At the request of the user, I've advanced the routines to convert arbitrary profiles (including nurbs perimeters) into the structural analysis section profiles capable of approximating this shape.
I've started with GSA, and will look into the other software equivalents shortly. In GSA the perimeter is defined as a polyline (I have enabled an input to define acceptable deviation from original curve), and properties such as area and inertia are computed from the polyline bounds.
The torsion property is not calculated, so I also enabled a section property modifier component to allow user specification of this value (as well as the others). There is a means to compute the torsional stiffness using soap film (which was the original reason I started coding mesh inflation), and I'll try to test this approach soon. If you have any papers or technical explanations/demonstrations of this technique, it can only help accelerate this if you can share it. Grasshopper definition can be accessed from here.
I've started with GSA, and will look into the other software equivalents shortly. In GSA the perimeter is defined as a polyline (I have enabled an input to define acceptable deviation from original curve), and properties such as area and inertia are computed from the polyline bounds.
The torsion property is not calculated, so I also enabled a section property modifier component to allow user specification of this value (as well as the others). There is a means to compute the torsional stiffness using soap film (which was the original reason I started coding mesh inflation), and I'll try to test this approach soon. If you have any papers or technical explanations/demonstrations of this technique, it can only help accelerate this if you can share it. Grasshopper definition can be accessed from here.
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Are you looking into methods of calculating a minimal surface for a given polygonal boundary?
ReplyDeleteThere is a nice algorithm in
Pinkall, Polther: Computing discrete minimal surfaces and their conjugates :
http://projecteuclid.org/euclid.em/1062620735
I'm not exactly sure how you get the torsional stiffnes from the actuall minimal surface though.
Hi,
ReplyDeleteThanks for the suggestion, but we're looking for a soap film (inflation) surface. Google for Prandtl, something like this:
http://www.public.iastate.edu/~e_m.424/Prandtl%20torsion.pdf
I had a look at http://en.wikipedia.org/wiki/Membrane_analogy.
ReplyDeleteAre we looking at finding the surface for a given (constant) pressure?
You can approximate solutions to Airy functions using NURBS for example, would that help?
For solid sections (with or without openings) most FE modellers calculate the torsion constant using the Prandtl membrane analogy, i.e. solving Poisson's differential equation, and they most often calculate this using the finite difference method.
ReplyDeleteMight be worth taking a look at this article for some comments on the 'physical analogy':
http://web.mit.edu/course/3/3.11/www/modules/torsion.pdf
For thin-walled sections it's a fair bit easier to calculate (at least approximately). In summary for solid shafts you can use membrane analogy fairly readily, for closed thin-walled sections, a shear flow analogy is most useful, but for the generic section FEM is really the only way to do it... but actually not that hard to implement and calculate I wouldn't imagine.
And this article provides an excellent summary of dealing with torsion in structural analysis including all the theory and background with lots of good references.
http://people.virginia.edu/~ttb/torsion.pdf