79. Most successful people do it poorly, until they do it well. Just keep blundering along; you can’t wait until it’s exactly right. The product of your quest for perfection is paralysis.
Perfection is paralysis.
Note: In no way is any of this stuff following complete in any sense, but again, perfection is paralysis. Any and all (negative) feedback is welcomed.
I posted, in the media library of this wordpress.com blog, a pdf, SME.pdf, with what I have for notes on Structural Mechanics and Elasticity, in general, with a strong slant on aerospace applications and a strong flavor for the kind of mathematical physics of elasticity by Marsden and Hughes (1994), and T. Frankel (2004).
- I work out, using Differential Geometry, the mathematical physics foundation of elasticity and some plasticity, as needed because I’d like a manifestly covariant formulation; I rely heavily on Marsden and Hughes and T. Frankel and try to compare and come up with a dictionary between that and usual engineering texts; but I also point out where previous works were either not general enough, miscalculated, or flat-out wrong.
- Engineering material I used to learn about Structural Mechanics and Elasticity (for aerospace applications) included MIT OCW 16.20 and MIT OCW 16.225 and I try to write up some notes on what I read; in no way do I aim to be complete and comprehensive (you should look at the stuff on the website in parallel) but I try to improve upon it or pick out what I need
- implementations using Python and FEniCS: it’s all on my github repository SME, including the LaTeX .tex file for this SME.pdf; you should copy and edit the LaTeX file as you’d like; just remember to share.
Here are some videos I posted on YouTube, implementing linear elasticity with linearelast01.py on a rectangular beam of square cross section of 2.54×2.54 cm^2 and (longitudinal) length of 0.6 m, with Dirichlet boundary conditions and for steel, in units of Newtons (N), to try to model a strut on the SpaceX Falcon 9 second stage CRS-7.
From what I read off the MIT OCWs and engineering position posts in general, it seems like ANSYS, a commercial product, is used heavily to do finite element analysis for structural mechanics. I’m using FEniCS because it’s the only, fairly complete, open-source software (OSS) that’s available to me and of which I can ask other academics for help. Help, donation, funds, and support for new computer equipment would help; if you can, please help at ernestyalumni.tilt.com and there’s also a PayPal link there too; nevertheless, I remain committed to providing this material open, public, and freely available for usage, in the spirit of OSS.
Help I still need with implementation
I’m getting errors when I do FacetNormal on a (rectangular) Box Mesh. Because I wanted to get out a scalar quantity for the stress tensor that I could plot. And what do engineers use for a scalar quantity for the stress tensor?
Also, I’m having errors when trying to save the tensor into a file.
The specific errors are in linelast01.py of the github repository SME.