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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics 2

Section 15.1Basics of ExplicitDynamicsKey Concepts

!mplicit !ntegration (ethos

Explicit !ntegration (ethos

Sol)tion *cc)racy

!ntegration #ime Steps

*)tomatic (ass Scaling

Static Damping

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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics "

Implicit Integration Methods

+#ransient Str)ct)ral, sol&es the abo&e e)ation )sing the follo'ing

algorithm:

#he parameters an are chosen to control characteristics of the

algorithm s)ch as acc)racy n)merical stability etc.

!t is calle an implicit methodbeca)se the response at the c)rrent time

step epens on not only the historical information b)t also the c)rrent

information/ iterations are neee in a single time step.

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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics $

Explicit Integration

Methods

+Explicit Dynamics, sol&es the abo&e e)ation )sing the follo'ing

algorithm:

!t is calle explicit methodsbeca)se the response at the c)rrent time can

be calc)late explicitly/ no iterations 'ithin a time step is neee.

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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics 5

Solution Accuracy

+Explicit Dynamics, )ses theprinciple of conservation of energyto

monitor the sol)tion acc)racy.

!t calc)lates o&erall energy at each cycle. !f the energy error reaches a

threshol the sol)tion is regare as )nstable an stops. #he efa)lt

threshol is 10.

#he Energy Erroris ene by

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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics 3

#he re c)r&eis the energyerror. !n this

case thesol)tion is

)ite stable.

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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics 4

Integration Time Steps

ith explicit methos the integration time step nees to be small eno)gh

to ens)re stability an acc)racy of the sol)tion. #he 6erman

mathematicians Co)rant 7rierichs an 8e'y s)ggeste that in a

single time step a 'a&e sho)l not tra&el f)rther than the smallestelement si9e i.e.

'here his the smallest element si9e cis the 'a&e spee in the element.

Beca)se of the C78 conition 'hen generating meshes for +Explicit

Dynamics, mae s)re that one or t'o &ery small elements o not control

the time step. !n general a )niform mesh si9e is esirable for +Explicit

Dynamics, sim)lations.

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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics ;

Automatic Mass Scaling

#he 'a&e spee in an element is 'here E is the

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Chapter 15 Explicit Dynamics Section 15.1 Basics of Explicit Dynamics >

Static Damping

+Explicit Dynamics, is primarily

esigne for sol&ing transient

ynamic problems.

?sing +Static Damping, option a

steay-state sol)tion can also be

obtaine.

#he iea is to intro)ce a amping

force to critically amp the lo'est

moe of oscillation.

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Chapter 15 Explicit Dynamics Section 15.2 High-Spee !mpact 10

Section 15.2High-Spee !mpact

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Chapter 15 Explicit Dynamics Section 15." Drop #est 11

Section 15."Drop #est

10

R"

20o

5 m@s

30

120

R20

?nit: mm.

A1 #he phoneboy is mae

of an al)min)malloy.

A2 #he concrete oor canbe moele 'ith arbitrary

si9es 'e 'ill )se130x;0x10 mm.