## Introducing springs to a point/face as a boundary condition

Numerical methods and mathematical models of Elmer
mika
Posts: 155
Joined: 15 Sep 2009, 07:44

### Re: Introducing springs to a point/face as a boundary condition

When looking at this, I found that the (mass) moments of inertia were computed erroneously by the shell solver. The effect was an erroneous multiplication with the thickness h. This has been corrected in the devel version today so that the elementwise contributions to the rotational mass matrix now scale as m/12 * h^2, with m being the mass of the element. Anyhow, here this correction doesn't change the eigenvalues virtually any way. This may not be a surprise since the inertia associated with translational DOFs usually dominates in shell analysis.
MoTN wrote:
17 Apr 2020, 00:43
But the first eigenvalue I obtained via Elmer is 6.697305E+01.

I think in the simplified calculation the moment of inertia should be taken to be I = 1/3 M L^2 where M = 272.5 is the total mass of the structure. Then K/I = 3K/(ML^2) = 66.97, which is close to the value given by Elmer.

-- Mika

MoTN
Posts: 16
Joined: 17 Mar 2020, 04:25
Antispam: Yes

### Re: Introducing springs to a point/face as a boundary condition

Finally solved! Many thanks again, Kevin and Mika!

That also explains why the results are different for Target Nodes(1) = 6, 8, and 9.
So, essentially Spring 4 and Spring 5 are rotation about Y and X, respectively.

for Spring 5 (rotation around X), depending on the node, I = 1/3 M L^2 (node 6 and 8) or I = 1/12 M L^2 (node 9),
while for Spring 4 (rotation around Y), for all the three nodes, I = 1/12 M W^2

are there any reasons why Spring 4 is rotation Y instead of X?
is it the same syntax to include mass points?

mika
Posts: 155
Joined: 15 Sep 2009, 07:44

### Re: Introducing springs to a point/face as a boundary condition

MoTN wrote:
17 Apr 2020, 19:33
are there any reasons why Spring 4 is rotation Y instead of X?
is it the same syntax to include mass points?
Springs and DOFs are enumerated in the same way. To understand the enumeration, the "rotational" DOFs should not be thought of as (approximate) rotations, but in the first place they just give the components of the partial derivative of the displacement field with respect to the normal coordinate, with the components being evaluated with respect to the basis of the global coordinate frame.

It follows that in the case of your model the fourth DOF (the directional derivative component along the X-axis) tends to create a rotation around the Y-axis, while the fifth DOF (the directional derivative component along the Y-axis) tends to create a rotation around the X-axis. Here the sixth DOF is not a rotation at all, but is the normal strain. Thus the physical interpretation of "Spring 6" would be some reaction disturbing the free straining of the shell normal according to the basic energy principle, which far from clamped edges tends to produce the state of vanishing normal stress.

If you associate "masses" (mass moments of inertia) with "rotational" DOFs, masses and DOFs are also enumerated in the same way. For example "Mass 4" would tend to add inertia with respect to a rotation around the Y-axis.

-- Mika