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Selective Mass Scaling(SMS) Theory and Practice Theory and Practice Thomas Borrvall Dynamore Nordic AB October 2011 1 LSDYNA information
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Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

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Page 1: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Selective Mass Scaling (SMS)g ( )

Theory and PracticeTheory and Practice

Thomas BorrvallDynamore Nordic AB

October 2011 1LS‐DYNA information

Page 2: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Content

B k d• Background– Is SMS newsworthy?h d l• Theory and Implementation– Difference between CMS and SMS

d h h d– Under the hood– When and how to use SMSR t d l t• Recent developments– Rotational SMSS t d f t– Supported features

• Examples

Page 3: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

SMS originsg

• Lars Olovsson et.al., Selective Mass Scaling for Explicit Finite Element Analyses, Int. J. Num. Methods Eng. (2005)

• Implemented in LS‐DYNA for SMP in May 2006• Supported for MPP in September 2006• Supported trivial boundary constraints and adaptivity• Supported trivial boundary constraints and adaptivity• Initially intended for metal forming• Since then things have evolved…

Page 4: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Explicit Finite Elementsie 1 )( ffMa

p

tnnn

nnn

2/12/1

)(avv

ffMa

• Geometry updatetnnn 2/11 vuu

• Mass matrix diagonal ImmMn

meee ne

m2 • Stability

e

eeee El

mlE

t minmin2

max

emax

Page 5: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Conventional Mass Scalingg

• Augment mass matrix maintaining diagonal structure

ImmmM meeee

ne

t

e

e

e

eee m

mt

tEl

mmt

1min newnew

ee

)( tttNt

newother )(~

tttNt CMSCPU

• Shorter simulation times …so far so good…

Page 6: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Problems with CMS• Adding diagonal mass affects all eigenmodes equally much

ω/ ω ω/ ωω/ ω0 ω/ ω0

• In particular rigid body and low frequency modes are affectedi i

p g y q y• Structure tends to deform in low frequency modes• Inertia effects put a practical limit to the time step p p p

Page 7: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

SMS idea

• High frequency modes relatively unimportant for structural response, only limits time step 

• Suppress high frequency content and leave lowSuppress high frequency content and leave low freqency modes unaffected

ω/ ω0 ω/ ω0

i i

• Modify the structure of the added mass matrix to select affected modesselect affected modes

Page 8: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Selective Mass Scalingg• Augment mass matrix projecting out rigid body 

dmodes

mie

i

Tii

ee

eee n

m eeImmmM

• For rigid body mode, no inertia is added

ie

g y ,

0emee ieijjTi

• Time step increase the same as with CMS

ieijji

• Time step increase the same as with CMS

Page 9: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Example p• 3D membrane• Projecting out translational rigid body modes only

TTT

1113321 100e010e001e TTT

13111131

3

41

4 44

4

mmm

m ee

m

3111131144 4

4

4

me

• Generalization to other elements straightforwardThi i th d f lt SMS h

• This is the default SMS scheme

Page 10: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Usageg

*CONTROL TIMESTEP

DT2MS

_

IMSCL RMSCL

• SMS can be applied to entire model (IMSCL=1) or a part set (‐pp ( ) p (IMSCL is part set ID)

• Rotational mass scaling activated by RMSCL

Page 11: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Tip‐loaded cantileverp

Page 12: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

(A)No mass scaling(A)No mass scaling,

(B) Conventional mass scaling

(C) Selective mass scaling

Page 13: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Deep drawp

Page 14: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

No mass scaling

22 i 6

Selective mass scaling

1 i 5022 min 6 sec 1 min 50 sec

Page 15: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

E b lEnergy balance –no mass scaling

Energy balance –selective mass scaling

Page 16: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Problem #1 with SMS • Mass matrix not diagonal, requires solution of linear system of equations

• Solved using a Preconditioned Conjugate Gradient (PCG) fMa

g j g ( )with Jacobi preconditioner

• Linear convergence, number of iterations depends onLinear convergence, number of iterations depends on condition number of system matrix M

th

newiter ~~)(~ tttNtt

tnSMSCPU

M

newother

iter ~ tttNt

Ntt SMSCPU

• Saturation in CPU time, manifested in large problems

Page 17: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

SMS on Adaptive Fenderp

TiTime step 1 5 10 15 20Speedup 1 1.88 2.13 2.06 1.58

Page 18: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Modelling recommendationsg

• Apply SMS to critical parts that require fine pp y p qmesh– Spotweldsp– Bolts– Steering wheelSteering wheel– Adhesive bondingsCh ti t ith• Choose time step with care– Beyond some value nothing is gained, only inertia i dd dis added

– Problem dependent, trial and error

Page 19: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Problem #2 with SMS

TTDI MafCaCMCaaa

~~~

II

CICID fM

MafCaCMCaCaa

• Each constraint imposed directly on accelerations must be individually treatedmust be individually treated– Boundary prescribed motion– Boundary SPCBoundary SPC– Adaptivity– Rigid bodies (including nodal rigid bodies)Rigid bodies (including nodal rigid bodies)– Rigid walls– Tied contact– Tied contact– …

Page 20: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Planar rigid wallsg

• Implemented March 2009p

Page 21: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Tied contacts

• Implemented October 2010

Page 22: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Peak buckling forceg

Page 23: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

NCAC Neon model1056383 quad shells130 b130 beams2852 solids1 contact for the entire modelTermination time 0 080 secsTermination time 0.080 secsTimestep 3.618e-6 secsAscii and binary outputs disableddisabled.Pre-decomposed with 1cpu

23

Page 24: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

NCAC Neon model

24

Page 25: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

NCAC Neon model

128x2x4 Dt=7.85e-7

6 minutes 18 secs

8% mass increaseConventional mass scaling128 2 4 5 i t128x2x4Dt=3.618e-6Selective mass scaling

5 minutes

Selective mass scalingOngoing development to support more features for selective mass

liscaling

25

Page 26: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Geometric rigid wallsGeometric rigid walls

• Implemented June 2011p

Page 27: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Rotational SMS

• Include rotational rigid body modes in projection of added mass matrixp j

• Further reduce inertia for problems involving rotationsrotations

• Coupled dimensions makes the scheme CPU intensive

• Practical use remains to be seen• Practical use remains to be seen

Page 28: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Rotational SMSRotational SMS

No mass scaling Selective mass scalingmass scaling

Conventional mass scaling

Rotational selective mass scaling

Page 29: Selective Mass Scaling (()SMS)€¦ · Microsoft PowerPoint - sms.ppt [Kompatibilitätsmodus] Author: werbos Created Date: 10/26/2011 7:15:46 PM ...

Summaryy

• SMS increases the stable time step in explicitSMS increases the stable time step in explicit simulations without significantly affecting inertial propertiesproperties

• It has evolved to be an important ingredient in automotive industryautomotive industry

• It requires some experience for maximal efficiency• It is not a final product but continuously developed to support new features added and/or required in the front end of simulations