Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

Abstract

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix