Introducing springs to a point/face as a boundary condition

Numerical methods and mathematical models of Elmer
kevinarden
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Re: Introducing springs to a point/face as a boundary condition

Post by kevinarden »

I added the other two rotational DOF constraints to the node, but still received a zero eigenvalue. I suspect it is because the shell element only has 5 DOF, many shell elements do not have the rotation DOF in plane of the element sometimes called the drilling DOF. When I restrained a boundary to stop rotation about the Z axis the zero eigenvalue went away.
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MoTN
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Re: Introducing springs to a point/face as a boundary condition

Post by MoTN »

I still cannot reconcile the two equivalent problems (a) and (b) above.
In my case, X and Y are in-plane coordinates, while Z is the out-of-plane one. The new BC you introduced (U 2 = Real 0.0) restraints the in-plane deflection, and I expected no change in the lowest eigenvalue.

I am confused about how to introduce the nodal spring BC in the shell solver. My Shell solver seems to ignore the spring 5 BC; as I vary its value, none of the eigenvalues changes. Also, unexpectedly, the first eigenvalue is very sensitive to material properties (Youngs mod. and Poisson ratio).

My understanding is that the shell is fully constrained against the rigid-body motion if the spring is in effect.
Node 2 is constrained in five degrees of freedom, allowing only movement in the pitch (Y) rotation direction via the spring.

Boundary Condition 1
Name = "TorsionalSpringY"
Target Nodes(1) = 2
Spring 5 = Real 4.019e3
U 2 = Real 0.0
U 1 = Real 0.0
U 3 = Real 0.0
DNU 4 = Real 0.0
DNU 6 = Real 0.0
End
kevinarden
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Re: Introducing springs to a point/face as a boundary condition

Post by kevinarden »

However shell elements, in this orientation, may not be connected to DOF 6 so
DNU 6 = Real 0
would have no effect of elimination the rigid body rotation about Z.
Some shell elements only define 5 DOFs.

Not sure what the case is in Elmer.
MoTN
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Re: Introducing springs to a point/face as a boundary condition

Post by MoTN »

Ok, now I see. Now when I set U 2 = Real 0.0 to eliminate rotation around Z (as you did), the zero eigenvalue vanishes. Yet, the spring has nothing to do with the output, neither DNU 4 or even DNU 5=0(no spring).
mika
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Re: Introducing springs to a point/face as a boundary condition

Post by mika »

To prevent (infinitesimal) rigid displacements

(c1,c2,c3) + (b1,b2,b3) x (x,y,z) = (c1,c2,c3) + (b2*z-b3*y,-b1*z+b3*x,b1*y-b2*x)

of the shell mid-surface one should give at least six constraints for the translational DOFs of the shell model. Constraining DOFs which are associated with the directional derivatives of the displacement in the normal direction is not useful so as to prevent the rigid displacements of the mid-surface. Therefore I'd expect to see six constraints for the components of the mid-surface displacement.

-- Mika
kevinarden
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Re: Introducing springs to a point/face as a boundary condition

Post by kevinarden »

Is this 6 constraints?

Spring 5 = Real 4.019e3
U 2 = Real 0.0
U 1 = Real 0.0
U 3 = Real 0.0
DNU 4 = Real 0.0
DNU 6 = Real 0.0
mika
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Re: Introducing springs to a point/face as a boundary condition

Post by mika »

kevinarden wrote: 12 Apr 2020, 16:09 Is this 6 constraints?

Spring 5 = Real 4.019e3
U 2 = Real 0.0
U 1 = Real 0.0
U 3 = Real 0.0
DNU 4 = Real 0.0
DNU 6 = Real 0.0
These six constraints do not prevent rigid body rotations since only three constraints are given for the translational DOFs (in this case they are U 1, U 2 and U 3). Constraints for the other DOFs of the shell model specify how bending deformation and through-thickness normal straining can occur and do not constrain the placement of the mid-surface in any way, since the displacement field associated with these modes vanishes at the mid-surface. So I'd expect that

- U 1 is specified at least at two separate nodes
- U 2 is specified at least at two separate nodes
- U 3 is specified at least at two separate nodes

to prevent rigid body rotations.

Moreover, in the case of the default variable names the definition

DNU 4 = Real 0.0
DNU 6 = Real 0.0

is inconsistent and makes no effect, while

DNU 1 = Real 0.0
DNU 3 = Real 0.0

might do. However, as already mentioned in my earlier message, I'd forget the (default) component names of the shell solver variable and use a single name for the entire solution to get well-organized eigenvector output.

-- Mika
kevinarden
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Re: Introducing springs to a point/face as a boundary condition

Post by kevinarden »

I revisited the Elmer's Models Manual. I had the wrong impression that U were translation constraints and DNU was rotation constraints. From the manual I take it to mean that DNU is a constraint that varies from the bottom of the shell to the top of the shell.

However

U 1 = Real 0.0
U 2 = Real 0.0
U 3 = Real 0.0
U 4 = Real 0.0
U 5 = Real 0.0
U 6 = Real 0.0

at one node still produces a negative eigenvalue.
mika
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Re: Introducing springs to a point/face as a boundary condition

Post by mika »

Oops, forget my previous message about minimal conditions to prevent rigid displacements. A combination of translational and rotational DOFs constraints should of course do as well.

-- Mika
mika
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Re: Introducing springs to a point/face as a boundary condition

Post by mika »

As already discussed, the shell element needs some constraint to resist rotation around the normal to the shell mid-surface. The remaining zero-eigenvalue should be due to the lack of such constraint. With Elmer the only way to exclude the rotation around the shell normal is a sufficient number of constraints given in terms of the translational DOFs. In the case of this example a minimal set of constraints might be for example

Boundary Condition 1
Target Nodes(1) = 2
U 1 = Real 0.0
U 3 = Real 0.0
DNU 1 = Real 0.0
Spring 5 = Real ...
End

Boundary Condition 2
Target Nodes(2) = 1 3
U 2 = Real 0.0
End

or, when Variable = U in the section for the shell solver,

Boundary Condition 1
Target Nodes(1) = 2
U 1 = Real 0.0
U 3 = Real 0.0
U 4 = Real 0.0
Spring 5 = Real ...
End

Boundary Condition 2
Target Nodes(2) = 1 3
U 2 = Real 0.0
End

It is good to know that the sixth DOF of the shell model, which is nonstandard as compared with the usual 5-DOF approach, is not related to the rotation around the shell normal. It describes instead the elongation in the direction of the shell normal. Therefore setting DNU 3 = 0 (or U 6 = 0) would't prevent the rotation around the shell normal.

-- Mika
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