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2000-01-5585

Fasteners Modeling for MSC.Nastran Finite Element Analysis

Alexander Rutman, Adrian Viisoreanu
The Boeing Company

John A. Parady, Jr.

MSC.Software Corporation

Copyright © 2000 by The Boeing Company & MSC.Software Corporation, all rights reserved. Published by SAE International and the American
Institute of Aeronautics and Astronautics, Inc. with permission

ABSTRACT and efficient tool that creates fasteners connecting a

selected group of nodes.
The distribution of loads between the components of a
structural assembly depends not only on their INTRODUCTION
dimensions and material properties but also on the
stiffness of fasteners connecting the components. So, the The common practice in aircraft structural analysis is the
accuracy of the finite element analysis is influenced much creation of large finite element models with a coarse
by the fastener representation in the model. mesh with further extraction of separate parts along with
applied loads for hand analysis or for preparation of more
This paper describes an approach designed specifically detailed models. As a rule, these parts are connected in
for joints with connected plates modeled by shell large models rigidly, i.e. they share the common grid
elements located at plates mid planes. The procedure is points. However, the distribution of loads between
based on definition of independent components of a structural parts depends not only on the parts dimensions
fastener joint flexibility, analysis of each component, and and mechanical properties of selected materials, but also
their assembly to represent a complete plate-fastener on the stiffness of connecting elements, such as bolts
system of the joint. and rivets.

The proposed modeling technique differs from the With increase of computers speed along with the volume
traditional approach where all the connected plates are of available memory, the trend for creation of more
modeled coplanar. The traditional approach is based on detailed models has arisen. These models more
calculating a single spring rate for a particular realistically represent not only structural parts but also
combination of fastener and plate properties. The their interaction including fastener joints.
application of this approach is limited by single shear joint
of two plates or symmetric double shear joint of three The widely used method of fastener joints modeling is
plates. It cannot be used for other joint configurations the joining of co-linear or co-planar finite elements of
and for joints with larger number of connected plates. connected structural parts with elastic elements
The proposed procedure is free of those limitations. representing fasteners. The stiffness of these elastic
elements, or springs, is calculated using formulae
Considering each fastener requires the creation of developed by empirical or semi-empirical methods. As a
additional nodes and elements, it is obvious the manual rule, these formulae consider the combination of
use of this procedure is practically impossible for large mechanical and geometric properties of a fastener and
models of aircraft structures that could have thousands of joined plates. Their application is usually limited to single
fasteners. A new MSC.Patran utility that automates the shear and double shear symmetric joints.
fasteners modeling was written and is described in the
paper. It takes advantage of the CBUSH element With developing models more closely representing
formulation in MSC.Nastran and provides a user friendly structures but still consisting of plate elements, the joined
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elements are no longer located in the same plane. In this

case, the single elastic element cannot fully reflect the
work of a fastener joint.

The procedure for modeling of fastener joints for detailed

finite element models with non-coplanar joined parts was
described in the paper presented at the First MSC
Conference for Aerospace Users [1]. However, the
practical use of this method showed some of its
disadvantages, which will be discussed later.

The approach to 3-dimensional modeling of fastener

joints is based on definition of each deformation
component contributing to a joint flexibility and modeling
them by corresponding finite elements. Combination of
these elements represents the complete work of a
fastener joint. Some relative displacements in the model
of a fastener joint were limited to ensure the compatibility
Figure 1. Fastener joint.
of deformations.

This paper presents an updated method for the finite

element modeling of fastener joint for MSC.Nastran and
an example of a model with fasteners. It also describes a where E cpi - compression modulus of plate i material;
new MSC.Patran utility for fastener joints modeling. The
method does not consider the effect of fastener t pi - thickness of plate i.
pretension and fit. Following the aerospace industry
common analysis practice, the friction between joint parts The fastener translational bearing flexibility at plate i
was not taken into account.
1
STIFFNESS OF FASTENER JOINT C btfi =
E cf t pi
In a fastener joint (Figure 1) the following stiffness
components are considered: where E cf - compression modulus of fastener
• translational plate bearing stiffness; material .
• translational fastener bearing stiffness;
• rotational plate bearing stiffness; Combined fastener and plate translational bearing
• rotational fastener bearing stiffness; flexibility at plate i
• fastener shear stiffness;
• fastener bending stiffness. C bt i = Cbtp i + Cbtf i

Combined translational bearing stiffness at plate i

Under load, the plates slide relative to each other. This
causes the translational bearing deformations of joined
1
plates and a fastener. The translational bearing flexibility S bt i =
of plate i is: C bt i

1 The relative rotation of the plate and fastener creates a

C btp i =
E cpi t pi moment in the plate-fastener interaction (Figure 2). The
bearing deformations caused by this relative rotation are
assumed distributed linearly along the plate thickness
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t pi
2 t p3i
M = E cpi ϕ ∫t x dx = E cpi ϕ
2
12
−
pi

The rotational bearing flexibility of plate i

ϕ 12
C brpi = =
M E cp t 3
i p i

The fastener rotational bearing flexibility at plate i

12
C brfi =
E cf t p3
i

Combined fastener and plate rotational bearing flexibility

at plate i
Figure 2. Rotational bearing stiffness definition.
C bri = C brpi + C brfi

Combined rotational bearing stiffness at plate i

δ = xϕ
1
where x - coordinate along the plate thickness; Sbri =
ϕ - angle of relative rotation of the plate and
Cbri
fastener.
The bearing stiffness is modeled by elastic elements.
Stiffness of a dx thick slice of plate i is: The shear and bending stiffness of a fastener are
represented by a beam element.
dSbtpi = E cpi dx
MODELING OF A FASTENER JOINT

Load on dx thick slice of plate i caused by the plate Modeling of a fastener joint is illustrated here using
bearing deformation MSC.Nastran.

dF = δ dSbtpi = xϕE cpi dx REPRESENTATION OF A FASTENER JOINT

Moment of dF force about the plate i center line Idealization of a plate-fastener system includes the
following:
dM = x dF = E cpi ϕ x 2 dx • Elastic bearing stiffness of a plate and fastener at
contact surface;
Moment in the plate-fastener contact caused by the plate • Bending and shear stiffness of a fastener shank;
deformation • Compatibility of displacements of a fastener and
connected plates at the joint.

The presented method creates the plate-fastener system

illustrated in Figure 3.
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Figure 3. Fastener joint modeling.

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FASTENER MODELING fastener axis and defining the fastener shear plane and
rotational stiffness about the same axes.
A fastener is modeled by CBAR or CBEAM elements [2]
with corresponding PBAR or PBEAM cards for properties For the modeling of the bearing stiffness, two sets of
definition. For the CBAR or CBEAM elements coincident grid points mentioned above are used. Each
connectivity, a separate set of grid points coincidental pair of coincident grid points, i.e. the plate node and
with corresponding plate grid points (Figure 3) is created. corresponding fastener node, is connected by CBUSH
This set also includes grid points located on intersection element [2] or combination of CELAS2 elements with
of the fastener axis and outer surfaces of the first and equal translational stiffness along the axes normal to the
last connected plates. fastener axis and equal rotational stiffness about the
same axes. The connectivity card CBUSH must be
All CBAR or CBEAM elements representing the same accompanied by PBUSH card defining the stiffness. The
fastener reference the same PBAR or PBEAM card [2] CELAS2 card accomplishes both functions, but 4
with following properties: CELAS2 elements are required to replace one CBUSH
element. However it is difficult to interpret CELAS2
• MID to reference the fastener material properties. element forces.
• Fastener cross-sectional area
For correct definition of a fastener shear plane and its
π d f2 axial direction, a coordinate system with one of its axis
A=
4 parallel to the fastener axis must be defined in the bulk
where df - fastener diameter. data. This coordinate system must be used as analysis
coordinate system for both sets of grid points.
• Moments of inertia of the fastener cross section
An example of the bearing stiffness modeling using the
π d f4 CBUSH and PBUSH cards is given in Table 3. It is
I1 = I 2 = assumed in the example that the fastener axis is parallel
64
to x-axis of corresponding coordinate system. An
• Torsional constant alternative method for the bearing stiffness modeling
using CELAS2 elements is shown in Table 4.
π d f4
J= COMPATIBILITY OF DISPLACEMENTS IN THE JOINT
32
The fastener joint model was designed under the
• Area factors for shear of circular section
following assumptions:
K 1 = K 2 = 0. 9
• The plates are incompressible in transverse
An example of CBAR element and its properties direction;
definition for .375” dia. fastener is shown in Table 1. An • The plates mid planes stay parallel to each other
alternative form of CBAR properties definition is under the load;
presented in Table 2. • Planes under the fastener heads stay parallel to the
plate mid planes under the load.
Definition of a fastener using CBEAM and PBEAM cards
is similar to that shown in Table 2 for CBAR and PBAR These goals are reached by using RBAR elements.
with small differences described in Reference [2].
An example of a group of RBAR elements satisfying the
MODELING OF INTERACTION BETWEEN FASTENER above compatibility conditions is given in Table 5. It is
AND JOINED PLATES also assumed in this example (Figure 3) that the fastener
axis is parallel to the x-axis of the corresponding
The interaction between a fastener and plate results in coordinate system.
bearing deformation of all parts of the joint on their
surfaces of contact. The bearing stiffness of a fastener The first RBAR card forces the plane under the fastener
and connected plates is defined in Section “Stiffness of head to stay parallel to the first plate mid plane under the
fastener joint”. The bearing stiffness is presented as load. It also prevents the fastener movement as a rigid
translational stiffness in direction of axes normal to the body. The middle RBAR cards support the first two
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assumptions. They keep the constant distance between rotation of plates keeping them parallel to each other.
the plate mid planes, i.e. assume that plates are The last card forces the plane under the other head of
incompressible. They also guarantee zero relative the fastener to stay parallel to the last plate mid plane.

CBAR EID PID GA GB X1 X2 X3

CBAR 21 206 1011 2011 1.0 0.0 0.0

PBAR PID MID A I1 I2 J NSM

PBAR 206 2 .11 9.7E-4
C1 C2 D1 D2 E1 E2 F1 F2
0.0 0.0
K1 K2 I12
0.9 0.9
Table 1. Example CBAR and PBAR cards.

PBARL PID MID GROUP TYPE

PBARL 206 2 ROD
DIM1 NSM
.375
Table 2. Example PBARL card.

CBUSH EID PID GA GB G0/X1 X2 X3 CID

CBUSH 210 12 1005 2005 0

PBUSH PID “K” K1 K2 K3 K4 K5 K6

PBUSH 12 K 1.6E7 1.6E7 5.2E3 5.2E3

Table 3. Example CBUSH and PBUSH cards.

CELAS2 EID K G1 C1 G2 C2
CELAS2 210 1.6E7 1005 2 2005 2
CELAS2 211 1.6E7 1005 3 2005 3
CELAS2 212 5.2E3 1005 5 2005 5
CELAS2 213 5.2E3 1005 6 2005 6

Table 4. Example CELAS2 cards.

RBAR EID GA GB CNA CNB CMA CMB

RBAR 310 905 1005 123456 1456
RBAR 311 1005 2005 123456 156
… … … … … … … … … … … … … … … … … …
RBAR 314 5005 6005 123456 156
RBAR 315 6005 915 123456 56
Table 5. Example RBAR cards for compatibility of displacements in the joint.
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MODELING EXAMPLE Figure 5 presents the analysis results. The

displacements at a fastener location consist of the
A symmetric double shear joint was modeled as an fastener movement as a rigid body, the combined plates
example (Figure 4). The modeled structure consists of and fastener bearing deformations, and the fastener
three aluminum plates and two titanium fasteners. The bending and shear deformation. The results of analysis
thickness is 0.15” for outer plates and 0.2” for inner plate. are in good agreement with the expected behavior of the
The fastener diameter is 0.25”. The inner plate is loaded joint under load.
by a distributed load of 5000 pound/in. The model is
constrained at outer plates. The bulk data file is given in
Appendix.

Figure 4. Example of finite element model with fasteners.

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Figure 5. Displacements of example finite element model.

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COMPARISON OF MODELING TECHNIQUES fastener-plate contact are distributed through the model
structural parts and causes additional stresses not
To compare the modeling technique described in this existing in real structure.
paper with one developed in Reference [1] the finite
element model with fine mesh was created (Figure 6). Figure 7 illustrates the behavior of a fastener joint
This model is the same example model presented in modeled using the both discussed techniques. Plates in
previous section with the only difference in mesh density. the joint modeled using the proposed technique have
The fine mesh was employed to show deformation of only in-plane deformations. If the Reference [1] technique
fasteners and particularly the joined plates. is employed, plates have clear out-of-plane deformations.

Outer plate

Reactions Inner plate

Z
Y
Outer plate Applied
X
Fasteners loads

Figure 6. Fine mesh finite element model for comparison

of modeling techniques.

Under the load, the joined plates slide along each other
due to combined plates and fastener translational
bearing deformation and the fastener bending and shear
deformation. The fastener deformation causes change of
angle between fastener and plate or in other words their
relative rotation. This relative rotation results in non- Figure 7. Comparison of results obtained by two
uniform distribution of bearing stress through the plate modeling techniques.
thickness. The resultant load transferred through the
contact area between the fastener and plate consists of a
force in the plate mid plane and out-of-plane moment. In
the structure, the moment is reacted by loads on the MSC.PATRAN UTILITY
plate contact surfaces and does not cause the plates
local bending. This section presents the algorithm of the newly
developed MSC.Patran utility, the data input forms
The proposed modeling technique takes this (Graphical User Interface) and an example of fastener
phenomenon into account ensuring the plates mid planes joint modeling using this utility.
stay parallel to each other under load. This is reached by
use of rigid elements RBAR’s connecting the plate nodes UTILITY DESCRIPTION
at the fastener location and forcing them to keep the
same angle of rotation during the deformation. Extraction of plate nodes for connection by fastener

The modeling technique presented in Reference [1] The MSC.Patran utility for modeling of fastener joints is
assumes that plates follow locally the fastener applied to a group of nodes selected by user in the model
deformation. It means the fastener guides the connected area where the group of fastener joints must be created.
plates and it results in bending of plates and interference
between them. The plates bending moments in the
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The program extracts sub-groups of nodes from the Fastener Coordinate System
entire group. Each sub-group is associated with one
fastener. The criterion for node subgroups creation: the Two options of the fastener coordinate system definition
distance between any two nodes of the subgroup must are available to the user: manual and automatic.
be smaller than or equal to the fastener length supplied
by user. The fastener length chosen by user should be If the user selects the manual option the program
bigger than the longest fastener but smaller than the requires ID of one of previously defined coordinate
distance from any of subgroup nodes to grid points not systems and ID of coordinate axis parallel to the fastener
belonging to the subgroup to avoid creation of axis. This coordinate axis will be addressed as reference
undesirable elements. This condition can influence not axis of the fastener coordinate system.
only the user’s definition of fastener length but also the
selection of initial group of nodes. If the automatic option is chosen, the program either
selects one of previously defined coordinate systems or
The procedure assumes that fasteners in considered creates a new one. With the automatic option, the X-axis
group have the same diameter and material. Fasteners of the fastener coordinate system is always directed
with different diameters or material cannot be combined along the fastener axis. The direction of X-axis of the
in one group. In this case separate groups of nodes must fastener coordinate system is defined as weighted
be selected. average of normals of all elements adjacent to the
fastener nodes:
Plate properties
ni
r
n
Nki
Thickness and material properties of plate elements ∑∑
i =1 k =1
r
Nki Rki
using a subgroup node for connectivity are extracted
X=
r
from the MSC.Patran database and do not require the n ni
1
user’s input.
∑∑ R
i =1 k =1
i
k
If connected structural parts include tapered plates, the
thickness of plate elements adjacent to the fastener can
be different. Moduli of elasticity for those elements can where X - X-axis vector;
also differ if the influence of temperature distribution Ri - distance from node NPi to centroid of
along the structure is considered in the analysis. To take element i adjacent to node NPi ;
these phenomena into account the thickness and
modulus of elasticity for bearing stiffness analysis are Nki - normal of element i ;
calculated as weighted average of plates adjacent to i
N ki - length of vector Nk ;
node NPi :
n - number of plate nodes NPi .
ni ni
1 1
∑ t ki i
Rk
∑ Eki i
Rk
The program performs an alignment check before
t pi = k =1ni E pi = k =1ni computing the direction of the X-axis. If the angle
1 1
∑ ∑
between normal of element k adjacent to node i and
i i normal of element 1 adjacent to node 1 is greater than
k =1 R k k =1 R k 0
90 , then direction of normal of element k is reversed for
computational purposes.
where tPi - average plate thickness at node NPi ;
EPi - average plate modulus at node NPi ; To reduce the number of coordinate systems in the
t ki - thickness of element k adjacent to node model, the program checks the MSC.Patran database for
NPi ; existing coordinate systems that could be used to define
Rki - distance between centroid of element k and the orientation of the current fastener with the following
test:
node NPi ;
E ki - modulus of element k adjacent to node
NPi ;
n i - number of plates adjacent to node NPi .
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Model symmetry
Xj ×X
≤ sin α The symmetry coefficient η is used to scale the
Xj X properties of fasteners located on symmetry planes.

If the structure has one symmetry plane and only half of

where X j - X axis vector of existing coordinate the structure is modeled, η = 0.5 for the fasteners located
system CIDj ; on the symmetry plane.
X j × X - vector product of X j and X ;
For structures with two symmetry planes, when only
α - tolerance angle, default value 1 .
0
quarter of the structure is modeled, a fastener located on
the intersection of the two symmetry planes has η = 0.25.
If an existing coordinate system satisfying the above test For other fasteners located on symmetry planes, η = 0.5
is found, the program uses it to define the axis of the is used.
current fastener. Otherwise a new coordinate system is
created and committed to the database. Coordinates of For fasteners not located on symmetry planes, η = 1.0.
the new coordinate system origin are
Modeling of fasteners
n n n

∑X i ∑Y i ∑Z i Each fastener is represented by a group of CBAR

X0 = i =1
Y0 = i =1
Z0 = i =1
elements. The program creates CBAR elements between
n n n nodes NH1, NF1, ... , NFn, NH2 (see Figure 3). The orientation
vector of the CBAR elements is given by one of axes
where Xi, Yi, Zi - coordinates of plate nodes NPi . normal to the reference axis of the fastener coordinate
system. Calculation of CBAR elements section properties
Two other axes of the fastener coordinate system must is described in Section “Modeling of a fastener joint”.
be in plane normal to the fastener axis. Area, moments of inertia, and torsional constant of
fasteners located on symmetry planes are multiplied by
Alignment of plate nodes coefficient η.

When different structural parts are modeled separately If a PBAR property card with same data already exists,
and sometimes by different modelers, it is possible that the program associates the current CBAR to the existing
some plate nodes, which should be connected by a property. Otherwise a new PBAR record is created.
single fastener, are not collinear. If the maximum
deviation of those nodes normally to the fastener Fastener-plate interface
direction is smaller than the tolerance established by
user, the program defines the fastener axis as passing CBUSH elements created between plate nodes NPi and
through point (Xo, Yo, Zo) parallel to the reference axis of their corresponding fastener nodes NFi represent
the fastener coordinate system. If the deviation of plate fastener-plate interface. An example of expressions for
nodes exceeds the established tolerance, program stops the CBUSH stiffness coefficients when the fastener axis
and the corresponding message is displayed. is parallel to X-axis of the fastener coordinate system:

Creation of fastener nodes η t pi

S1 = 0 S2 = S3 =
The new fastener nodes NFi are created as duplicates of 1 1
corresponding plate nodes NPi. In addition to these
+
E cp i E cf
nodes, the program creates the fastener head node NH1
at distance tP1 / 2 from node NF1 and fastener node NH2 at
distance tPn from node NFn along the fastener axis, as η t p3
shown in Figure 3. The analysis coordinate system of all S4 = 0 S5 = S6 = i
fastener nodes is the fastener coordinate system.  1 1 
12 +
 E cp E cf 
 i
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Where S1-6 - CBUSH stiffness coefficients method has been chosen, the user is required not only
(Reference [2]) identify the existing coordinate system as a fastener
coordinate system but also to tell the program which axis
The program then checks the MSC.Patran database for of the system is parallel to the fastener axis. When the
existence of a property card PBUSH with the same data. automatic option was selected, the user is not required to
If such PBUSH record is found, then the current CBUSH supply any additional information. In this case, the
element is associated with the existing property. program either selects an existing coordinate system
Otherwise a new PBUSH record is created. according to established criterion or creates a new one.
When the fastener is on intersection of two symmetry
Compatibility of displacements planes identification of coordinate system is not required
and the fastener axis selection panel is dimmed (Figure
Compatibility of displacements in the fastener joint is 10).
enforced by RBAR elements. The RBAR elements are
created as shown in Figure 3. If the fastener is on a The user has to identify the region where fasteners will
symmetry plane, the degrees of freedom already be created by giving the program the list of plate nodes.
constrained by symmetry are eliminated from the It is not necessarily the program will use all this nodes for
dependant set of the RBAR elements. connection by fasteners. The fasteners will be created
only between nodes located not further from each other
MSC.PATRAN INPUT PANEL than the established by user maximum fastener length.

Figure 8 shows the input form for the MSC.Patran utility.

The starting ID of the new nodes and elements can be
selected, as it is usually done in majority of input forms.
On the symmetry coefficient panel the user has three
choices:

• 1.0 - for fasteners not located on symmetry

planes (Figure 8);

• 0.5 – for fasteners belonging to one plane of

symmetry (Figure 9);

• 0.25 – for fasteners located on the intersection of

symmetry planes (Figure 10).

If the fasteners are on a symmetry plane (Figure 9), the

user must identify the coordinate system with one of
coordinate planes coplanar with the symmetry plane.
This coordinate plane is indicated by perpendicular to its
coordinate axis.

When the fastener axis is on the intersection of two

symmetry planes (Figure 10), the user must to identify
the coordinate system with one axis collinear wit
intersection line. Two other axes are in symmetry planes.

The fastener diameter and material are self-explanatory.

The fastener material listbox (Figure 8) contains all the
materials currently defined in the MSC.Patran database.
The fastener material must be created before this utility is
executed.

The user has two options for the fastener coordinate

system definition: manual and automatic. If the manual
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Figure 8. MSC.Patran utility input panel when fasteners

are not on symmetry plane.

Figure 9. MSC.Patran utility panel when fasteners are

on symmetry plane.
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EXAMPLE OF MSC.PATRAN UTILITY APPLICATION

Figure 11 shows a fragment of example model consisting

of three plates made from different materials. The shown
plate nodes were selected for connection by a fastener.

Figure 11. Example model before fastener creation.

The fastener axis is X-axis of local coordinate system 1.

Figure 12 shows the fastener created between the three
selected nodes. Degrees of freedom of CBUSH and
RBAR elements refer to the same local coordinate
system 1.

Figure 10. MSC.Patran utility panel when fasteners are

on intersection of two symmetry planes.

Figure 12. Example model with created fastener.

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REFERENCES

1. Multi-Spring Representation of Fasteners for

MSC/NASTRAN Modeling. A. Rutman, J. B. Kogan.
Proceedings of The First MSC Conference for Aerospace
Users, Los Angeles, CA, 1997
2. MSC.Nastran Version 70.5 Quick Reference Guide, The
MacNeal-Schwendler Corporation, Los Angeles, CA 1998

CONTACT

Alexander Rutman, Ph.D. Adrian Viisoreanu, Ph. D. John A. Parady, Jr., P.E
Principal Engineer Principal Engineer Sr. Application Engineer
The Boeing Company The Boeing Company MSC.Software Corporation
P.O. Box 7730, MS K89-04 P.O. Box 3707, MS 9U-RF 1000 Main Street #190
Wichita, KS 67277 Seattle, WA 98124-2207 Grapevine, TX 76051
alexander.rutman@boeing.com adrian.viisoreanu@boeing.com Phone: 817-481-4812
john.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 OUTPUT2 = ’dsh_new_course.op2’, UNIT = 12
$
$ Linear Static Analysis, Database
$
SOL 101
TIME 600
CEND
$
SEALL = ALL
SUPER = ALL
TITLE = MSC/NASTRAN job created on 17-Feb-00 at 17:37:42
ECHO = NONE
MAXLINES = 999999999
$
SUBCASE 1
$ Subcase name : Tension
SUBTITLE=Tension
SPC = 2
LOAD = 2
DISPLACEMENT(SORT1,REAL)=ALL
SPCFORCES(SORT1,REAL)=ALL
OLOAD(SORT1,REAL)=ALL
STRESS(SORT1,REAL,VONMISES,BILIN)=ALL
FORCE(SORT1,REAL,BILIN)=ALL
$
$
BEGIN BULK
$
$
PARAM POST -1
PARAM PATVER 3.
PARAM AUTOSPC YES
PARAM INREL 0
PARAM ALTRED NO
PARAM COUPMASS -1
PARAM K6ROT 10.
PARAM WTMASS 1.
PARAM,NOCOMPS,-1
PARAM PRTMAXIM YES
$
$ Elements and Element Properties for region : pshell.1
$
PSHELL 1 1 .2 1 1
$
CQUAD4 1 1 12 11 15 14
CQUAD4 2 1 14 15 19 18
CQUAD4 3 1 18 19 23 22
CQUAD4 4 1 11 25 27 15
CQUAD4 5 1 15 27 31 19
CQUAD4 6 1 19 31 35 23
$
$ Elements and Element Properties for region : pshell.2
$
PSHELL 2 1 .15 1 1
$
CQUAD4 7 2 36 37 39 38
CQUAD4 8 2 38 39 43 42
CQUAD4 9 2 42 43 47 46
CQUAD4 10 2 37 49 51 39
CQUAD4 11 2 39 51 55 43
CQUAD4 12 2 43 55 59 47
CQUAD4 13 2 60 61 63 62
CQUAD4 14 2 62 63 67 66
CQUAD4 15 2 66 67 71 70
CQUAD4 16 2 61 73 75 63
CQUAD4 17 2 63 75 79 67
CQUAD4 18 2 67 79 83 71
$
$ Elements and Element Properties for region : pbar.4
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$
PBAR 4 1 1. 1. 1. 1.
$
CBAR 27 4 22 23 11 + A
+ A 1
CBAR 28 4 23 35 11 + B
+ B 1
$
$ Elements and Element Properties for region : pbar.5
$
PBARL 5 2 ROD + C
+ C .125
$
CBAR 19 5 84 85 1. 0. 0.
CBAR 20 5 86 87 1. 0. 0.
CBAR 21 5 85 89 1. 0. 0.
CBAR 22 5 87 91 1. 0. 0.
CBAR 23 5 92 84 1. 0. 0.
CBAR 24 5 89 95 1. 0. 0.
CBAR 25 5 96 86 1. 0. 0.
CBAR 26 5 91 99 1. 0. 0.
$
$ Referenced Material Records
$
$ Material Record : aluminum
$ Description of Material : Date: 03-Feb-00 Time: 15:39:23
$
MAT1 1 1.05+7 .33
$
$ Material Record : titanium
$ Description of Material : Date: 08-Feb-00 Time: 17:45:11
$
MAT1 2 1.6+7 .3
$
$ Nodes of the Entire Model
$
GRID 11 1. 0. 0.
GRID 12 1. 1. 0.
GRID 14 1.5 1. 0.
GRID 15 1.5 0. 0.
GRID 18 3. 1. 0.
GRID 19 3. 0. 0.
GRID 22 4.5 1. 0.
GRID 23 4.5 0. 0.
GRID 25 1. -1. 0.
GRID 27 1.5 -1. 0.
GRID 31 3. -1. 0.
GRID 35 4.5 -1. 0.
GRID 36 0. 1. .175
GRID 37 0. 0. .175
GRID 38 1.5 1. .175
GRID 39 1.5 0. .175
GRID 42 3. 1. .175
GRID 43 3. 0. .175
GRID 46 3.5 1. .175
GRID 47 3.5 0. .175
GRID 49 0. -1. .175
GRID 51 1.5 -1. .175
GRID 55 3. -1. .175
GRID 59 3.5 -1. .175
GRID 60 0. 1. -.175
GRID 61 0. 0. -.175
GRID 62 1.5 1. -.175
GRID 63 1.5 0. -.175
GRID 66 3. 1. -.175
GRID 67 3. 0. -.175
GRID 70 3.5 1. -.175
GRID 71 3.5 0. -.175
GRID 73 0. -1. -.175
GRID 75 1.5 -1. -.175
GRID 79 3. -1. -.175
GRID 83 3.5 -1. -.175
GRID 84 1.5 0. .175
GRID 85 1.5 0. 0.
GRID 86 3. 0. .175
GRID 87 3. 0. 0.
 Downloaded from SAE International by Univ of Nottingham - Kings Meadow Campus, Saturday, August 11, 2018

GRID 89 1.5 0. -.175

GRID 91 3. 0. -.175
GRID 92 1.5 0. .25
GRID 95 1.5 0. -.25
GRID 96 3. 0. .25
GRID 99 3. 0. -.25
$
$ Loads for Load Case : Tension
$
SPCADD 2 1 3 4
$
LOAD 2 1. 1. 1
$
$ Displacement Constraints of Load Set : spc_2
$
SPC1 1 2 37
$
$ Displacement Constraints of Load Set : spc_1
$
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. -5000. 1. -5000.
PLOAD1 1 28 FYE FR 0. -5000. 1. -5000.
$
$ Bearing Stiffnesses
$
PBUSH 6 K 1267925.1267925. 4226. 4226.
PBUSH 7 K 950943. 950943. 1783. 1783.
$
CBUSH 31 7 39 84 0
CBUSH 32 6 15 85 0
CBUSH 33 7 63 89 0
$
CBUSH 34 7 43 86 0
CBUSH 35 6 19 87 0
CBUSH 36 7 67 91 0
$
$ Compatibility Conditions
$
RBAR 41 92 39 123456 3456
RBAR 42 39 15 123456 345
RBAR 43 15 63 123456 345
RBAR 44 63 95 123456 45
$
RBAR 45 96 43 123456 3456
RBAR 46 43 19 123456 345
RBAR 47 19 67 123456 345
RBAR 48 67 99 123456 45
$
$
ENDDATA