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)
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?