I have a stiffness matrix where units within columns and rows are inconsistent. I tried to inverse the matrix but it said " The matrix element units are not compatible with this operation". How can I fix this? If possible. Or I just did this wrong.
ps: I this question a few years ago. The very same question. However, the solution is no longer working.
Thank you for any inputs!
1 ACCEPTED SOLUTION
Accepted Solutions
If you assign suitable units to the zero values
then your matrix k.free ends up like this
and can be inverted without errors
Hi,
Typical structural stiffness matrices are of multiple units for various elements. Inversion or decomposition of the matrices will result in unit inconsistent equations.
For this reason it is best to work in a consistent set of units so the value of the stiffness matrix elements are correct but without units.
A consistent set of units for imperial system is fps. This is from a commercial software suite.
You need to divide the stiffness matrix entry values to these consistent units.
If you assign suitable units to the zero values
then your matrix k.free ends up like this
and can be inverted without errors
Hi,
Setting a few zeroes to have units works easily for the current example with only two elements oriented in the same direction.
A more complex example with rotated members like this:
Produces with a additional node at quarter point of rafters a six by six matrix for each element without zeros due to the rotations in the xy plane assembled like this
green shows non-zero values, white shows zeros in the 33x33 matrix. You would need to set units for 810 zero values for solution.
This why I work unitless for global matrix using a consistent set of units.
Cheers
Terry
