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(c)2000 Ame rican Institute of Aeronautics & Astronautics or Published w ith Permission of Author(s) and/or Author(s)' Sponsoring Organization.AOO-45051 2000-01-5585

Fastners Modeling for MSC.Nastran FiniteElement AnalysisAlexander Rutman and Adrian ViisoreanuThe Boeing CompanyJohn A. Parady, Jr.MSC. Software Corportation

2000 W orld Aviation C onferenceOctober 10-12, 2000San Diego, CA

1 The Engineering Society' For Advancing Mobility

f Land Sea Air and Space^INTERNATIONALSAE International400 Commonwealth DriveWarrendale, PA 15096-0001 U.S.A.

AMA AAmerican Institute of Aeronauticsand Astronautics370 L'Enfant Promenade, S.W.Washington, D.C. 20024

For permission tocopy or republish, contact the American Institute ofAeronautics and Astronauticsor SAE International.

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Published by the American Institute of Aeronautics and Astronautics (AIAA) at 1801 Alexander Bell Drive,Suite 500, Reston, VA 22091 U.S.A., and the Society of Automotive Engineers (SAE) at 400Commonwealth Drive, Warrendale, PA 15096 U.S.A.Produced in the U.S.A. Non-U.S. purchasers are responsible for payment of any taxes required by theirgovernments.Reproduction of copies beyond that permitted by Sections 107 and 108 of the U.S. Copyright Lawwithoutthe permission of the copyright owner is unlawful. The appearance of the ISSN code at the bottom of thispage indicates SAE's and AlAA's consent that copies of the paper may be made for personal or internaluse of specific clients, on condition that the copier pay the per-copy fee through the Copyright ClearanceCenter, Inc., 222 Rosewood Drive, Danvers, MA 01923. This consent does not extend to other kinds ofcopying such as copying for general distribution, advertising or promotional purposes, creating newcollective works, or for resale. Permission requests for these kinds of copying should be addressed toAIAA Aeroplus Access, 4th Floor, 85John Street, New York, NY 10038 or to the SAE Publications Group,400 Commonwealth Drive, Warrendale, PA 15096. Users should reference the title of this conferencewhen reporting copying to the Copyright Clearance Center.ISSN #0148-7191Copyright 2000 by The Boeing Company. Publishedby American Institute of Aeronautics andAstronautics, Inc. and SAE International with permission.Copyright 2000 by MSC.Software Corporation. Publishedby American Instituteof Aeronautics and AstronauticsInc. and SAE International with permission.All AIAA papers are abstractedand indexed in International Aerospace Abstracts and AerospaceDatabase.All SAE papers, standards and selected books are abstracted and indexed in the Global Mobility Data-base.Copies of this paper may be purchased from:AlAA's document delivery serviceAeroplus Dispatch1722 Gilbreth RoadBurlingame, California 94010-1305Phone: (800) 662-2376 or (415) 259-6011Fax:(415)259-6047or from:SAExpress Global Document Servicec/o SA E Customer Sales and Satisfaction400 Commonwealth DriveWarrendale, PA 15096Phone: (724) 776-4970Fax: (724)776-0790SAE routinely stocks printed papers for a period of three years following date of publication. Quantityreprint rates are available.No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise,without the prior written permission of the publishers.Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAEor AIAA. The author is solely responsible for the content of the paper. A process is available by whichdiscussions will be printed with the paper if it is published in SAE Transactions.

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2000-01-5585Fasteners Modeling for MSC.Nastran Finite Element Analysis

Alexander Rutman and Adrian ViisoreanuThe Boeing Company

John A. Parady, Jr.MSC.Software Corporation

Copyright 2000 by The Boeing Company. Published by SAE International and the American Institute of Aeronautics andAstronautics, Inc. with permission.Copyright 2000 by MSC. Software Corporation. Published by SAE International and the American Institute of Aeronautics andAstronautics, Inc. with permission.

ABSTRACTThe distribution of loads between the components of astructural assembly depends not only on theirdimensions and material properties but also on thestiffness of fasteners connecting the components. So, theaccuracy of the finite element analysis is influenced muchby the fastener representation in the model.This paper describes an approach designed specificallyfor joints with connected plates modeled by shellelements located at plates mid planes. The procedure isbased on definition of independent components of afastener joint flexibility, analysis of each component, andtheir assembly to represent a complete plate-fastenersystem of the joint.The proposed modeling technique differs from thetraditional approach where all the connected plates aremodeled coplanar. The traditional approach is based oncalculating a single spring rate for a particularcombination of fastener and plate properties. Theapplication of this approach is limited by single shear jointof two plates or symmetric double shear joint of threeplates. It cannot be used for other joint configurationsand for joints with larger number of connected plates.The proposed procedure is free of those limitations.Considering each fastener requires the creation ofadditional nodes and elements, it is obvious the manualuse of this procedure is practically impossible for largemodels of aircraft structures that could have thousands offasteners. A new MSC.Patran utility that automates thefasteners modeling was written and is described in thepaper. It takes advantage of the CBUSH elementformulation in MSC.Nastran and provides a user friendlyand efficient tool that creates fasteners connecting aselected group of nodes.

INTRODUCTIONThe common practice in aircraft structural analysis is thecreation of large finite element models with a coarsemesh with further extraction of separate parts along withapplied loads for hand analysis or for preparation of moredetailed models. As a rule, these parts are connected inlarge models rigidly, i.e. they share the common gridpoints. However, the distribution of loads betweenstructural parts depends not only on the parts dimensionsand mechanical properties of selected materials, but alsoon the stiffness of connecting elements, such as boltsand rivets.With increase of computers speed along with the volumeof available memory, the trend for creation of moredetailed models has arisen. These models morerealistically represent not only structural parts but alsotheir interaction including fastener joints.The widely used method of fastener joints modeling isthe joining of co-linear or co-planar finite elements oconnected structural parts with elastic elementsrepresenting fasteners. The stiffness of these elasticelements, or springs, is calculated using formulaedeveloped by empirical or semi-empirical methods. As arule, these formulae consider the combination omechanical and geometric properties of a fastener andjoined plates. Their application is usually limited to singleshear and double shear symmetric joints.With developing models more closely representingstructures but still consisting of plate elements, the joined

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(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s) 1 Sponsoring Organization.

elements are no longer located in the same plane. In thiscase, the single elastic element cannot fully reflect thework of a fastener joint.The procedure for modeling of fastener joints for detailedfinite element models with non-coplanar joined parts wasdescribed in the paper presented at the First MSCConference for Aerospace Users [1]. However, thepractical use of this method showed some of itsdisadvantages, which will be discussed later.The approach to 3-dimensional modeling of fastenerjoints is based on definition of each deformationcomponent contributing to a joint flexibility and modelingthem by corresponding finite elements. Combination ofthese elements represents the complete work of afastener joint. Some relative displacements in the modelof a fastener joint were limited to ensure the compatibilityof deformations.This paper presents an updated method for the finiteelement modeling of fastener joint for MSC.Nastran andan example of a model with fasteners. It also describes anew MSC.Patran utility for fastener joints modeling. Themethod does not consider the effect of fastenerpretension and fit. Following the aerospace industrycommon analysis practice, the friction between joint partswas not taken into account.STIFFNESS OF FASTENER JOINT

Fastener

In a fastener joint (Figurecomponents are considered:1) the following stiffness

translational plate bearing stiffness;translational fastener bearing stiffness;rotational plate bearing stiffness;rotational fastener bearing stiffness;fastener shear stiffness;fastener bending stiffness.

Under load, the plates slide relative to each other. Thiscauses the translational bearing deformations of joinedplates and a fastener. The translational bearing flexibilityof plate / is:

1

1st plate2nd plate

) 3 rd plate j 4th plate

I

di

=

/

I

A

1

1LFigure 1. Fastener joint.

where ECp. - compression modulus of plate / material;tp. - thickness of plate /.

The fastener translational bearing flexibility at plate /Cbtf, =P .> = c f lp;

where Ecf - compression modulus of fastenermaterial.Combined fastener and plate translational bearingflexibility at plate /

Cbtj = Cbtpj +CbtfjCombined translational bearing stiffness at plate /

1

The relative rotation of the plate and fastener creates amoment in the plate-fastener interaction (Figure 2). Thebearing deformations caused by this relative rotation areassumeddistributed linearly along the plate thickness

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A x

dx

72P i2

The rotational bearing flexibility of plate /r -V - 12Uhn"-M~ F ,3

The fastener rotational bearing flexibility at plate /

C =--r

Figure 2. Rotational bearing stiffness definition.

8 = X(pwhere x - coordinate along the plate thickness;

< P - angle of relative rotation of the plate andfastener.

Stiffness of a dx thick slice of plate / is:=EcPdx

Load on dx thick slice of plate / caused by the platebearing deformation

j =x

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(c)2000 American Institute of Aeronautics & Astronautics or Published w ith Permission of Author(s) and/or Author(s) ' Sponsoring Organization.

NOTES:

CBAR element Orientation vector is

parallel to Y axis offastener coordinate system

REAR element Dependent DOF's are ijkArrow points todependent node

CBUSH elementStiffness DOF's 2356X axis is aligned withfastener axis

Nodes N pj and N fj arecoincident, bu t shown offset fo rclarity.The analysis coordinate system ofall nodes is the fastener coordinatesystem.

X axis of fastenerw coordinate system

Figure 3. Fastener joint modeling.

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FASTENER MODELINGA fastener is modeled by CBAR or CBEAM elements [2]with corresponding PBAR or PBEAM cards for propertiesdefinition. For the CBAR or CBEAM elementsconnectivity, a separate set of grid points coincidentalwith corresponding plate grid points (Figure 3) is created.This set also includes grid points located on intersectionof the fastener axis and outer surfaces of the first andlast connected plates.All CBAR or CBEAM elements representing the samefastener reference the same PBAR or PBEAM card [2]with following properties: MID to reference the fastener material properties. Fastener cross-sectional area

fwhere df - fastener diameter.Moments of inertia of the fastener cross section

/ r = / 2 = -Torsional constant

64

32 Area factors for shear of circular section/C, = K2 =0.9An example of CBAR element and its propertiesdefinition for .375" dia. fastener is shown in Table 1. Analternative form of CBAR properties definition ispresented in Table 2.Definition of a fastener using CBEAM and PBEAM cardsis similar to that shown in Table 2 for CBAR and PBARwith small differences described in Reference [2].MODELING OF INTERACTION BETWEEN FASTENERAND JOINED PLATESThe interaction between a fastener and plate results inbearing deformation of all parts of the joint on theirsurfaces of contact. The bearing stiffness of a fastenerand connected plates is defined in Section "Stiffness offastener joint". The bearing stiffness is presented astranslational stiffness in direction of axes normal to the

fastener axis and defining the fastener shear plane androtational stiffness about the same axes.For the modeling of the bearing stiffness, two sets ofcoincident grid points mentioned above are used. Eachpair of coincident grid points, i.e. the plate node ancorresponding fastener node, is connected by CBUSHelement [2] or combination of CELAS2 elements withequal translational stiffness along the axes normal to thefastener axis and equal rotational stiffness about thesame axes. The connectivity card CBUSH must beaccompanied by PBUSH card defining the stiffness. TheCELAS2 card accomplishes both functions, but 4CELAS2 elements are required to replace one CBUSHelement. However it is difficult to interpret CELAS2element forces.For correct definition of a fastener shear plane and itsaxial direction, a coordinate system with one of its axisparallel to the fastener axis must be defined in the bulkdata. This coordinate system must be used as analysiscoordinate system for both sets of grid points.An example of the bearing stiffness modeling using theCBUSH and PBUSH cards is given in Table 3. It isassumed in the example that the fastener axis is parallelto x-axis of corresponding coordinate system. Analternative method for the bearing stiffness modelingusing CELAS2 elements is shown in Table 4.COMPATIBILITY OF DISPLACEMENTS IN THE JOINT

The fastener joint model was designed under thefollowing assumptions: The plates are incompressible in transversedirection; The plates mid planes stay parallel to each otherunder the load; Planes under the fastener heads stay parallel to theplate mid planes under the load.These goals are reached by using REAR elements.An example of a group of RBAR elements satisfying theabove compatibility conditions is given in Table 5. It isalso assumed in this example (Figure 3) that the fasteneraxis is parallel to the x-axis of the correspondingcoordinate system.The first RBAR card forces the plane under the fastenerhead to stay parallel to the first plate mid plane under theload. It also prevents the fastener movement as a rigidbody. The middle RBAR cards support the first two

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assumptions. They keep the constant distance betweenthe plate mid planes, i.e. assume that plates areincompressible. They also guarantee zero relativerotation of plates keeping them parallel to each other.The last card forces the plane under the other head ofthe fastener to stay parallel to the last plate mid plane.

CBARCBAR

EID21

PID206

GA1011

GB2011

XI1.0

X20.0

X30.0

PBARPBAR

PID206Cl

0.0Kl

0.9

MID2C2

0.0K2

0.9

A.11Dl

112

119.7E-4D2

12

El

J

E2

NSM

Fl F2

Table 1. Example CBAR and PBAR cards.PEARLPBARL

PID206DIM1.375

MID2NSM

GROUP TYPEROD

T a b l e 2 . Example PBARL car d.CBUSHCBUSH

EID210

PID12

GA1005

GB2005

GO/X1 X2 X3 CID0

PBUSHPBUSH

PID12

"K"K

Kl K21.6E7

K31.6E7

K4 K55.2E3

K65.2E3

Table 3. Example CBUSH and PBUSH cards.CELAS2CELAS2CELAS2CELAS2CELAS2

EID210211212213

K1.6E71.6E75.2E35.2E3

Gl1005100510051005

Cl2356

G22005200520052005

C22356

Table 4. Example CELAS2 cards.REARREARREAR... ... ...REARREAR

EID310311... ... ...314315

GA9051005... ... ...50056005

GB10052005... ... ...6005915

CNA123456123456... ... ...123456123456

CNB CMA CMB1456156... ... ...15656

Table 5. Example RBAR cards for compatibility of displacements in the joint.

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MODELING EXAMPLEA symmetric double shear joint was modeled as anexample (Figure 4). The modeled structure consists ofthree aluminum plates and two titanium fasteners. Thethickness is 0.15" for outer plates and 0.2" for inner plate.The fastener diameter is 0.25". The inner plate is loadedby a distributed load of 5000 pound/in. The model isconstrained at outer plates. The bulk data file is given inAppendix.

Figure 5 presents the analysis results. Thedisplacements at a fastener location consist of thefastener movement as a rigid body, the combined platesand fastener bearing deformations, and the fastenerbending and shear deformation. The results of analysisare in good agreement with the expected behavior of thejoint under load.

Constraints Outer platesInner plate

5.00+03

5.00+03 Distributed^ LoadFasteners

Figure 4. Example of finite element model with fasteners.

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(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

1351235

135

Fastenerbeforedeformation

Outer platebearingdeformation

Undeformedmodel

Deformedmodel

Fastenerbending and shear

deformation

Rigid elements(RBAR's)

Fastenerafterdeformation

Inner platebearing

deformation

Figure 5. Displacements of example finite element model.

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COMPARISON OF MODELING TECHNIQUESTo compare the modeling technique described in thispaper with one developed in Reference [1] the finiteelement model with fine mesh was created (Figure 6).This model is the same example model presented inprevious section with the only difference in mesh density.The fine mesh was employed to show deformation offasteners and particularly the joined plates.

Outer plateReactions Inner plate

FastenersAppliedloads

Figure 6. Fine mesh finite element model for comparisonof modeling techniques.

Under the load, the joined plates slide along each otherdue to combined plates and fastener translationalbearing deformation and the fastener bending and sheardeformation. The fastener deformation causes change ofangle between fastener and plate or in other words theirrelative rotation. This relative rotation results in non-uniform distribution of bearing stress through the platethickness. The resultant load transferred through thecontact area between the fastener and plate consists of aforce in the plate mid plane and out-of-plane moment. Inthe structure, the moment is reacted by loads on theplate contact surfaces and does not cause the plateslocal bending.The proposed modeling technique takes thisphenomenon into account ensuring the plates mid planesstay parallel to each other under load. This is reached byuse of rigid elements RBAR's connecting the plate nodesat the fastener location and forcing them to keep thesame angle of rotation during the deformation.The modeling technique presented in Reference [1]assumes that plates follow locally the fastenerdeformation. It means the fastener guides the connectedplates and it results in bending of plates and interferencebetween them. The plates bending moments in the

fastener-plate contact are distributed through the modestructural parts and causes additional stresses noexisting in real structure.Figure 7 illustrates the behavior of a fastener jointmodeled using the both discussed techniques. Plates inthe joint modeled using the proposed technique haveonly in-plane deformations. If the Reference [1] techniqueis employed, plates have clear out-of-plane deformations

Deformation of joint modeled using proposed techniquesFastenerbeforedeformation Fastener afterdeformation

P/2

P/2Plates deform only in their planes

Deformation of joint modeled using Reference Ml techniquesFastenerbeforedeformation Fastener after Deformeddeformation model

P/2

Undeformedmodel

P/2

Figure 7. Comparison of results obtained by twomodeling techniques.

MSC.PATRAN UTILITYThis section presents the algorithm of the newlydeveloped MSC.Patran utility, the data input forms(Graphical User Interface) and an example of fastenejoint modeling using this utility.UTILITY DESCRIPTIONExtraction of plate nodes for connection by fastenerThe MSC.Patran utility for modeling of fastener joints isapplied to a group of nodes selected by user in the modearea where the group of fastener joints must be created.

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The program extracts sub-groups of nodes from theentire group. Each sub-group is associated with onefastener. The criterion for node subgroups creation: thedistance between any two nodes of the subgroup mustbe smaller than or equal to the fastener length suppliedby user. The fastener length chosen by user should bebigger than the longest fastener but smaller than thedistance from any of subgroup nodes to grid points no tbelonging to the subgroup to avoid creation ofundesirable elements. This condition can influence notonly the user's definition of fastener length but also theselection of initial group of nodes.The procedure assumes that fasteners in consideredgroup have the same diameter and material. Fastenerswith different diameters or material cannot be combinedin one group. In this case separate groups of nodes mustbe selected.Plate propertiesThickness and material properties of plate elementsusing a subgroup node for connectivity are extractedfrom the MSC.Patran database and do not require theuser's input.If connected structural parts include tapered plates, thethickness of plate elements adjacent to the fastener canbe different. Moduli of elasticity for those elements canalso differ if the influence of temperature distributionalong the structure is considered in the analysis. To takethese phenomena into account the thickness andmodulus of elasticity for bearing stiffness analysis arecalculated as weighted average of plates adjacent tonode /\L:

14k= 1 t

where tpl - average plate thickness at node NPI;Epi - average plate modulus at node NP!;t' k - thickness of element k adjacent to node

N P , ;R ' k - distance between centroid of element k andnode A / p , ;

E ' k - modulus of element k adjacent to nodeN P !;H I - number of plates adjacent to node NPI.

Fastener Coordinate SystemTwo options of the fastener coordinate system definitionare available to the user: manual andautomatic.If the user selects the manual option the programrequires ID of one of previously defined coordinatesystems and ID of coordinate axis parallel to the fasteneraxis. This coordinate axis will be addressed as referenceaxis of the fastener coordinate system.If the automatic option is chosen, the program eitherselects one of previously defined coordinate systems orcreates a newone. With the automatic option, the X-axisof the fastener coordinate system is always directedalong the fastener axis. The direction of X-axis of thefastener coordinate system is defined as weightedaverage of normals of all elements adjacent to thefastener nodes:

n n/IIi=1 k=1

where X - X-axis vector;R , - distance from node N P ! to centroid ofelement / adjacent to node Npi;N k - normal of element /;

- length of vector N k ;n - number of plate nodes NP!.

The program performs an alignment check beforecomputing the direction of the X-axis. If the anglebetween normal of element k adjacent to node / andnormal of element 1 adjacent to node 1 is greater than90 then direction of normal of element k is reversed forcomputational purposes.To reduce the number of coordinate systems in themodel, the program checks the MSC.Patran database forexisting coordinate systems that could be used to definethe orientation of the current fastener with the followingtest:

10

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X

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Where S1-6 - CBUSH stiffness coefficients(Reference [2])The program then checks the MSC.Patran database forexistence of a property card PBUSH with the same data.If such PBUSH record is found, then the current CBUSHelement is associated with the existing property.Otherwise a new PBUSH record is created.Compatibility of displacementsCompatibility of displacements in the fastener joint isenforced by REAR elements. The RBAR elements arecreated as shown in Figure 3. If the fastener is on asymmetry plane, the degrees of freedom alreadyconstrained by symmetry are eliminated from thedependant set of the RBAR elements.MSC.PATRAN INPUT PANEL

Figure 8 shows the input form for the MSC.Patran utility.The starting ID of the new nodes and elements can beselected, as it is usually done in majority of input forms.On the symmetry coefficient panel the user has threechoices:

1.0 - for fasteners not located on symmetryplanes (Figure 8);

0.5 - for fasteners belonging to one plane ofsymmetry (Figure 9); 0.25- for asteners located on he ntersection of

symmetry planes (Figure 10).If the fasteners are on a symmetry plane (Figure 9), theuser must identify the coordinate system with one ofcoordinate planes coplanar with the symmetry plane.This coordinate plane is indicated by perpendicular to itscoordinate axis.When the fastener axis is on the intersection of twosymmetry planes (Figure 10), the user must to identifythe coordinate system with one axis collinear witintersection line. Two other axes are in symmetry planes.The fastener diameter and material are self-explanatory.The fastener material listbox (Figure 8) contains all thematerials currently defined in the MSC.Patran database.The fastener material must be created before this utility isexecuted.The user has two options for the fastener coordinatesystem definition: manual and automatic. If the manual

method has been chosen, the user is required not onlyidentify the existing coordinate system as a fastenecoordinate system but also to tell the program which axisof the system is parallel to the fastener axis. When theautomatic option was selected, the user is not required tosupply any additional information. In this case, theprogram either selects an existing coordinate systemaccording to established criterion or creates a new oneWhen the fastener is on intersection of two symmetryplanes identification of coordinate system is not requiredand the fastener axis selection panel is dimmed (Figure10).The user has to identify the region where fasteners wilbe created by giving the program the list of plate nodesIt is not necessarily the program will use all this nodes forconnection by fasteners. The fasteners will be createdonly between nodes located not further from each othethan the established by user maximum fastener length.

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Help

ID of first newfastener nodeStarting Node to .-J1108Starting )en tojiSO -*\~~~~~~~Node Alignment Tolerance (Deg.) \P S . O ' ' - .Symmetry Coefficient

ID of first new fastenerelementNode alignmenttolerance

j Select Mocts1 1 Mode 2:10:41

Symmetry panelFastener diameter

Fastener not to exceedlength

Fastener material

Fastener axismanually selected

Selectedplate nodes

Figure 8. MSC.Patran utility input panel when fastenersare not on symmetry plane.

posStarting Bern ID,__

Node Alignment Toterance (Deg.)]SiSSymmetry Coefficient

I J-0I 0.5I J0.25

Select Sjfm, WaneMormal: .Coord 0,2?

Coordinate axisnormal to symmetryplane

Fastener InformationDiamter length' C M S ! i^^.-..MatertaJ

Fastener Axis Method,iAutomaticSelect fastener AxisCoord 3.25

Auto Execute! Select Nodes

Node2:10:4l

Apply Cancel

Figure 9. MSC.Patran utility panel when fasteners areon symmetry plane.

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Show Description...StartingNode ID|:10SStarting Bern ID

Node Alignment Tolerance (DegJ

Symmetry coefficientJ-1,0 ' \J0.5 I;I0.2SSelect Fastener Axis

-v "

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REFERENCES1. Multi-Spring Representation of Fasteners forMSC/NASTRAN Modeling. A. Rutman, J. B. Kogan.Proceedings of The First MSC Conference for AerospaceUsers, Los Angeles, CA, 19972. MSC.Nastran Version 70.5Quick Reference Guide, TheMacNeal-Schwendler Corporation, Los Angeles, CA 1998CONTACTAlexander Rutman, Ph.D.Principal EngineerThe Boeing CompanyP.O. Box 7730, MS K89-04Wichita, KS67277alexander.rutman@ boeing.com

Adrian Viisoreanu, Ph. D.Principal EngineerThe Boeing CompanyP.O. Box 3707, MS 9U-RFSeattle, WA [email protected]

John A. Parady, Jr.,P.ESr. Application EngineerMSC.Software Corporation1000 Main Street #190Grapevine, TX 76051Phone:817-481-4812john.parady@ mscsoftware.com

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APPENDIX. BULK DATA FILE FOR EXAMPLE MODEL$ NASTRAN input file created by the MSC MSC/NASTRAN input file$ translator (MSC/PATRAN Version 8.5 ) on May 26, 2000 at$ 12:37:02.$ASSIGN OUTPDT2 = 'dsh_new_course.op2', UNIT = 12$$ Linear Static Analysis, Database$SOL 101TIME 600CEND$SEALL = ALLSUPER = ALLTITLE = MSC/NASTRAN job created on 17-Feb-OO at 17:37:42ECHO = NONEMAXLINES = 999999999$SUBCASE 1$ Subcase name : TensionSUBTITLE=Tension

SPC = 2LOAD = 2DISPLACEMENT(SORT1,REAL) =ALLSPCFORCES (SORT1, REAL) =ALLOLOAD(SORT1,REAL) =ALLSTRESS(SORT1, REAL, VONMISES, BILIN) =ALLFORCE(SORT1, REAL, BILIN) =ALL

$$BEGIN BULK$$PARAM POST -1PARAM PATVER 3.PARAM AUTOSPC YESPARAM INREL 0PARAM ALTRED NOPARAM COUPMASS -1PARAM K6ROT 10.PARAM WTMASS 1.PARAM,NOCOMPS,-!PARAM PRTMAXIM YES$$ Elements and Element Properties for region : pshell.1$PSHELL 1 1 .2 1 1$CQUAD4 1 1 12 11 15 14CQUAD4 2 1 14 15 19 18CQUAD4 3 1 18 19 23 22CQUAD4 4 1 11 25 27 15CQUAD4 5 1 15 27 31 19CQUAD4 6 1 19 31 35 23$$ Elements and Element Properties for region : pshell.2$PSHELL 2 1 .15 1 1$CQUAD4 7 2 3 6 3 7 3 9 3 8CQUAD4 8 2 38 39 43 42CQUAD4 9 2 42 43 47 46CQUAD4 10 2 37 49 51 39CQUAD4 11 2 39 51 55 43CQUAD4 12 2 43 55 59 47CQUAD4 13 2 60 61 63 62CQUAD4 14 2 62 63 67 66CQUAD4 15 2 66 67 71 70CQUAD4 16 2 61 73 75 63CQUAD4 17 2 63 75 79 67CQUAD4 18 2 67 79 83 71$$ Elements and Element Properties for region : pbar.4

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$PBAR 4$CBAR 27+ ACBAR 28+ B$$ Elements a nd$PBARL 5+ C .125$CBAR 19CBAR 20CBAR 21CBAR 22CBAR 23CBAR 24CBAR 25CBAR 26$

1 1. 1.4 22 2314 23 351

Element Properties for2 ROD

5 84 855 86 875 85 895 87 915 92 845 89 955 96 865 91 99

1.1111

region

1.1.1.1.1.1.1.1.$ Referenced Material Records$$ Material Record : aluminum$ Description$MAT1 1$

of Material : Date: 03-Feb-OO1.05+7 .33

$ Material Record : titanium$ Description$MAT1 2$$ Nodes of the$GRID 11GRID 12GRID 14GRID 15GRID 18GRID 19GRID 22GRID 23GRID 25GRID 27GRID 31GRID 35GRID 3 6GRID 3 7GRID 3 8GRID 39GRID 42GRID 43GRID 46GRID 47GRID 49GRID 51GRID 55GRID 59GRID 60GRID 61GRID 62GRID 63GRID 66GRID 67GRID 70GRID 71GRID 73GRID 75GRID 79GRID 83GRID 84GRID 85GRID 86GRID 87

of Material : Date: 08-Feb-OO1.6+7 .3

Entire Model1. 0.1. 1.1.5 1.1.5 0.3. 1.3. 0.4.5 1.4.5 0.1. -1.1.5 -1.3. -1.4.5 -1.0. 1.0. 0.1.5 1.1.5 0.3. 1.3. 0.3.5 1.3.5 0.0. -1.1.5 -1.3 . -1.3.5 -1.0. 1.0. 0.1.5 1.1.5 0.3. 1.3. 0.3.5 1.3.5 0.0. -1.1.5 -1.3. -1.3.5 -1.1.5 0.1.5 0.3. 0.3. 0.

0.0.0.0.0.0.0.0.0.0.0.0..175.175.175.175.175.175.175.175.175.175.175.175-.175-.175-.175

-.175-.175-.175- .175- .175-.175-.175-.175-.175.1750..1750.

1.A

B

pbar.5

0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

Time: 15:39:23

Time: 17:45:11

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7/29/2019 Rutman_2000

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GRIDGRIDGRIDGRIDGRIDGRID$$ Loads$SPCADD$LOAD

899192959699

for Load Case :2 ^2 1.

13.11.33

.5

.5.5

: Tension31

0.0.0.0.0.0.

-.175-.175.25

-.25.25-.25

$$ Displacement Constraints of Load Set : spc_2$SPC1 1 2 37$$ Displacement Constraints of Load Set : spc_l$SPC1 3 135 36 37 49$$ Displacement Constraints of Load Set : spc_3$SPC1 4 15 60 61 73$$ Distributed Loads of Load Set : Tension$PLOAD1 1 27 FYE FR 0.PLOAD1 1 28 FYE FR 0.$$ Bearing Stiffnesses$

-5000.-5000.

1.1.

-5000.-5000.

PBUSH 6 KPBUSH 7 K$CBUSH 31 7 39CBUSH 32 6 15CBUSH 33 7 63$CBUSH 34 7 43CBUSH 35 6 19CBUSH 36 7 67$$ Compatibility Conditions$REAR 41 92 39REAR 42 39 15REAR 43 15 63REAR 44 63 95$REAR 45 96 43REAR 46 43 19REAR 47 19 67REAR 48 67 99$$ENDDATA

1267925.1267925.950943. 950943.

848589868791

123456123456123456123456123456123456123456123456

4226.1783.

4226.1783.

345634534545345634534545

Rutman_2000

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