EXPLICIT VS IMPLICIT.pdf

11 /87Ch 6Department of Mechanical Engineering, Ming Chi University of Technology

Computer-Aided Analyses of Vehicle Structures

()

Chapter 6: Transient dynamics and ANSYS LS-DYNA 6-1. Introduction

Thomas Jin-Chee Liu ()Department of Mechanical Engineering

Ming Chi University of TechnologyTaiwan

Feb. 2009


References: , . ANSYS. , ,

2006.

ANSYS training materials ANSYS/LS-DYNA. (). Training Manual Explicit Dynamics with ANSYS LS-DYNA. (ANSYS,

Inc.) ANSYS on-line help. , , . ANSYS/LS-DYNA 8.1.

, , 2004.

(Taiwan Auto-Design Company)ANSYS LS-DYNA


Transient dynamics

Time-dependentDynamics Inertia effects

ANSYS200611


Transient dynamics (cont.)

Transient dynamics (time-domain) analysis

Frequency-domain vibration analysis

Static analysis

Equations of motion


Transient dynamics (cont.)

Crash simulation. Courtesy of S.W. Kirkpatrick, Applied ResearchAssociates, Inc. http://www.arasvo.com/crown_victoria/crown_vic.htm

Ford Crown Victoria


Direct integration

(direct integration)(explicit method)(implicit method)

ANSYS MultiphysicsANSYS MechanicalANSYS Structural(1)

ANSYS LS-DYNA(1)LS-DYNA

: ANSYS200611 p. 509.


Linear and nonlinear9.65


Nonlinear

Ref: ANSYS training materials ANSYS LS-DYNA (ANSYS, Inc.)

(geometry nonlinearity) (material nonlinearity) (contact analysis)


Implicit vs. explicit

11.1 (Reproduced with permission from ANSYS, Inc.)


,

,


Implicit vs. explicit (cont.)Implicit Time Integration: Average acceleration - displacements evaluated at time t+t:

{ } [ ] { }a tttt FKu ++ = 1Linear Problems: Unconditionally stable when [K] is linear Large time steps can be taken

Nonlinear Problems: Solution obtained using a series of linear approximations (Newton-Raphson) Requires inversion of nonlinear stiffness matrix [K] Small iterative time steps are required to achieve convergence Convergence is not guaranteed for highly nonlinear problems



Implicit vs. explicit (cont.)


Explicit Time Integration Central difference method used - accelerations evaluated at time t:

where{Ftext} is the applied external and body force vector,{Ftint} is the internal force vector which is given by:

Fhg is the hourglass resistance force and Fcont is the contact force. The velocities and displacements are then evaluated:

{ } [ ] [ ] [ ]( )inttextt1t FFMa =

contacthgn

T FFdBF +

+=

int

{ } { } { } tttttt tavv += + 2/2/{ } { } { } 2/2/ ttttttt tvuu +++ +=



Explicit Time Integration (continued): The geometry is updated by adding the displacement increments to the

initial geometry {xo}:

Nonlinear problems: Lumped mass matrix required for simple inversion Equations become uncoupled and can be solved for directly (explicitly) No inversion of stiffness matrix is required. All nonlinearities (including

contact) are included in the internal force vector. Major computational expense is in calculating the internal forces. No convergence checks are needed Very small time steps are required to maintain stability limit (10-6 sec)

{ } { } { }ttott uxx ++ +=






This course

We use ANSYS LS-DYNA.

ANSYS LS-DYNA combines the LS-DYNA explicit finite element program with the powerful pre- and postprocessing capabilities of the ANSYS program. The explicit method of solution used by LS-DYNA provides fast solutions for short-time, large deformation dynamics, quasi-static problems with large deformations and multiple nonlinearites, and complex contact/impact problems. Using this integrated product, you can model your structure in ANSYS, obtain the explicit dynamic solution via LS-DYNA, and review results using the standard ANSYS postprocessing tools.You can also transfer geometry and results information between ANSYS and ANSYS LS-DYNA to perform sequential implicit-explicit / explicit-implicit analyses, such as those required for droptest, springback and other applications.

(ANSYS on-line help)


ANSYS LS-DYNA Crashworthiness analysis ANSYS LS-DYNA well suited to wave propagation applications: Full car crash Car component analyses Nonlinear impact problems



ANSYS LS-DYNA (cont.)

ANSYS, Inc.crashworthiness analysis



ANSYS, Inc.

drop simulation



ANSYS, Inc.

impact problem

10



ANSYS, Inc.

deep drawing


LSTC LS-DYNA Headquartered in Livermore, California, Livermore Software

Technology Corporation (LSTC) develops LS-DYNA and a suite of related and supporting engineering software products.

LSTC was founded in 1987 by John O. Hallquist to commercialize as LS-DYNA the public domain code that originated as DYNA3D. DYNA3D was developed at the Lawrence Livermore National Laboratory, by LSTCs founder, John O. Hallquist.

http://www.lstc.com

ANSYS LS-DYNA is the result of a collaborative effort between ANSYS, Inc. and Livermore Software Technology Corporation.

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Using ANSYS LS-DYNA


Get into ANSYS LS-DYNA (ANSYS ED 8.0)

12


Get into ANSYS LS-DYNA (ANSYS ED 8.0) (cont.)


Get into ANSYS LS-DYNA (ANSYS Univ.10.0)

13


Get into ANSYS LS-DYNA (ANSYS Univ. 10.0) (cont.)


On-line help

14


Limitation

ANSYS ED 8.0, 9.0 - limited ANSYS LS-DYNA (University 10.0) - unlimited

www.ansys.com


Element types

LINK160 : 3D truss member (axially loaded)BEAM161 : 3D frame (beam)PLANE162 : 2D plane stress, plane strain, axisymmetrySHELL163 : 3D shell (thin shell)SOLID164 : 3D solid (brick element)COMBI165 : 3D spring-damperMASS166 : 3D mass

These elements assume a linear displacement function; higher order elements with a quadratic displacement function are not available. Therefore, the explicit dynamic elements are not available with extra shape functions, midside nodes, or p-elements. Explicit elements with linear displacement functions and one point integration are best suited for nonlinear applications with large deformations and material failure.

15


Element types (cont.)


Element types (cont.)Three nodes are used to define the element.

The 3rd node is for the initial orientation of the beam.

Several standard beam cross sections can be defined.

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17



8 (2x2x2) points integration


SOLID168 element SOLID168 : 3D 10-node tet solid element

5 points integration

SOLID168 element is a higher order 3-D, 10-node explicit dynamic element. SOLID168 has a quadratic displacement behavior and is well suited to modeling irregular meshes such as those produced from various CAD/CAM systems. SOLID168 can be used with the existing ANSYS Workbench. The element is defined by ten nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions.

Models made up entirely of SOLID168 elements may not be as accurate as hexahedral SOLID164 models.

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Element formulation element formulations , key options

, , . ANSYS LS-DYNA , (reduced integration),

. SOLID164 :

reduced integration(constant stress)

fully integration(linear stress, but shearlocking and volumetric locking)


Element formulation (cont.)

SHELL163 : KEYOPT(1)Element formulation:1 -- Hughes-Liu

0, 2 -- Belytschko-Tsay (default)

3 -- BCIZ triangular shell

4 -- C0 trianglar shell

5 -- Belytschko-Tsay membrane

6 -- S/R Hughes-Liu

7 -- S/R corotational Hughes-Liu

8 -- Belytschko-Levithan shell

9 -- Fully integrated Belytschko-Tsay membrane

10 -- Belytschko-Wong-Chiang

11 -- Fast (corotational) Hughes-Liu

12 -- Fully integrated Belytschko-Tsay shell

reduced integration

reduced integration

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Reduced integration ANSYS LS-DYNA , (reduced integration)

Gaussian pointnode

4-node plane element(low order)

2x2

Reduced integration saves CPU time by minimizing element processing. Therefore, this is the default formulation used in ANSYS LS-DYNA


Reduced integration (cont.)

(reduced integration)

8-node brick element(low order)

2x2x2

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Hourglassing zero-energy mode () hourglassing (),

. Hourglassing,.


Hourglassing (cont.)


?!

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Hourglassing (cont.)

Hourglassing is a zero-energy mode of deformation that oscillates at a frequency much higher than the structures global response. Hourglassing modes result in stable mathematical states that are not physically possible. They typically have no stiffness and give a zigzag deformation appearance to a mesh.

Single-point (reduced) integration elements are prone to zero energy modes.

The occurrence of hourglass deformations in an analysis can invalidate results and should always be minimized or eliminated.

If the overall hourglass energy is more than 10% of the internal energy of a model, there is likely a problem with the analysis. Even 5% can be considered excessive, in some cases.



Hourglassing control

Minimizing hourglassing in ANSYS LS-DYNA

(A) Avoid single point loads, which are known to excite hourglass modes. Since one excited element transfers the mode to its neighbors, point loads should not be applied. Try to apply loads over several elements as pressures, if possible. (, )

(B) Refining the mesh often reduces hourglass energy, but a larger model corresponds to increased solution time and larger results files. (mesh)

(C) Use fully integrated elements, which do not experience hourglassing modes. However, penalties in solution speed, robustness, and even accuracy may result, depending on the application. Full integration is not available for PLANE162 elements and beam elements do not require it. ()


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Hourglassing control (cont.) Minimizing hourglassing in ANSYS LS-DYNA (continued)

(D) Globally adjust the models bulk viscosity to reduce hourglass deformations. It is possible to increase the bulk viscosity of a model using the linear and quadratic coefficients of the EDBVIS command. () Solution > Analysis Options > Bulk Viscosity

It is not recommended to dramatically change the default values (1.5 and 0.06)of the EDBVIS command.

Viscous hourglass control is recommended for problems deforming with very high velocities(e.g., shock waves).

Applicable elements include PLANE162 and SOLID164.



Hourglassing control (cont.)


Minimizing hourglassing in ANSYS LS-DYNA (continued)

(E) Globally add elastic stiffness to reduce hourglass energy. This can be done for the entire model by increasing the hourglassing coefficient (HGCO) of the EDHGLScommand. () Solution > Analysis Options > Hourglass Ctrls > Global

Care should be used when increasing the hourglassing coefficient. Values above 0.15 have been found to over-stiffen the models response during large deformations and cause instabilities.

Stiffness hourglass control is recommended for problems deforming with lower velocities (e.g., metal forming and crash).

Applicable elements include PLANE162, SHELL163, and SOLID164.

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Hourglassing control (cont.)


Minimizing hourglassing in ANSYS LS-DYNA (continued)

(F) Locally reduce hourglassing in high risk areas of a model without dramatically changing the models global stiffness. The EDMP, HGLS command is used to apply hourglass control only to a specific material. Define the hourglass control type (viscous or stiffness), hourglass coefficient, bulk viscosity coefficient, and shell bending and shell warping coefficients. (hourglassing) Solution > Analysis Options > Hourglass Ctrls > Local

LS-DYNA locally applies hourglass control on a Part ID basis (not on a material basis), so any Part with the specified material will have this hourglass control.

VAL1=5 is often used to reduce hourglassing.


ANSYS LS-DYNA

Explicit elements with linear displacement functions and one point integration

Minimizing hourglassing

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Real constants

LINK160 : cross-sectional areaBEAM161 : cross-sectional dataPLANE162 : none SHELL163 : thickness data SOLID164 : none


Material models

* (elastic)* (elasto-plastic)

(ductile materials)

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Material models (cont.)



Popov

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Material models (cont.)E.P. Popov, Engineering Mechanics of Solids. New Jersey: Prentice Hall, 1990.



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(a) (b)

strain hardening



(a) (b)(1 2 3)

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(a) (b)isotropic hardening kinematic hardening

strain hardening



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Material models (cont.) Time-independent

plasticity (rate-independent) Time-dependent plasticity

(rate-dependent)

E.P. Popov, Engineering Mechanics of Solids. New Jersey: Prentice Hall, 1990.



Elastic IsotropicOrthotropic Anisotropic Fluid

Nonlinear ElasticBlatz-Ko rubber Mooney-Rivlin rubber Viscoelastic

Elastoplastic Elastic-plastic hydrodynamic Bamman rate-dependent Zerilli-Armstrong rate-dependent Bilinear isotropic Bilinear kinematic Plastic kinematic Powerlaw plasticity Strain rate-dependent plasticity Rate-sensitive powerlaw plasticity Three-parameter Barlat Barlat anisotropic plasticity Piece-wise linear plasticity Transversely anisotropic elastic

plastic

ANSYS LS-DYNA :

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FoamClosed-cell Low-density Viscous Crushable Honeycomb

DamageComposite Concrete

Equations of State Johnson-Cook Null

OthersRigid Cable Geologic Cap


Material models (cont.) Elastoplastic model

(a)-(b)(c)(d)

bilinear bilinear

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Material models (cont.) Elastic

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Material models (cont.) Bi-linear elastoplastic model


Parts and contact

Part 1

Part 2

Part 1

Part 2

contact

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Parts and contact (cont.)


Part 1

Part 2

contact




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Parts and contact (cont.) Edge contact is needed when the shell surface normals are orthogonal to

the impact direction. Shell edge (SE) contact selects all shell edges automatically.

SE contact is also included in automatic general (AG) contact.


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Single Surface Nodes to Surface Surface to Surface

General (Basic) SS NTS STS, OSTS Automatic ASSC, AG ANTS ASTS Rigid RNTR ROTR Tied TDNS TDSS, TSES Tied with Failure TNTS TSTS Eroding ESS ENTS ESTS Edge SE Drawbead DRAWBEAD Forming FNTS FSTS, FOSS Two-Dimenional ASS2D


Contact types


Parts and contact (cont.)Define parts

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Parts and contact (cont.)Define contact


Rigid body Rigid body Rigid body deep drawing

Rigid body

Rigid bodies

contact

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Rigid body (cont.)


Initial velocity

Part 1

Part 2

V0

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Initial velocity (cont.)


Constraints

GUI : Solution > Constraints > Apply > On Nodes (etc.)

The D command can only be used to apply zero displacements (bothtranslational and rotational) to nodes.

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LoadingUnlike an implicit static analysis, an explicit dynamic analysis must have all loads

applied as a function of time. The load step concept of general ANSYS does not apply.

Because of the time dependence, many standard ANSYS loading commands (e.g., F and SF) are not valid in ANSYS LS-DYNA.

There is a unique procedure for applying loads in an explicit dynamic analysis using two array parameters. One array is for the time values and the other array is for the loading condition.

Damping is used to reduce unwanted dynamic response from the loading.

TIME

FORCE



Loading (cont.)

nsel,26,node,...

cm, end-node ,node

nsel,all

*dim,time,,4

*dim,yforce,,4

time(1) = 0, 0.1, 0.25, 0.35

yforce(1) = 0, 85, 85, 100

edload,add, FY, , end-node ,time, yforce

F(t)

F(t)

t

85100

00.1 0.25 0.35

end-node(node no. 26)

85

APDLx

y

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Gravitational acceleration

g=9.81

nsel, (nodes)cm, ball ,node

nsel,all

*dim,time,,2

*dim,grav,,2

time(1) = 0, 2

grav(1) = 9.81, 9.81

edload, add, ACLY, , ball ,time, grav

APDL

g=9.81

x

y

g(t)

t

9.81

02


Gravitational acceleration (cont.)


nsel,all

*dim,time,,2

*dim,grav,,2

time(1) = 0, 2

grav(1) = 9.81, 9.81

edload, add, ACLY, , ball ,time, grav


nsel,all

*dim,time,,2

*dim,grav,,2

time(1) = 0, 2

grav(1) = -9.81, -9.81

edload, add, AY, , ball ,time, grav

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Gravitational acceleration (cont.)

*dim,time,,2

*dim,grav,,2

time(1) = 0, 2

grav(1) = 9.81, 9.81

*dim,time, array,2,1,1

*dim,grav, array,2,1,1

*SET, time(1,1,1) , 0

*SET, time(2,1,1) , 2

*SET, grav(1,1,1) , 9.81

*SET, grav(2,1,1) , 9.81


Damping

Damping is needed to minimize unrealistic oscillations in the response of a structure during a transient dynamic analysis.

Both mass-weighted (alpha) and stiffness-weighted (beta) damping can be applied in ANSYS LS-DYNA using the EDDAMP command:Preprocessor > Material Props > Damping ...

OR a constant damping coefficient


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Damping (cont.)


Time step

ANSYS LS-DYNA checks all elements when calculating the required time step. For stability reasons a scale factor of 0.9 (default) is used to decrease the time step:

The characteristic length l and the wave propagation velocity c are dependent on element type:

clt 9.0=

Ec=elementtheoflength=l

)-1(E

)LL(LmaxA2

)LLL(LmaxA

2

3214321

c=

,,l=shells: triangular for ,,,,l=

L1

L4L3

L2A

Shell Elements:

Beam Elements:


(solid elements)

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Time step (cont.)

Note: The critical time step size is automatically calculated by LS-DYNA. It depends on element lengths and material properties (sonic speed). It rarely needs to be over-ridden by the user.

10-6 sec is typical.


Files


ANSYS /SOLULS-DYNA solver taskWrites and submits Jobname.K- standard LS-DYNA ASCII input file

ANSYS /PREP7 Preprocessing (database) Creates Jobname.DB-mesh, materials, loads, etc.

ANSYS /POST1General postprocessingReads Jobname.RST- general binary result dataEDRST,Freq

LS-POST (phase 3) & ANSYS /POST26Postprocess ASCII output files- GLSTAT, MATSUM, SPCFORC, etc.EDOUT,File and EDREAD, ,File

ANSYS /POST26Time history postprocessingReads Jobname.HIS- selective binary results dataEDHIST,Comp and EDHTIME,Freq

LS-POST (phase 1)Postprocess binary files- d3plot Similar to Jobname.RSTEDRST,Freq

LS-POST (phase 2)Postprocess time history binary results files- d3thdtSimilar to Jobname.HISEDHIST,Comp and EDHTIME,Freq

Restart file (d3dump) written at frequency specified by EDDUMP.

EDSTART continues analysis from specified d3dump (restart) file.

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Impact Mechanics

: Impact Mechanics. : , . . . , . . LS-DYNA, error.

http://911review.com/coverup/nist.html

Documents

EXPLICIT VS IMPLICIT.pdf