Dear Thomas,
You are right of course, this brick is not adapted to 3D geometry and
for the moment it is for plates only (not for curved structures).
This plate is only for the bending part. For a complete bricks, it would
be necessary to add the membrane term and make the good projections of
the gradients, yes.
Best regards,
Yves.
Le 04/10/2018 à 12:30, Thomas Ward a écrit :
Hello,
I have a question about the shell elements, MITC or Reissner Mindlin.
Will the shell elements in GetFem work in 3D geometry space? i.e. with
2d elements but inclined at arbitrary angles
I have been looking at the source code of the "brick" for Mindlin
Reissner and I think that currently the brick will not work in 3D
space :- I can see that the variational form for the Mindlin Reissner
region is something like
/bending_stiffness = (E*t**3)/(12.0*(1.0 - nu**2))/
///G=0.5*E*t*kappa/(1+nu)//
//
Bending energy density =0.5* (bending_stiffness*((1.0 - nu)*(0.5*(
grad(Theta)+grad(Theta.T)) :///(0.5*(
grad(test_Theta)+grad(test_Theta.T))/+ nu*Div(Theta)*Div(test_Theta)/
//
/shear Bending energy density = G( (Grad(w)-Theta). (Grad_(test_w)
-test_Theta/)
Since the form is defined with test and trial function for a 2D
"Theta" representing bending abut the two local element axis, then
taking the gradient of Theta in 3d space gives a 2x3 matrix and then
trying to add this to the gradient of its transpose obvliusly makes no
sense. When you try to use a Mindlin Reissner "brick" which is
inclined then the following error is printed byt GetFem
((E)*pow(plate_thickness,3))/(12*(1-sqr(nu)))*((
1-(nu))*((Grad_theta+(Grad_theta)')/2):((Grad_Test_theta+(Grad_Test_theta)')/2)+(nu)*Trace(...
---------------------------------------------------------------------^
Grad_theta+(Grad_theta)' - Addition or subtraction of expressions
of different sizes: (2, 3) != (3, 2)
Is there a way to use the Mindlin Reissner brick in 3D Space?
If not then would the fix be as simple as projecting the gradient from
the local element "D coordinate system into 3D space? Or is it more
complicated than that?
thanks for your help
Regards
Thomas
--
Yves Renard ([email protected]) tel : (33) 04.72.43.87.08
INSA-Lyon
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard
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