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Traction boundary condition: Linear Elasticity

Posted Mar 16, 2023, 9:43 a.m. EDT 2 Replies

Krishna Kumar Narayanan
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Hi,

An I-section beam (h=0.01,w=0.008,l=0.125,th=tb=5e-4; all dim in m) is simulated for deformation and cauchy stresses for linear elasticity. The body load is 1 N at the open end. The length of the beam is oriented along y-axis, width along x-axis and height along z-axis. The simulation provided me the x,y,z coordinates and the 6 cauchy stresses. When i analyse the output in python against neumann (traction) boundary condition, i found a discrepancy that i could not explain.

According to the equations, at the open end the traction boundary condition is

Since the load is acting along the negative z-axis downwards, , where f = -1 N and sa is the surface area calculated using

Thus plugging in this into the equation where n = [0,1,0], one should expect

(on the boundary points at y = L),

which i did not find. Am i checking the boundary conditions wrong? Attached are the exported comsol text file and the python code to test.

Thank you very much

2 Replies Last Post May 24, 2023, 6:22 a.m. EDT
Henrik Sönnerlind COMSOL Employee

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Posted: 2 years ago Mar 20, 2023, 9:55 a.m. EDT

The information in your question is not complete. How are loads applied? You mention a body load at an end, but a body load would act over a volume.

Anyway, the scatter plot looks very much like a text book example of shear stress distribution over an I-beam section: A weakly parabolic distribution over the web, and almost no stresses (in the load dirction) over the flanges.

See for example https://www.ae.msstate.edu/tupas/SA2/chA14.6_text.html

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Henrik Sönnerlind
COMSOL
The information in your question is not complete. How are loads applied? You mention a body load at an end, but a body load would act over a volume. Anyway, the scatter plot looks very much like a text book example of shear stress distribution over an I-beam section: A weakly parabolic distribution over the web, and almost no stresses (in the load dirction) over the flanges. See for example
Krishna Kumar Narayanan
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Posted: 2 years ago May 24, 2023, 6:22 a.m. EDT
Updated: 2 years ago May 24, 2023, 6:25 a.m. EDT

Dear Henrik, thank you very much for your reply. Sorry to revisit this topic two months later. I saw the reference and i can immediately see that the is a weak parabolic distribution along the web. Nevertheless, maybe you can help me with one curiosity here. According to the theory, the shear stress must be maximum at the neutral axis and minimum at the either end of the web. But what is see is that the distribution has an inverted parabolic shape in that it is maximum at the web ends and minimum in the center. (see attachment) Any idea as to why this could be? Thanks

Dear Henrik, thank you very much for your reply. Sorry to revisit this topic two months later. I saw the reference and i can immediately see that the \sigma_{yz} is a weak parabolic distribution along the web. Nevertheless, maybe you can help me with one curiosity here. According to the theory, the shear stress \sigma_{yz} must be maximum at the neutral axis and minimum at the either end of the web. But what is see is that the distribution has an inverted parabolic shape in that it is maximum at the web ends and minimum in the center. (see attachment) Any idea as to why this could be? Thanks

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