- 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

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.

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

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.

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.

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