Timoshenko Beam Theory Part 2 of 3: Hamilton's Principle
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- Опубликовано: 6 июл 2024
- Determining expressions for the strain and kinetic energies and the external work, taking their variations and substituting into Hamilton's Principle.
A detailed derivation of the kinetic energy of a beam can be found in this video:
• Kinetic and Strain Ene...
Download notes for THIS video HERE: bit.ly/3ED8pU0
Download notes for my other videos: bit.ly/37OH9lX
Reference: Dym & Shames, Solid Mechanics: A Variational Approach
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CHAPTERS:
0:00 Continuing
0:25 Getting Started
1:03 Displacement Field
4:09 Strains
7:28 Stresses
11:57 Strain Energy
19:17 Variation of the Strain Energy
24:35 Kinetic Energy
31:13 Variation of the Kinetic Energy
31:48 External Work
32:11 Variation of External Work
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wonderful explanation, thank you
Excelent series. Congrats
amazing series. thank you!
Nice one. You have me hooked.
Excellent video. Which software are you using to display your hand notes? It looks very nice. Congratulations.
The app is called "Paper" by WeTransfer running on an iPad Pro 13 inch and using Quicktime to record the screen. The handwriting is mine.
what is the 'm' in the equation of shear correction factor for hollow cylinder?
The original source of this table is from G.R. Cowper's paper on shear correction factors,"The Shear Coefficient in Timoshenko’s Beam Theory". Journal of Applied Mechanics, June 1966, p. 335. It shows that m = b/a (the ratio of the inner to outer radius). Also it shows that there is an error in the formula for k as printed!! It should read
k = 6*(1+ν)*(1+m^2)^2 / ( (7+6*ν)*(1+m^2)^2 + (20+12*ν)*m^2 )
NOTE the squares on each of the m's.
in calculating u*, I thing it does not have 1/2 in, u*=inegral(....)
Yes, you're correct. We get the 1/2 as a result of performing the integration (and assuming linear stress-strain relations). So, the 1/2 should NOT appear in front of the integral, but should appear in the lines that follow.
hey man can u show us how to implement the euler-lagrange of soft matter in python?
Not sure what that is. Do you have a link I can look at?