lanbpa.v2004, AN SSSALTER FOR CORRECT BUCKLING RESULTS WITH THE LANCZOS METHOD, (lanbr.txt readme file)



1.  SUMMARY.  



If the LAN method of eigensolution is selected for buckling analysis and the model contains an lm-set, 

the results may be incorrect.  The lm-set is used for large displacement rigid elements at present, and 

may be used in other contexts in the future.  Its rows and columns are used for the coeffients of 

Lagrange Multiplier Technique (LMT) variables, present in the lm-set.  The cause of the error is that 

the lm-set adds constraints to the stiffness matrix.  This makes the model solveable for static analysis, 

the first step in a buckling analysis.  However, the stiffness matrix is used for sweeping trial 

eigenvectors in the Lanczos phase.  A requirement of the present Lanczos method is that the matrix used

 for sweeping may not be indefinite.  The LMT coeffiecients make the stiffness matrix indefinite, leading 

to errors in eigensolutions.



The alter leaves the LMT coefficients in the stiffness matrix for static analysis, but then shifts them 

to the differential stiffness matrix for the eigensolution.  This allows correct sweeping in the Lanczos 

operations while providing the correct boundary solution for the inverse iteration steps.  A second alter 

lanbchka.v2004 is also provided.  It provides checks on the eigensolution, and may be run by itself without

 the main correction alter package.  Its output is described below.



2.  INPUT

 

When large displacement rigid elements are input the lm-set variables are set up automatically, and no 

input other than the alter package is required.  Place 



include 'lanbpa.v2004' $ required.  Repairs error.

include 'lanbchka.v2004 $ optional.  Checks eigensolution



before the CEND entry.



For research purposes, LMT variables may also be input on extra scalar or grid points, and their coefficients

 input on DMIG entries.  For this case only, place the LMT variables on USET, LM entries.



3.  OUTPUT

 

The eigensolution output is conventional.  The generalized stiffness, GK = PHI'*K*PHI and the generalized 

differential stiffness, GKD = PHI'*KD*PHI are computed.  The largest off-diagonal term in each is printed, 

and both matrices are printed if the off-diagonal terms are larger than 1.E-6.  The diagonals of these 

matrices are used to compute the Rayleigh quotients ROOTS(i) = GK(i)/GKD(i).  This quantity should equal the 

computed roots EIGVMAT.  The difference in the two roots calculations, divided by the computed roots, is also

 output.  The lm-set constraint forces for the static analysis are printed in the SPC forces.  The lm-set

 constraint forces in the buckling analysis are printed in the QAGF output.



4.  EXAMPLE PROBLEM



File lanbpr1.dat has a large displacement rigid element between two bar elements.  The USET table is printed 

to show the existence of the lm-set.  A buckling load is applied.  The off-diagonal orthogonality check terms 

and errors in roots are less than 1.E-10.  If this problem is modified to remove the first error alter, but 

leave in the last check alter, these check quantities are as large as .1, and the solutions are quite different

 (and wrong) compared to the original problem.  The answers are plausible but incorrect.



The file lanbp.zip contains a .doc file giving the theory used in the alter package and a series of unit 

test problems useful for research and updating the alter on new versions of MSC/NASTRAN, until such time as 

the technique is built into the production Solution Sequences.  The unit problems demonstrate use of DMIG 

matrices for LMT effects.



A related error found during testing is that if the buckling solution shifts near a zero value the run may 

crash with zero divide diagnostics, or crash for other reasons.  An avoidance is to not include the origin 

the buckling eigenvalue range.  Compute the positive roots on one run, and the negative roots on another.



5.  DOCUMENTATION AND UNIT TESTERS



File lanb.zip is also present on the web site, and provides input and output files for several unit testers 

that can be used when version changes require an update of the alters.  Several other alters useful for 

research purposes and a .doc file that gives the theory for the techniques used in the alter package are 

also provided.