- the Condition Number of the stiffness matrix
- the reactions at the constraints
- the "resultant" of the reactions about the origin
- the "resultant" of the applied loads about the origin
- THE CONDITION NUMBER OF THE STIFFNESS MATRIX
K * D = F
to give D
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.
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
FYO = FYN
MYO = MYN + FXN*Z - FZN*X
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.
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.