ignored. And the final thing is the anti-symmetry constraint on the centre line. So as you can see, this is trying to represent what happens to the overall car by just loading half of it. And to do this, it effectively constrains, of the six degrees of freedom, if one, two, and three were the translational x, y, and z coordinates, and four, five, and six were the rotational x, y, and z, it constrains degree of freedom one, three, and five.
And that is effectively the three that you wouldn’t constrain if you were doing symmetry. It’s the exact opposite, which is why we call it anti-symmetry. And that does fairly accurately represent what happens during this kind of loading.
Dr. Keith Martin, The Open University
Lewis describes it as a 2D orthotropic material. He assumes that it is a homogeneous, linear, elastic material, having two planes of symmetry at every point in terms of mechanical properties, these two planes being perpendicular to each other.
End transcript: Video 9
Video 9
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If you compare the chassis tub to the hub, material behaviour is probably the most different aspect. The hub is made of steel, a linear, elastic, homogenous and isotropic material, and can be described using only a couple of numbers.

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Transcript: Video 10

Narrator
The material of the tub has complicating features. This is due to the directional nature of the plies of carbon fibre set in the material matrix. In addition to this, the plies themselves can be orientated in layers, each layer direction being different
And there is a core material in the centre of the sandwich, having its own set of properties. So instead of entering just a couple of numbers, the orientations and numbers of plies have to be entered and the analysis package will determine the overall stiffness of the laminate, including the core.
Notice the use of symmetry in the model. Only half the tub was modelled. This can save a lot of time and computing resource -- not just the 50% of the missing piece.
If we double the size of a model, it is likely to increase the solver time by something like 10 times. Larger models might not even solve at all. So, using such symmetry shortcuts is a valuable saving. The only complication is the anti-symmetry boundary condition on the cut face. We’ll say a bit more about that during the next step.
End transcript: Video 10
Video 10
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