Thanks, Calc_em.
I think the subject is very interesting and deserves a final conclusion.
I have seen that book on the net but is fully in Polish. ¿ Do you have the leaf .step file or dimensions proposed in the book so I can have a look with the orthotropic approach?.
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It’s a really old (written in 1958) book, only in Polish. However, it has 457 pages and focuses entirely on leaf springs so it’s a very comprehensive resource. I haven’t modeled this leaf spring yet and thus I can’t provide the step file but here are the values and drawings from the book:
- Young’s modulus: 210.8 GPa
- number of leaves: 6
- arc height: 128 mm
- leaf thickness: 13 mm
- leaf width: 90 mm
- subsequent leaf lengths (measured for straight leaves): 1500 mm, 1250 mm, 1000 mm, 750 mm, 500 mm, 250 mm
For the force of 2000 kgf (19 613 N) the measured deflection is 102.5 mm while the analytical solution is 99.3 mm.
That is a really nice workaround. I really like it. Good find!
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thanks @Calc_em for took a time to make simple benchmark comparison. i’m only predict by theoretical of both software implementation from available documents. Abaqus approach look similar but is not really clear for me.
agree, benchmarks should not only for simple cases. expanding to moderate and complex (real world project) will give an insight about discrepancy & validity.
I went back to this topic and got really close to solving it but there’s one strange thing here. I decided to base my further investigations on your model which gives good results when compared with the analytical solution (which is likely around 23 mm) even when the trick with orthotopic layers is not used and leaves are merged together with no contact interactions between them. I changed my geometry a bit - added a gap to the eye and merged the leaves. Then I recreated your setup but with my geometry. I tried different meshes and variants of symmetry. What’s really surprising is that only your approach (1/2 symmetry with two layers of C3D20 elements in the depth direction and symmetry BC between them) gives good results for my model:
A 1/4 symmetry version of this model (the same mesh but with one layer of elements removed) also works:
However, if I change it in any other way (add more layers of elements of the same or different hex type or use tetrahedrons) the results are wrong. For example, here’s the deflection with more C3D20 elements (and no other changes):
That’s really strange, I don’t get why more layers of C3D20 elements in the depth direction could stiffen the model so much. Different changes to the model (like other contact types) give even worse results (deflection of a few millimeters).
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Could you share the different input files? To try and reproduce.
it seems related to element type selections, you may try reduced type instead
Sure, you can find them here:
I tried with reduced integration elements as well but they didn’t help unfortunately. Only one or two layers of C3D20 elements work for now which is really strange.
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A video to sum it all up:
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It’s look the model using continuous mesh is over simplified the problems. This assumption also known as fully composite approach were in actually can be partial. Transfer of shear trough rebound clip and clamp prestresed may have some amount of limited values.
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