Frequency Domain Convergence |
 
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Frequency Domain Convergence |
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Flexcom uses a standard technique from numerical analysis, which is termed relaxation, to improve the rate of convergence of frequency domain dynamic analyses. Using this technique, the solution of the equations of motion from a particular iteration is replaced by a weighted average of the solutions for that iteration and the previous one.
For example, consider where the value of a typical displacement as predicted by the nth iteration of Flexcom is denoted Xn, while the corresponding term from the previous iteration is denoted Xn-1. Both Xn and Xn-1 are of course complex. The relaxation procedure may be described by the assignment statement:
rxn + (1 - r) xn-1 => xn
Here r is termed the relaxation parameter and is in the range 0 < r < 1. Note that the above is not an equation. The use of the arrow indicates that the expression on the left hand side is first evaluated, and that this then becomes (is assigned to) the value of the variable on the right hand side, replacing its existing value.
Relaxation as noted is a common numerical procedure and has the effect of improving the rate of convergence of iterative techniques, particularly in cases where results from successive iterations oscillate about the correct solution. As for the convergence parameters, the default value of 0.8 for r is adequate in the vast majority of cases. The value of r should be changed only when:
(i)a dynamic analysis repeatedly fails to converge, even though the tolerance measure and/or the maximum number of iterations have been altered (within reason)
(ii)you are certain the finite element model is indeed physically reasonable and capable of withstanding the specified environmental conditions
•*TOLERANCE is used to define the analysis convergence tolerance measure and related data.