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[Getfem-users] MITC/Reissner shell elements in 3d space

From: Thomas Ward
Subject: [Getfem-users] MITC/Reissner shell elements in 3d space
Date: Thu, 4 Oct 2018 11:30:19 +0100


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))

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




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