The residual kinetic energy calculation described in Section 3.4.2 provides guidance in adding DOF, but does not automatically add DOF. The residual kinetic energy (RKE) can be used in an iterative algorithm (IRKE), which sequentially adds DOF until a sufficient number is reached. This algorithm starts with a small set of DOF selected by the user. At each step it calculates the residual kinetic energy for all target modes, and selects one or more DOF based on the sum of residual kinetic energy terms across the modes. These DOF are added to the selected list, the Guyan reduction is repeated and optionally the psuedo-orthogonality of the target modes with respect to the reduced mass matrix is calculated. A candidate set can be used to limit the choices of the DOF that are added.
Two variations of this algorithm are provided with TAMKIT. This first variation iter_rke performs a standard Guyan reduction at each step. This is applicable to all structures as long as the initial DOF are sufficient to restrain rigid body motion, but can be very computationally intensive for large models. Because of this limitation, support for the iter_rke alter has been discontinued after NX Nastran 11.The second variation fast_iter_rke takes advantage of the following identity:
(2.5.3-1)
where
= OA partition of flexibility shapes
=
AA partition of flexibility shapes
This method is much faster because the large stiffness
matrix is only decomposed once, and
the matrix solution involved in each step only requires a forward backward
substitution (FBS) to calculate additional columns of
, and decomposition of an A-set size matrix
. Because
this method requires the initial decomposition of the F-set stiffness
matrix it does require a grounded structure. If the structure is free-free,
soft springs can be added to eliminate the zero frequency rigid body modes.
The fast IRKE algorithm should be selected for most models.
After running IRKE, Matlab function evaluate_irke_dof.m can be used to help determine the incremental benefit of each IRKE iteration. The function reads the output .pch file from the IRKE run and generates a plot of the IRKE error metrics vs. number of DOF as shown in the figure below. If desired, the user can select an iteration number from the graph and all DOF up to that iteration can be written to Nastran ASET cards in a text file. For more information see the evaluate_irke_dof.m help at the Matlab command prompt.
For this function to work the error norm calculation must be activated in the fast_iter_rke.xxx alter using PARAM,ENORM,YES (default). For the example shown below, adding DOF beyond iteration 40 does not appreciably decrease the error metrics so a candidate set TAM using the first ~120 DOF would be sufficient.