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Weak form boundary condition, a problem of mechanics.
Posted May 9, 2014, 11:32 p.m. EDT Version 4.3a, Version 4.3b 2 Replies
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As i tried to do the poroelastic simulation in PED , weak form, i firstly built up the weak equation for linear elastic part.
All ran fine, and was tested and compared with results obtained in Solid Mechanics(solid).
Then i tried to apply pressure (stress) to boundaries, as the equation : D*(ux+mu*vy)-1e6, where D is constant; ux is the derivitive of u( displacement along x-axis), and ux means the strain along x direction, and D*(ux+mu*vy) is stress along x. For simplification, D*ux-1e6 could be used for testing, which means at this boundary, the stress along x is 1e6 Pa.
And i tried all 3 weak boundaries: weak constraint, pointwise constraint, weak contribution.
If i use weak constraint, it seemed only the filed variables can be correctly used, i.e. set the weak constraint like a dirichlet BC. And if i write: D*ux-1e6, the stress seemed to be confined in the first adjacent layer of elements.
And if i use weak contribution, no such problem remained, but the BC could be affected by other equations. And although sometimes i could get the right distribution of wanted result, but the value is so not right. Like in one caculation, it was expected the stress to be 1e6, and the result turned out to be 5e5; and the displacement u and v were expected to be about 0.001, and the reults turned out to be like 3e-15.
So can any one would kindly help me with this problem? thx in advance~
All ran fine, and was tested and compared with results obtained in Solid Mechanics(solid).
Then i tried to apply pressure (stress) to boundaries, as the equation : D*(ux+mu*vy)-1e6, where D is constant; ux is the derivitive of u( displacement along x-axis), and ux means the strain along x direction, and D*(ux+mu*vy) is stress along x. For simplification, D*ux-1e6 could be used for testing, which means at this boundary, the stress along x is 1e6 Pa.
And i tried all 3 weak boundaries: weak constraint, pointwise constraint, weak contribution.
If i use weak constraint, it seemed only the filed variables can be correctly used, i.e. set the weak constraint like a dirichlet BC. And if i write: D*ux-1e6, the stress seemed to be confined in the first adjacent layer of elements.
And if i use weak contribution, no such problem remained, but the BC could be affected by other equations. And although sometimes i could get the right distribution of wanted result, but the value is so not right. Like in one caculation, it was expected the stress to be 1e6, and the result turned out to be 5e5; and the displacement u and v were expected to be about 0.001, and the reults turned out to be like 3e-15.
So can any one would kindly help me with this problem? thx in advance~
2 Replies Last Post May 15, 2014, 3:08 a.m. EDT
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Posted:
1 decade ago
I think I may had the answer:
1. the equations and weak forms were all right
2. notice that: several operators can be used for derivative, as ux, d(u,x), dtang(u,x), tec. Although I can't quite tell the differences, but I tested them one by one, and discovered that I could use d(u,x) in weak contribution to apply force( stress, pressure, etc) as BC
it writes like this:
(D*(d(u,x)+mu*d(v,y))-1e6*nx)*test(u)
(D*(d(v,y)+mu*d(u,x))-1e6*ny)*test(v)
this could apply a 1e6 pressure to boundaries
meanwhile, I tried ux, dtang(u,x), and swept the test(u) and test(v), all attempts failed to get the right result
3. use weak constraint to apply displacement BC , like u-0.001
1. the equations and weak forms were all right
2. notice that: several operators can be used for derivative, as ux, d(u,x), dtang(u,x), tec. Although I can't quite tell the differences, but I tested them one by one, and discovered that I could use d(u,x) in weak contribution to apply force( stress, pressure, etc) as BC
it writes like this:
(D*(d(u,x)+mu*d(v,y))-1e6*nx)*test(u)
(D*(d(v,y)+mu*d(u,x))-1e6*ny)*test(v)
this could apply a 1e6 pressure to boundaries
meanwhile, I tried ux, dtang(u,x), and swept the test(u) and test(v), all attempts failed to get the right result
3. use weak constraint to apply displacement BC , like u-0.001
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Posted:
1 decade ago
I inspected the results:
displacement=sqrt(u^2+v^2)
stress along x: sigma_x = D*(ux+mu*vy) (here both ux, and d(u,x) get the right result)
von mises stress (equivalent stress): = sqrt(0.5*(sigma_x^2+sigma_y^2-sigma_x*sigma_y+3*txy^2))
all be equal to results caculated in Elastic Module
:)
displacement=sqrt(u^2+v^2)
stress along x: sigma_x = D*(ux+mu*vy) (here both ux, and d(u,x) get the right result)
von mises stress (equivalent stress): = sqrt(0.5*(sigma_x^2+sigma_y^2-sigma_x*sigma_y+3*txy^2))
all be equal to results caculated in Elastic Module
:)