## Additional Output for Checking the FEM solution

About the development of the FEM module/workbench.

Moderator: bernd

mac_the_bike
Posts: 11
Joined: Sun Jun 30, 2019 12:56 pm

### Additional Output for Checking the FEM solution

Is it possible to have calculix display the following information and make it available to freecad:
• the Condition Number of the stiffness matrix
• the reactions at the constraints
• the "resultant" of the reactions about the origin
• THE CONDITION NUMBER OF THE STIFFNESS MATRIX
The the following matrix equation is solved:
K * D = F
to give D
where:
K - stiffness matrix
D - displacements, unknown
F - the applied forces, known

What is the "Condition Number of the stiffness matrix"?
It gives a measure of the accuracy of the solution process. Large values indicate that there could be problems with the model, such as insufficient constraints.
See K_J Bathe, "Finite Element Procedures" see: Solution of Equilibrium Equations in Static Analysis Page 738 Chap. 8
Also, MSC NASTRAN has a parameter called MAXRATIO, which gives a similar value.
To evaluate an estimate of the solution errors, assume a T-digit precision computer, this is generally 16.
We can obtain an estimate of the number of accurate digits obtained in the solution, S, as:
S = T - log10 [condition number of(K)]
For example, if the condition number = 1E8
S = 16 - log10(1E8) = 8
Thus the first 8 digits of the displacements are accurate; this is sufficient to give reliable strains and stresses.
• NOTE: the condition number doesn't give any information about how well, or not, the physical object is modelled.
• THE "RESULTANT" OF THE REACTIONS AND THE "RESULTANT" OF THE APPLIED LOADS ABOUT THE ORIGIN
The "resultant" is calculated thus, for example in the y direction:
FYO = FYN
MYO = MYN + FXN*Z - FZN*X
where:
FYO - force in y direction at origin
FXN, FYN, FZN - forces in x, y and z directions at node
MYO - moment about the y axis at origin
MYN - moment about the y axis at node
X , Z - the x and z coordinates of the node
This is repeated for the x and z directions.
These two "resultants" should be equal and opposite. They should have same value, apart from the sign, up to the 7th or 8th digit.
If they are different, the finite element model should be checked. A possible cause could be that there are constraints in the model which are absorbing energy.

mac

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