The Rigid Elements
Cosmic
NASTRAN I MSC/NASTRAN
~~-~~-=-RTRPLT
RBE1
RBE2
RSPLINE
'ASTROS
Version 6
RROD
ReAR
Rigid "Elements" in NASTRAN
Warren C. GibsonVice President, CSA Engineering, Inc.
(Originally published in "ASIAC CurrentAwareness Bulletin," Winter 1992)
The "rigid elements" in COSMICNASTRAN, MSC/NASTRAN and ASTROSconfuse many analysts. This note is intendedto clarify these elements which can be veryuseful, but perilous if misused.
The elements in question, listed in thetable below, are not really finite elements inthe mathematical sense. They are actuallyconvenient means of generating multi-pointconstraint eg!lations for certam modellingsituations. Nevertheless, it is convenient tocall them elements because the share many ofthe superficial aspects of finite elements: theyconnect nodes, have identifying numbers, anacan be plotted.
RBE1
RBE2
As the table indicates, these elementscan be divided into two classes: true rigidelements and distribution elements. In a sense,the two classes are opposite in that the truerigid elements are like elements with infinitestiffness while the RBE3 is like an elementwith limited stiffness or zero stiffness. Thisimportant distinction is not always clear. tousers because the NASTRAN documentatIonunfortunately groups both kinds under thecategory "ngia elements." The two classeswill now be explained in more detail.
True Rigid Elements
The true rigid elements are easy tovisualize. They act like very stiff finite
GRIGDR
CR8AR
CRIGID1
CR8E1, CRIGD3
CR8E2, CGRGD2
Distribution elements
CRBE3 IRBE3 IABE3
~lements (~finitely stiff, in fact). They cannove .as n~d bodies .but cannot defonn: One)otential difficulry WIth these elements IS that
me analysts must carefully choose six degreesof freedom that are capable of representingrigid body motion as independent degrees offreedom (sometimes fewer than six). as inplanar structures). These degrees of rreedomare retained in the equations of motion and aretherefore called independent, the rest beingdependent. DOF's assigned as dependent inone rigid element may not be depen<1ent in anyother ngid elements or multi-pomt constraints.Another pitfall is that these elements cannot beused when thennalloads are present.
Most of the true rigid elements differonly superficially: they connect differentnumbers of griq points and provide differeIftfonnats; the ChOIce of one type over another ISoften s~ly a matter of convenience. TheRSPLINF element is somewhat different: it isused to ensure that a line of nodes defonns inthe same sha~e that an ordinary beam elementwould. RSPLINE elements can be used toIIstitc;~ two plane regions with different meshdensItIes.
Distribution Elements
The RBE3 element is generally used intwo situations: to distribute static 1oads orinertia forces from a single point in space to anumber of points on the structure and to serveas a transItion between two portions of astructure that are modelled differently.
Load Distribution Applications
To illustrate the first situation, supposea piece of equipment is attached to a base plateat four points around the base.,." numberea 101through ~ 04 (F~gure 1). 1 ne .equipmentstiffness IS consIdered small relative to thebase structure, so an RBE3 (which is perfectlyflexjble) is considered .aJJ.propriate. (If theequIpment were very stiff comQared to thebase structure an RBE2 would be usedinstead.) The RBE3 serves to distribute the
Equipment (~11nIC1Ur8I)Grid at e.g. wtth concentratedmaa and moment of Inertia
~RBE3 tranat- WlerUlloada
uounGnv pla8 to U1I four mount DoInta
Figl:lfe 1. Representation of a piece ofequipment using an RBE3
inertia forces (or applied static forces) from theequipment to the support structure. Grid Qoint200 IS assigned to the center of gravity of theequipment, and a CONM2 cara is used toattacn the eguipment's mass (7.5 lb) to thatgI:id point. The following bulk data cards areadded to the model:
Figgre 2. Using RBE3 to transition from ashell model to a stick model.
GRID 200 (x) (y) (z)CONM2 200 200 7.SRBE3 101 200 123 1.0 123 101 102 +RB
103 104
The RBE3 card says that at grid 200,degrees of freedom 1, 2, and 3, are to becomputed as fixnctions of degrees of fteedom1,2, and 3 at grid points 101 Through 108. Theexact dep~ndency will be computed byNASTRAN using the relative geometriclocations of the vanous grid points.
Now suppose the user wanted toinclude the equipment's moment of inertia onthe CONM2. Althou~ moments of inertia areno~ always a~~ilable, it is. usually ! ossible toestImate radiI of gyratIon an co~utemoments of inertia from I=M~. The RBE3 ismodified so that rotation degrees of freedomare, also computeq at grid 20G, since these nowcarry moments of Inertia.
would be obtained by rigid links to each of theindependent grid poin"ts separately. If therefe~ence degrees of freed~~ are called~,q andthe mc;iependent pOF Ui' .l -~ ..., l~, theresult IS a constramt equatIon or the form
N-[J]{Uq} + L [Gj]{Uj} = 0
i=1
+CM The t:igid-1'ody beaming equation from point ito pOint q IS
102 +RB
where [S;q] is
1 0 0 0(Zi-Zq
01 0
~q-Yi
(Xi -Xq
01(xq -Xi)
(zq -Zi
~i-yq0
1
0
0
1
}.
The least-squares weighted fit results in thefollowing constraint equations:
N{Uq} = [~b][A]-1 1: [TgbS;q JT[WJ{u,}
1=1
A continuation line has been added tothe CONM2 for entry of the moments ofinertia, and field 5 of the RBE3 has beenchanged from 123 to 123456. Field 7 is left as123; use of all six degrees of freedom at theinde2endent grid pOInts (i.e., 123456) ispossIble, but not recommended.
Transition applications
Another valid use for RBE3's is intransitioning from a shell model-of a fuselageto a stick model, as in Figure 2. An RBE3 canbe used to stipulate that the motions of the gridpoint at the center of the fuselage be computedas an average of the motions of thesurrounding grId points on the shell model.The RBE3 transmits beam forces withoutpreventing deformation of the shell'scross-sectIon.
Mathematics of the RBE3
The mathematics underlying the RBE3is presented in Reference 4 ana may besummarized briefly as follows. In essence, themotion of the reference grid point is computedas a weighted average of the motions that
where ~b is the transformation from basic toglobal coordinates at grid point q, [W;Jis a
user-supplied diagonal matrix of weightingfactors, and
The wei~ting matrix defaults to an identitymatrix. These wei~tin~ factors may beentered by the user on RBE3 cards, but shouldgenerally be a allowed to default.
In order to determine exactly whatconstraint equations are generated by a~articular set of rigid elements, the followingDMAP alter can be used:
ALTER 102 $TRNSP GM/GMT $MATGPR GPL,USET,SIL,CMT//MIN $
.This p~ts the coefficients of theconstraInt equatIons that are generated. Thealter is for SOL 24, version 65 ofMSC/NASTRAN. For other solutions orversions, substitute the line number of theMCEI module for 102 in the ALTERstatement.
The following sources may beconsulted for further infonnation.
1. MSC/NASTRAN Application Manual,section 2.1°1 "Rigid Elements and Multi-pointConstraints.'
2. MSC/NASTRAN Application Manual, June1985 Application Note, "Modelin,g CheckoutTechniques for RBE3 Elements.' This Notemay be out of print.
3. MSC/NASTRAN Application Manual,December 1984 ~PQlication Not~~ "Checks forMPC's and Rig1;d Elements." Note that theDMAP alter given in this note is nowincoIporated in SOL 60. This Note may be outof pnnt.
4. MSC memo MAG-4, "MathematicalSpecification for the RBE3 Element," April,1975. Available from ASIAC.
