## Regarding Stiffness Matrix & Element Nodal Forces

## Regarding Stiffness Matrix & Element Nodal Forces

(OP)

Hello Everyone, I am calculating stiffness matrix for a hexahedron element using C code and I am using gauss points. However if I compare my output with the stiffness matrix output by Abaqus, I see some differences ? Is it normal ?

Also I am trying to transfer element nodal forces from one mesh to another. The transfer has to be conservative, so what is the best way to acheive this ?

Also I am trying to transfer element nodal forces from one mesh to another. The transfer has to be conservative, so what is the best way to acheive this ?

## RE: Regarding Stiffness Matrix & Element Nodal Forces

Doug Jenkins

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## RE: Regarding Stiffness Matrix & Element Nodal Forces

Other things to check:

- Make sure you have the same number of Gauss points. It might be 1 or 8.
- Make sure the row order is the same. It might be ordered by the element's node numbering or by the global node numbers or arbitrarily mixed up in some other way.
- See if the non-zero structure is the same.
- Check for correctness by summing the rows. Each row should sum to zero.

Not sure how you'd transfer node forces to a different mesh. I guess the most correct way would be to first find a continuous (ie. not discrete) force field that the node forces define, and then apply that distributed load to each element in the new mesh by integrating it over the element's face. For that second stage, you could use Gauss points to sample the field, but there's no guarantee they'll capture all the details if it's very non-uniform. You could use a much larger number of integration points to sample it more accurately. If you already know the field that the node forces represent then that will take care of the first stage which I have no idea how to do otherwise.That's a very complex job. If you a dirty shortcut, maybe just sum them to find the net force then apply a uniform force that's the same? That might cause the wrong moment though.

## RE: Regarding Stiffness Matrix & Element Nodal Forces

@whitwas, The row sum came to be zero. I will try your suggestions and update. Thanks a lot.

## RE: Regarding Stiffness Matrix & Element Nodal Forces

## RE: Regarding Stiffness Matrix & Element Nodal Forces

"dilational" ... relating to "dilation" (oh, great !) ... "or compression" ... ok, that's more helpful.

another day in paradise, or is paradise one day closer ?

## RE: Regarding Stiffness Matrix & Element Nodal Forces

For dilational stresses, think of a balloon floating in a chamber of gas. As the pressure in the surrounding gas goes up, the balloon shrinks in size. If you slowly increase the pressure the balloon will keep shrinking in size, but is unlikely to pop. Dilational stresses usually aren't what cause material failure, though they still cause strain. Deviatoric is more like shear stresses. They cause materials to fail. If you tried to cut that balloon with scissors after it shrank it would definitely pop. The scissors are introducing mostly deviatoric stresses.

In reality, both of these are derived from the typical stress tensor. When you add the two together it should give you back your typical stress tensor.