Fastener Modeling for Joining Composite Parts

Alexander Rutman, Associate Technical Fellow, Spirit AeroSystems

Chris Boshers, Stress Engineer, Spirit AeroSystemsJohn Parady, Principal Application Engineer, MSC.SoftwareLarry Pearce, Senior Lead Application Engineer, MSC.Software

AM-VPD09-006

References

• Fastener Modeling for Joining Composite Parts, Alexander Rutman, Chris Boshers (Spirit AeroSystems), Larry Pearce, John Parady (MSC.Software Corporation), To Be Presented at the 2009 Americas Virtual Product Development Conference, April 21-22, 2009, Phoenix, AZ

• Fastener Modeling for Joining Parts Modeled by Shell and Solid Elements, Alexander Rutman, Chris Boshers (Spirit AeroSystems), Larry Pearce, John Parady (MSC.Software Corporation), 2007 Americas Virtual Product Development Conference, October 11-12, 2007, Detroit, MI

• Fastener Modeling for MSC.Nastran Finite Element Analysis, Alexander Rutman, Adrian Viisoreanu (Boeing), John Parady (MSC.Software Corporation), 2000 World Aviation Conference, October 10-12, 2000, AIAA-2000-01-5585

Objective

• Accurately represent fastener behavior

• Rapid model preparation of each fastener

• Can be used with parts modeled by shell elements with isotropic or orthotropic material properties, parts modeled by solid elements with isotropic properties, or any combination of these parts

• Accounts for the effects of variable bearing stiffness of a fastener -composite plate interface

Develop an FEM representation of a fastener installed through multiple metal and composite plates.

Representation of a Fastener Joint

• Elastic bearing stiffness of a plate and fastener at the contact surface

• Bending and shear stiffness of a fastener shank

• Compatibility of displacements of a fastener and connected plates in the joint

Idealization of a plate-fastener system includes the following:

Compatibility of Joint Displacements

• No interference of the plates under load

• The plate’s mid-planes remain parallel to each other under load

• Planes under the fastener head and nut remain parallel to the plate mid-planes under load

Modeling displacement assumptions

Examples of Fastener Joint Models

DOF1,5,65,6

1,4,5,61

DOF2,3,5,6

RBAR

RBE2

Interaction Between Fastener Shank and Joined Plates

• Bearing stiffness between fastener shank and plate is represented by CBUSH element

• Each CBUSH element contains two non-zero axial and two non-zero rotational springs

• Translational and rotational bearing stiffnesses are defined in PBUSH cards

1st plate

2nd plate

3rd plate

Solid Element

x

Shell Element

Solid Element

CBUSHElements

Fastener

1st plate

2nd plate

3rd plate

4th plate

fd

1pt

2pt

3pt

4pt

Stiffness of a Fastened Joint in a Metallic Plate• Combined plate and fastener translational bearing

stiffness

• Combined plate and fastener rotational bearing stiffness

E - comp. modulus of plate i material- comp. modulus of fastener material

- thickness of the platecfE

pt

cf

pybrxbr

EE

tSS

11121

2

3

+−⋅==

ν

cf

ybtxbt

EE

tSS11 2

+−

==ν

Stiffness of a Fastened Joint – Change from Previous Formulation

• Comparison of Finite Element and Analytical Results for Translational Bearing Stiffness

%100⋅−

=FEM

FEManalytical

SSS

Δ

tE

21 ν−tE

Analysis Method Translational Bearing Stiffness, lb/in

Finite Element Analysis 1,192,871 -

1,030,000 -13.65

1,155,875 -3.10

Stiffness of a Fastened Joint in a Composite Plate - Extension

• Combined plate and fastener translational bearing stiffness

∑= +

=n

i

cfi

ixbt

EQ

tS1

)(11

11 ∑= +

=n

i

cfi

iybt

EQ

tS1

)(22

11

)(11

iQ

( ) 4)(22

22)(66

)(12

4)(11

)(11 22 i

iii

iii

ii nQnmQQmQQ +++=

- compression modulus of fastener material

- transformed reduced stiffness for ply i in the x-direction

- transformed reduced stiffness for ply i in the y-direction

cfE

)(22

iQ

( ) 4)(22

22)(66

)(12

4)(11

)(22 22 i

iii

iii

ii mQnmQQnQQ +++=

)(21

)(12

)(1)(

11 1 ii

ii E

Qνν−

=)(

21)(

12

)(2)(

22 1 ii

ii E

Qνν−

=)(

21)(

12

)(1

)(21

)(21

)(12

)(2

)(12)(

12 11 ii

ii

ii

iii EE

Qνν

ννν

ν−

=−

= )(12

)(66

ii GQ =

iim θcos=

iin θsin=

Where,

Stiffness of a Fastened Joint in a Composite Plate - Rotation

• Combined plate and fastener rotational bearing stiffness

• Centroid Location

( ) ( )∑=

−

+

−−−==

n

i

cfi

xixi

x

xxbr

EQ

czczMS1

)(11

31

3

1131

φ( ) ( )

∑=

−

+

−−−==

n

i

cfi

yiyi

y

yybr

EQ

czczMS

1)(

22

31

3

1131

φ

xbt

n

i

cfi

ii

x SEQ

zz

c

∑=

−

+

−

⋅=

1)(

11

21

2

11

21

ybt

n

i

cfi

ii

y SEQ

zz

c

∑=

−

+

−

⋅=

1)(

22

21

2

11

21

Analysis Procedure and Limitations

• The bearing stiffness in the joint depends on the direction of the fastener reactions. Because these directions are not known prior to running the model, an iterative procedure is required to accurately determine fastener reactions.

• For composite plates with variable in-plane stiffnesses, the spring analogy used in this analysis does not take coupling between transverse displacements into account. The error induced by this approximation is expected to be small and will decrease with each iteration.

Procedure for Analysis of a Fastened JointConstruct FEM, Determine

Initial Properties

Determine Fastener Reactions –Magnitude and Direction

Run FEM

CompareReactions toPrevious Run

SummarizeReactions

Update FastenerStiffnesses

ConvergedNot

Converged

Initial Run? YesNo

Example – Composite Plate in Double ShearDesign Configuration

FEM – UpperPlate RemovedFEM – Isoview

Fasteners

Finite Element Model

100 lb

Example – Bearing Stiffnesses as a Function of Resultant Fastener Direction

θ0°

90°

Example – Fastener Reactions After Initial Run

Fastener ID Rx Ry θ

1 -29.5 46.9 122.2°

2 29.3 46.9 58.0°

3 -49.9 3.13 176.4°

4 50.1 3.02 3.4°

100 lb

Example – Fastener Reactions After 2nd

RunFastener ID Rx Ry θ

1 -25.8 49.5 117.5°

2 25.6 49.6 62.7°

3 -49.4 0.5 179.4°

4 49.6 0.395 0.5°

100 lb

Example – Fastener Reactions After Final Run

Fastener ID Rx Ry θ

1 -25.2 49.7 116.9°

2 25.1 49.8 63.3°

3 -49.5 0.3 179.7°

4 49.6 0.2 0.2°

100 lb

Example – Summary of Analysis Results

Fastener Load Convergence

0

1

2

3

4

5

1 2 3Run #

Cha

nge

in L

oad

(lb)

Fastener 1, Px

Fastener 1, Py

Fastener 3, Px

Fastener 3, Py

4

1

2

3

4

Patran Fastener Builder

• MSC.Software is currently developing a PCL procedure consisting of two parts:

– The first part shall quickly and easily create fasteners in Patran for models containing plates with composite and optionally metal material properties.

– The second part is needed for updating bearing stiffnesses in the composite plate-fastener interface.

• An MSC.Nastran procedure for automatically iterating the process is very desirable to increase the speed of the analysis.

Patran Fastener Builder Panel

Patran Iterative Analysis Panel

Conclusions

• The fastener modeling technique developed for isotropic materials has been extended to models containing composite plates.

• The previous formulae for computing bearing stiffnesses for fasteners in a metal plate has been modified to better account for plate behavior.

• Due to the variation of in-plane stiffnesses of a composite material, an iterative procedure is necessary to accurately determine fastener loads.

• An automated PCL procedure is under development to quickly and easily create fastener representations in MSC Patran.

13/05/2009 22

Contact Details :

• For further information please contact

Alexander Rutman316-523-7048alexander.rutman@spiritaero.com

Chris Boshers316-523-0374chris.boshers@spiritaero.com

Spirit AeroSystemsP.O. Box 780008Mail Zone K78-20Wichita KS, 67230USA

John Parady817-481-4812, ext. 15john.parady@mscsoftware.com

Larry Pearce770-252-6560larry.pearce@mscsoftware.com

MSC.Software2 MacArthur PlaceSanta Ana, CA 92707USA