教程5.13g加密所屬

1、SECTION 5GUYAN REDUCTIONTABLE OF CONTENTSPageINTRODUCTION TO DYNAMIC REDUCTION5-3STATIC CONDENSATION (INTERNAL CALCULATION)5-4SOLUTION CONTROL FOR GUYAN REDUCTION5-9DIFFICULTIES WITH GUYAN REDUCTION5-11INTRODUCTION TO DYNAMIC REDUCTIONDefinitionDynamic reduction means reducing a given dynamic math m

2、odel to one with fewer degrees of freedom.Why Reduction for Dynamics?The math model may be too big to be solved without reduction.The math model has more detail than required.Dynamic reduction is cheaper than the precise analysis of the big math model. Reduction is approximately quadratic in cost, w

3、hereas eigenanalysis is approximately cubic in cost.Dynamic reduction is more accurate (and probably cheaper) than constructing a separate, smaller dynamic model.STATIC CONDENSATION(INTERNAL CALCULATION)Let uf be the set of the unconstrained (free) structural coordinates.Partitionwhere ua = analysis

4、 setuo = omitted setSTATIC CONDENSATION (Cont.)(INTERNAL CALCULATION)Form a static equation for uf and partition the stiffness matrix into the O-set and the A-set. Assume Po is zero and solve for uo in terms of ua uo = Goa uawhere Goa = - Koo-1 KoaSTATIC CONDENSATION (Cont.)(INTERNAL CALCULATION)Tra

5、nsformation from the A-set to F-set isO-set is dependent upon the A-set. The motion of the O-set is a linear combination of the A-set motions. The columns of Goa are the static shape vectors.The equations of motion for the F-set are written in terms of the A-setSTATIC CONDENSATION (Cont.)(INTERNAL C

6、ALCULATION)Dynamics problems are solved in terms of the reduced coordinates (A-set). O-set components are recovered.O-set mass, damping, and stiffness is spread to the A-set.The largest cost is associated with the formulation of Maa and Baa, particularly for nondiagonal (coupled mass) Mff.The result

7、ing Kaa, Baa, and Maa are small and dense (i.e., matrix bandedness is destroyed).STATIC CONDENSATION (Cont.)(INTERNAL CALCULATION)SUMMARYSeparate free degrees of freedom (uf) into the omitted set (u0) and the analysis set (ua) by means of OMIT entries or ASET entries.Retain only a small fraction of

8、the DOFs (typically 10% or less) in the analysis set because the computer costs for static condensation increase rapidly with the size of the analysis set. Otherwise, retain all of the DOFs.Retain DOFs with large concentrated masses in the analysis set.Retain DOFs that are loaded (in transient and f

9、requency response analysis).Retain DOFs to adequately describe deflected shape or modes of interest.SOLUTION CONTROL FOR GUYAN REDUCTIONExecutive Control SectionAny SOLCase Control SectionNo special commands requiredBulk Data SectionASET (optional* - specifies A-set)OMIT (optional* - specifies O-set

10、)This will require a manual text entry into the .bdf file from Patran. The BDF section is used to input the ASET data line. 876543213ASET1 109 etc.ID12ID11ID10ID9ID8ID7ID6ID5ID4ID3ID2ID1CASET110987654321SOLUTION CONTROL FOR GUYAN REDUCTION (Cont.)From the menu Load/BC: Create/Displacement/NodalDIFFI

11、CULTIES WITH GUYAN REDUCTIONUser effort in selecting A-set pointsAccuracy depends on the users skill in selecting A-set pointsRegardless of users skill, high accuracy requires a large number of A-set points (cost consideration) - 2 to 5 times number of accurate modes wantedStiffness reduction is exact; mass and damping reductions are only approximateNo loss in accuracy of modes occurs when omitting massless degrees of freedomErrors are most pronounced in higher modesLocal modes may be missed altogetherNot generally mended, except when performing test-analysis correlationDIFFICULTIES