On Structural Mechanics and Elasticity; notes on it, (some) notes on MIT OCW 16.20, 16.225, implementation in Python using FEniCS, SME github repository

Force due to displacement (vector field) in the direction of the displacement by a stress tensor 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 model a strut on the SpaceX Falcon 9 second stage CRS-7

Force due to displacement (vector field) in the direction of the displacement by a stress tensor on a rectangular beam of square cross section of 2.54x2.54 cm^2 and (longitudinal) length of 0.6 m, with Dirichlet boundary conditions and for steel, in units of Newtons (N), to model a strut on the SpaceX Falcon 9 second stage CRS-7

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.

Dan Peña – The 50 Billion Dollar Man, “Ask The 50 Billion Dollar Man – Dan Peña – Special Episode: Penaisms”

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).

Features:

  • 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.

https://ernestyalumni.files.wordpress.com/2015/08/sme.pdf

https://github.com/ernestyalumni/SME

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.

Why FEniCS?

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.

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One thought on “On Structural Mechanics and Elasticity; notes on it, (some) notes on MIT OCW 16.20, 16.225, implementation in Python using FEniCS, SME github repository

  1. Hello ernestyalumni,

    I came across your blog and your question on fenics solid mechanics app installation. As Garth Wells replied to you – “make sure the DOLFIN libraries are in your path so they can be discovered by the solid mechanics library.”

    Can you please guide me on what exactly does this mean? I am not sure where Fenics is installed on my Ubuntu 14.10? Where should I place the fenics-solid-mechanics folder before starting the installation? Currently, it is placed in downloads and I am getting the following error. http://fenicsproject.org/qa/9757/error-installing-solid-mechanics-app

    I would be extremely grateful if you could help me out!

    Thank you,
    Chaitanya

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