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Weak form for 2-D elasticity

Posted Apr 15, 2011, 1:03 p.m. EDT Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers, Structural Mechanics Version 4.3, Version 4.3a, Version 4.3b 6 Replies

Evan Zamir
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In an effort to learn COMSOL, I decided to model the two-dimensional elasticity equations using the weak form. I was surprised looking through the documentation that there are very few example problems, so I didn't have much to go on. I think I'm deriving these correctly, but I could use another pair of eyes:

-(lamb+2*mu)*test(ux)*ux-mu*test(uy)*uy-(lamb+mu)*test(ux)*vy

-(lamb+2*mu)*test(vy)*vy-mu*test(vx)*vx-(lamb+mu)*test(vy)*ux

lamb and mu are the lame coefficients. u=u(x,y) and v=v(x,y) are the displacement fields.

One question that I can't figure out is how to apply stress boundary conditions. Can anyone help with that?

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6 Replies Last Post May 3, 2016, 5:20 a.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Apr 15, 2011, 3:36 p.m. EDT
Hi

another way around, to learn COMSOL is to study the underlaying equations, turn on the equation view /node in V4 under preferences or look at them in 3.5a under physics equations

--
Good luck
Ivar
Hi another way around, to learn COMSOL is to study the underlaying equations, turn on the equation view /node in V4 under preferences or look at them in 3.5a under physics equations -- Good luck Ivar
Evan Zamir
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Posted: 1 decade ago Apr 15, 2011, 4:24 p.m. EDT
Thanks! That will help a lot.
Thanks! That will help a lot.
Muamer Kadic
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Posted: 1 decade ago Nov 25, 2013, 4:01 a.m. EST
Dear All,
I am working with the PDE (weak forms) in Mechanics in 2D.
I would like to set the shear modulus to strictly 0! Why this problem can not converge?
This is corresponding to approximatelly "compressible metafluid case".
Thanks for your answear.
Best regards
Dear All, I am working with the PDE (weak forms) in Mechanics in 2D. I would like to set the shear modulus to strictly 0! Why this problem can not converge? This is corresponding to approximatelly "compressible metafluid case". Thanks for your answear. Best regards
Haosen Wang
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Posted: 1 decade ago May 9, 2014, 3:51 a.m. EDT

In an effort to learn COMSOL, I decided to model the two-dimensional elasticity equations using the weak form. I was surprised looking through the documentation that there are very few example problems, so I didn't have much to go on. I think I'm deriving these correctly, but I could use another pair of eyes:

-(lamb+2*mu)*test(ux)*ux-mu*test(uy)*uy-(lamb+mu)*test(ux)*vy

-(lamb+2*mu)*test(vy)*vy-mu*test(vx)*vx-(lamb+mu)*test(vy)*ux

lamb and mu are the lame coefficients. u=u(x,y) and v=v(x,y) are the displacement fields.

One question that I can't figure out is how to apply stress boundary conditions. Can anyone help with that?


hi, have u solved the problem?

since i'm using the poroelastic model, and want to perform periodic boundary condition on both solid and liquid phase, i turned to weak form module

but just like the problem u have mentioned, i cant figure how to set stress BC on boundaries, (including other user defined equations on boundaries)
[QUOTE] In an effort to learn COMSOL, I decided to model the two-dimensional elasticity equations using the weak form. I was surprised looking through the documentation that there are very few example problems, so I didn't have much to go on. I think I'm deriving these correctly, but I could use another pair of eyes: -(lamb+2*mu)*test(ux)*ux-mu*test(uy)*uy-(lamb+mu)*test(ux)*vy -(lamb+2*mu)*test(vy)*vy-mu*test(vx)*vx-(lamb+mu)*test(vy)*ux lamb and mu are the lame coefficients. u=u(x,y) and v=v(x,y) are the displacement fields. One question that I can't figure out is how to apply stress boundary conditions. Can anyone help with that? [/QUOTE] hi, have u solved the problem? since i'm using the poroelastic model, and want to perform periodic boundary condition on both solid and liquid phase, i turned to weak form module but just like the problem u have mentioned, i cant figure how to set stress BC on boundaries, (including other user defined equations on boundaries)
Sharmin Ara
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Posted: 9 years ago Mar 4, 2015, 1:43 a.m. EST
Hi there,
Will you please confirm me, whether this is the weak form of the equation attached in the doc?
Thanks
Hi there, Will you please confirm me, whether this is the weak form of the equation attached in the doc? Thanks
Said El-Jallal
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Posted: 8 years ago May 3, 2016, 5:20 a.m. EDT
Hi,

Did you solve the problem. How can I apply periodic bounbary condition of my geometry using weak form.

Thanks.
Said.
Hi, Did you solve the problem. How can I apply periodic bounbary condition of my geometry using weak form. Thanks. Said.

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