lsdyna 2009 5 2 - · pdf file1 ls-dyna 以及它在汽车行业中的应用 ls-dyna and its...

1

LS-DYNA 以及它在汽车行业中的应用

LS-DYNA and Its Application in Automotive Industry

鲁宏升 (Hongsheng Lu)

上海恒士达科技有限公司

www.hengstar.com

07/16 2009

LS-DYNALSTC恒士达科技

Copyright © 2009 Livermore Software Technology Corporation. All Rights Reserved. Copyright © 2009 上海恒士达科技有限公司. All Rights Reserved.

Outline 内容概要

• LS-DYNA introduction LS-DYNA介绍

• New Features in LS971 LS971新功能

• New Element Technology 新的单元技术

• Mesh Convergence

• Conclusions 结论

2

EFG壳单元, EFG实体单元ALE, Particle Method for Airbag ALE, 颗粒方法用于气囊



Paul A. Du Bois是一位德国资深咨询专家，从1987年以来一直从事于

工程计算模拟，特别专注于显示计算的动态模拟分析，如碰撞及撞击现象

的模拟。他已为绝大部分汽车生产厂如DaimlerChrysler, Porsche, Ford,

Toyota, Opel, GM, Fiat, Volvo, SAAB, PSA提供碰撞分析咨询。从1992-

1997，Paul 为FAT (德国汽车工业研究联合会) 中的“侧碰假人”工作组提

供咨询，1996-2006，为FAT 中的“泡沫材料”工作组提供咨询。除了计算

方法的研发和工程咨询以外，他也提供“LS-DYNA在碰撞分析中的应用”

高级培训。他的课程在欧洲各国如德国，英国，法国，意大利，及日本，

美国深受欢迎。本次培训主要重点为:

汽车碰撞仿真模拟高级培训 10月21-24日

3



第一天

碰撞模拟分析的工程应用。

汽车有限元碰撞模型的建模技术(网格总体布置，网格质量，网格

粗细密度要求，焊点建模，部件之间的连接，等等) 。

时间步长的控制。

数值计算中的衰减和噪音。

第二天

壳单元的基本原理。

壳单元的合理选择，及合理的沙漏控制。

接触算法。

碰撞模拟中的接触合理选择。


4



第三天

LS-DYNA 中的材料模型。

碰撞模拟中金属材料模型的合理选择，及参数确定。

碰撞模拟中热塑性材料(thermoplastics)模型的合理选择，及参数确定。

碰撞模拟中泡沫材料(foam)模型的合理选择，及参数确定。

第四天

用LS-DYNA进行部件分析。

数值模型结果的可信度保证。

假人模型，障碍物模型。

安全气囊。


5



Dummy/barrier developments

假人/障碍物的研发

6



• EuroSID 2re 欧标侧碰2版假人

• Hybrid III 3-year old 混合III 3岁模型

• Hybrid III 6-year old 混合III 6岁模型

• SID-IIs D Rigid-FE 侧碰-II 刚体假人

• Hybrid III 5th percentile female 混合III 5%女模型

• NCAC is beginning work on the Hybrid III 95th

percentile male

Dummy models under development 正在研发中的假人模型

7



Dummy distribution

• For licensed LS-DYNA usersl No separate licensing from LS-DYNA

对LS-DYNA用户没有额外的费用

• Feedback on dummy performance is welcome but not required. l Feedback will be used to improve future releases

• No encryption

公开的输入文件

• Continuous dummy update and support is provided by LSTC and LS-DYNA distributors

• The dummies generated by LSTC use TrueGrid® parametric meshing

8



Update EuroSID 2re 欧标侧碰2版假人

• Meshing completed

• Model build-up completed

• Some certification tests finished

Ongoing:

• Material adjustments

• Validation tests



Update EuroSID 2re

• Tests used for validation.

head drop test neck test lumbar spine test rip drop test

shoulder test abdomen test pelvis test

10



Update Hybrid III 3-year-old 混合III 3岁模型

• Mesh almost completed

Coming soon: • Build-up of the model

• Gathering of certification test data

• Material adjustments

• Certification test setup



Update Hybrid III 6-year-old 混合III 6岁模型

• Meshing of mechanical and interior components initialized

• Surface data received

Ongoing: • Meshing

12



Update SID-IIs D Rigid-FE 侧碰刚体假人

• Fast turn around time


• Model buildup completed

Ongoing:

• Material and part response adjustments


13



Update Hybrid III 5th percentile female 混合III 5%女模型


• Model buildup completed

• Initial simulations completed

• LSTC release planned later this year

Ongoing:

• Test for robustness


14



Available LSTC Dummy Models可使用的假人模型

• SID-II 侧碰-II 假人

• Hybrid III 50th percentile FE 混合 III50%有限元模型

• Hybrid III Rigid-FE Adults 混合III刚体有限元成人

• USSID 美标侧碰假人模型

• All available models can be obtained through LSTC’s ftp site: http://ftp.lstc.com/user/

• Feedback about performance and suggestions about further improvements should be sent to: [email protected]

15



Update SID-IIs D 侧碰-II 假人

• Validation of initial model with adjusted material properties completed

• First BETA testing completed• Initial customer feedback incorporated• Model stability and response improved• Released to all customers• ~300000 nodes and elements.

Coming soon: • Incorporation of material test results into model

16



Update Hybrid III 50th 混合 III 50%有限元模型

• Validation of initial model with adjusted material properties completed

• Model stability and response improved

• Alpha Version released to all customers

Coming soon: • Incorporation of material test results into model

17



• The Dummy Time-Step is exactly 0.5 Microseconds, with an Added Mass of 50-grams.

• Size: 228,000 Nodes and 256,000 Elements

• Computation Time for the Sled Model shown to 150ms:l 3-hours 20-minutes using 16-cpusl 2-hours 10-minutes using 32-cpus

• Material Models will change after Material Testing is complete

• The Dummy can be easily positioned in LSPP using much of the same methods we established for the previous Rigid_FE Dummy.

• We will continue to investigate correlations to known Test Results

18




Update Hybrid III Rigid-FE Adults混合III刚体有限元成人

• Model stability and response improved

• Customer feedback incorporated

• Further improvements planned

20



Update USSID 美标侧碰假人模型

Originally developed for KIA Motors based on NHTSA public domain version of USSID

Major enhancements include:• Improved discretization for jacket, arm, pelvis• Improved material data for foams• One global contact

NHTSA

21



Free Motion Headform 自由运动头部模型

• The headform was meshed using TrueGrid® based on NHTSA design drawings and outer surface scan data provided by an automotive supplier.

• The center of gravity (CG) , the total mass, and inertia are within the tolerances specified in the NHTSA

• Material constants are based on experimental test dated.

• The unit system used is mm-ms-kg-kN

• To obtain model or to make suggestions contact Dilip at: [email protected].

22



FMH Correlation

Response Test / Spec FEAPeak Resultant Accel, Gs (2.72m/s) 225 to 275 266

Peak Lateral Accel, Gs (2.72/ms) -15 to 15 -5.71

Peak Resultant Accel, Gs (4.02m/s) 437 449

Peak Resultant Accel, Gs (6.71m/s) 1067 1031

Total Mass, kg 4.54 ± 0.05 4.58

23



LSTC family of barriers

• Frontal offset barrierl Solidl Meshless (EFG)l Shells

• MDB (FMVSS 214)l Solidl Shell

• SICE (IIHS)l Solidl Shell

• ECE Rev 95l Shell

24



LSTC family of barriers

Solid ODB~50,000 elem.

Shell ODB~375,000 elem.

Shell IIHS~575,000 elem.

Solid IIHS~125,000 elem.

Solid 214~150,000 elem.

Shell 214~500,000 elem.

25



LSTC ODB Status Update LSTC 偏置变形障碍物

• Development based on 16 available OEM Tests

• Both Shell and Solid Version show promising results

• Solid version used to perform DOE (200+ runs) to study sensitivity of some important variables such as honeycomb shear damage, adhesive failure strength, cladding failure , etc.

• Verification runs made to reduce overall MSError compared to test

26



Solid Results

27



Shell Results

28



Remarks

• Current shell and solid ODB barriers are production ready and will be released shortly with documentation for public use

• Solid barrier takes roughly 10 minutes while the shell barrier takes 4 hours

• Future planned development includes but not limited to:Fine-tuning correlation for certain load-cases Adhesive area is better represented in shells. This approach will be incorporated in solids by using shells to model honeycomb at the cladding interfaceImprove Predictive Robustness using LS-OPT to eliminate sensitivity on intrusion numbers

• We thank all the OEMs who provided us with the test data and helped us in “beta” evaluation

29



ECE Rev 95ECE Rev 95

Pole Impact Setup Flat wall Impact Setup

30



ECE Rev 95 version 1ECE Rev 95 version 1

Pole impact Flat wall impact

31



ECE Rev 95 version 2ECE Rev 95 version 2

32



LS-Prepost 2.1 has been frozen and released, and LS-Prepost 2.2 is available and is in Beta test

LS-Prepost 2.1 and 2.2 can be freely download from ftp://ftp.lstc.com/outgoing2/lsprepost2_1ftp://ftp.lstc.com/outgoing2/lsprepost2_2ftp://ftp.lstc.com/outgoing2/lsprepost2_4

64bit version is available for both Unix, Linux, Win64 and Vista

Up-to-date online documentation is available at

http://www.lstc.com/lspp

There are 17 online tutorials that give step-by-step instructions on how to create model. More tutorials will be added over time

Frequently Asked Questions (FAQ) is also available online

Current status of LS-Prepost LS-Prepost的现状

33



LS-OPT Goals LS-OPT 目标

Provide a Design Environment for LS-DYNA

为LS-DYNA提供一个设计环境

Goals 目标l Improve Designe Performance in an Uncertain Environment. 改善在不确定情况下的设计

l Identify System or Material Properites 识别系统或材料性质

l Manage/monitor multiple Dyna runs 管理/监视多次DYNA运行

l Design Optimization and Robust Design 优化设计

Tasks 任务l Visualize statistics of multiple runs 对多次DYNA运行的统计

l Identify important design variables 识别重要的设计参数

l Identify sources of Uncertainty in FE models 识别有限元模型中的不确定的来源

l Optimize 优化

l Explore Design Space using Surrogate Models 拓展设计空间

l Manage a multi-stage process 管理多步骤的加工过程

Applications 应用l Multidisciplinary Design Optimization (Crashworthiness,…) l System and Material Identification (biomechanics, sheet metal, concrete, airbag properties…) l Process design (metal forming)

34



LSLS--OPT TasksOPT Tasks

Statistics of multiple runsl Mean, StdDev, …l Multiple history plotsl Histogramsl Stochastic contributions

of variables

Outlier Analysisl FE displayl Identify sources of

uncertainty

(b) Residual (Outliers)Low Predictability

35



Courtesy: Ford Motor Company

Shape Optimization 形状优化

Instrument panel with knee bolster system

36



LS-PREPOST

40ms Knee Impact: LS-DYNA Simulation

37



Gauge

Radius

Gauge

Width

Width

DepthDepth

Depth

Width

Gauge Radius

Design Variables 4 Screened out of 11 total设计变量从11个变量中筛选4个

38



Design Objective: 设计目标

min ( max (Knee_F_L, Knee_F_R) )

Design Constraints: 设计限制

Left Knee intrusion < 115mm

Right Knee intrusion < 115mm

Yoke intrusion < 85mm

Design variables 设计变量

Reduced from 11 to 4 (ANOVA)

Design Formulation 设计方式

39



0.8

0.9

1

1.1

1.2

1.3

1.4

0 8 16 24 32 40 48

Number of Simulations

Kne

e Fo

rce

L Knee Force (RSM)L Knee Force (RSM) (pred)R Knee Force (RSM)R Knee Force (RSM) (pred)L Knee Force (NN)L Knee Force (NN) (Pred)R Knee Force (NN)R Knee Force (NN) (Pred)

Optimization Convergence 优化设计的收敛

NN vs. RSM

40



Knee Forces: Baseline vs. Optimum

41




LS-DYNA introduction LS-DYNA介绍

New Features in LS971 LS971新功能

• New Element Technology 新的单元技术



42




Point elements (mass, inertia)节点质量单元

Discrete elements (springs, dampers)

离散单元 (弹簧与阻尼)

Beams 梁单元

Shells 壳单元

Solids 体单元

Seatbelts (and related components)安全带单元

Thick shells 厚壳单元

ALE, SPH and EFG (meshfree)

Element Types in LS-DYNA 单元类型

43*For more formulations please refer to user’s manual



FEM explicit(LS-DYNA, PAM-CRASH, ABAQUS …) structureSmooth Particle Hydrodynamics (SPH)(LS-DYNA, PAM-CRASH, PRONTO3D …)structure, fluid, fluid-structureMesh-free Galerkin Explicit Method(LS-DYNA, TAHOE, DYNA) structure

Mesh-free Galerkin Explicit Method(LS-DYNA) structure, fluid, fluid-structure, , , metal forming metal forming adaptivityadaptivity

Classification of Transient Dynamic Code 显式有限元程序的分类

Hydrocode

Lagrangian Hydrocode 拉格朗日法

Semi-Lagrangian (Eulerian) Hydrocode 半拉格朗日(欧拉)法

Arbitrary Lagrangian-Eulerian Hydrocode任意拉格朗日欧拉法

(LS-DYNA, MSC/DYTRAN,ALE3D,CALE …) fluid-structure interactioEulerian Hydrocode 欧拉法(LS-DYNA, MSC/DYTRAN, ALE3D, DYSMAS …) fluid flow

44



Solid 固体 Fluid 流体 Gas 气体

Ve l

o ci ty

速度

FE.B.C.

ρ 密度

P 压力Elastic Fluid Equation of State

Crashworthiness Airbag

Metal Forming

Material Strength材料强度

Momentum动量

ExtrusionForging

Hydroplaning

Sloshing

Bird strike

Explosion Penetration

Fracture

Incompressible fluid

Splashing

Foam packing

ALEEFG

SPH

Application Range 应用范围

CE/SEFEM-L

FEM-E

边界条件

45



Accuracy Efficiency Robust 精度效率鲁棒

46



Square Tube



“The major stumbling block for predictive simulationstoday is the structural use of non-steel materials.” 采用非金属材料

“Lack of suitable material models (plastics, foams,…)” 缺少合适的材料模型

“Discontinuous cell structures…” 不连续的CELL结构

“Inhomogeneous composites…” 不均匀的复合材料

“Brittle failure…” 脆性材料的失效

Many of these problems remain today.

Spot weld and fastener failure are current issues. 焊结点，紧固件的失效

To replace dummies with models of humans, therefore need better bio-material models. 用人体模型来替代假人

Major Stumbling Blocks (Paul Dubois, 1999)

51



Computational Challenges in Solids and Structures计算力学中的挑战

Mesh quality; mesh sensitivity. 网格的敏感性.

Large material distortion, e.g., crashworthiness, hyper-velocity impact.材料大变形：汽车碰撞，高速碰撞.

Moving boundaries, free surface, e.g., fluid and structure interaction.移动边界，自由表面：流体与固体耦合.

Adaptive procedure,e.g., forging and extrusion.自适应网格：锻造，挤压.

Multiple-scale phenomenon, e.g., shear band.多尺度的物理现象：剪切带.

Moving discontinuities, e.g., crack propagation.移动的不连续：裂缝传播.

52



Meshfree Collocation Method 无网格配点法

Meshfree Galerkin Method 无网格Galerkin法Element Free Galerkin (EFG) [Belytschko et al. 1994]Reproducing Kernel Particle Method (RKPM) [Liu et al. 1995]Partition of Unity Method [Babuska and Melenk 1995]HP-Clouds [Duarte and Oden 1996]Free-Mesh Method [Yagawa et al. 1996]Natural Element Method [Sukumar et al.1998]Meshless Local Petrov-Galerkin Meshfree Method(MLPG) [Atluri et al.1998]Local Boundary Integral Equation (LBIE) [Atluri et al. 1998]Finite Sphere Method [Bathe 1998], Particle Finite Element Method [Idelsohn et al.2004] …Reproducing Kernel Element Method [Liu et al 2004]NURBS-based isogeometric analysis [T.J.R. Hughes, et al. 2005]

(FEM, Control Volume, BEM …) + Meshfree Method无网格法与其它方法的结合

Smooth Particle Hydrodynamics (SPH) [Monaghan 1977] Finite Point Method [Onate et al.1996]

Coupled FEM/Meshfree Method [1995]Extended FEM Method [1999]Finite Particle Method [1999]

History and Research Trend 无网格法的发展

53

Meshfree least square method, …



Representative Applications现有EFG的应用

54

1. Smoother stress and strain 平滑的应变应力

2. Less sensitive to the discretization对网格的敏感性小

3. No hourglass control 无须沙漏控制

4. Higher accuracy 精度高

5. Natural in adaptivity自然的自适应

6. Higher CPU 费时

7. More memory 大内存

8. Difficult in parallel 并行处理难

9. More difficult in theory10. More developments and

refinements on theory

• Solid 固体EFG Plane strain #43

EFG Axisymmetric #44EFG 3D solid #41

EFG Basic Features

• Shell 壳EFG shell #41EFG shell #42

• Fluid 流体EFG 3D fluid #41(limited version)

• Rubber industry • Highly compressible foam• Human safety• Adaptive forging simulation• Bird striking

• Metal Forming• Crashworthiness

• Compressible fluid flow



EFG Method 无网格EFG法 Finite Element Method 有限元方法

Large material distortion, e.g., crashworthiness, manufacturing

Adaptive forming analysis

Moving boundary

Moving discontinuities; Multiple-scale phenomenon

Technology developed since 1960s

Can handle various scenarios

Well refined for fast analysis and low memory demand

Available in many commercial codes

New emerging technology since mid-1990s

Only tested for limited problems

Require high CPU and large memory

Accuracy strongly depends on mesh quality and order of approximation

Difficult in handling mesh topology for certain problems.

When Should I Use EFG ?什么时候选用EFG?

55

Improve Mesh Distortion Problem with Desired Accuracy改善处理网格扭曲问题来达到**希望的精度



eΩ

eΩ

eΩ

• Define the physical domain 定义物理边界• Provide the mass computation 计算质量• Impose boundary conditions 施加边界条件• Create stress points 创建应力点• Can not go beyond Lagrngian description

Background Mesh 背景网格“ Valid within Lagrangain description “

non-overlapping ‘mesh’不重叠

Usually in solid and structure !

56

*SECTION_SOLID_EFG



Reduced Integration 不完全积分

1. Hughes-Liu2. Belytschko-Tsay (default)8. Belytschko-Leviathan10. Belytschko-Wong-Chiang11. Fast Hughes-Liu

Membrane 薄膜单元

Fully Integration 完全积分

2-D 2维单元

6. S/R Hughes-Liu7. S/R Co-rotational Hughes-Liu16. Bathe-Dvorkin feartures in B-T41. EFG shell (local projection) 42. EFG shell (iso-parametric mapping)

12. Plane stress 平面应力13. Plane strain 平面应变

14. Axisymmetric solid –area weighted 轴对称

15. Axisymmetric solid –volume weighted 43. EFG 2D plane strain (x-y plane)44. EFG 2D axisymmetric (y-axis of symmetry)

5. Belytschko-Tsay membrane9. Fully integrated B-T membrane

Triangular shell 三角形壳单元

3. BCIZ triangular shell 4. C0 triangular shell

Shell Element Formulations 壳单元

57

*For more formulations please refer to user’s manual



Degenerated Continuum Approach by Meshfree Method 壳结构无网格法

• Mesh-free Shell Formulation无网格壳的公式形式

• Mesh-free Shell Surface Representation壳结构中心面的无网格表达

• Relieve of Numerical Locking数值锁定的减轻

• Global Approach 全部法

• Local Approach 局部法

• First-order Shear Deformable, Shell Theory

• Mix formulation

• Patch Test分片试验

• Lagrange strain smoothing

58



Meshfree Shell Surface I -- with Global Approach全部法

Meshfree Shell Surface Representation

Surface parameterization based on FE mesh + Moving least-squares [Krysl and Belystchko 1996] 基于有限网格的表面参数化+移动的小二乘.

Lagrange polynomials + Moving least-squares [Noguchi et al. 2000] 拉格朗日多项式+移动的小二乘.

3D RKPM with extra constraints [Chen and Wu 2001] 加约束的3维RKPM

Angle-based triangular flattening [Sheffer and Sturler, 2001]+ Moving least-squares.基于角度的三角形平面化+ 移动的小二乘.

( ) ( ) ηξ,ηξ,: midmid0 φ=∈= XX 3RE

ξ

η( )

Μ 0ε someand 1...3,j

1...N,i for0,εαg

w)φ(αF

2

2j

i(1)

ji,

N

1i

3

1j

ji

2ji

ji

>=

=>≥≡

−=∑∑= =

to subject

minimize α

Advantage: Handle complex manifold surface; Conforming shape functions 协调的形函数

Disadvantage: Requires multiple parametric domains for spherical, cylindrical …structures

Projection

59



Advantage: Handle complex geometry 可处理复杂的几何形状

Disadvantage: Non-conforming shape functions 不协调的形函数

Remedy: (Area-weighed) smoothing

planeNplaneM)X()X( JIJI −−

≠ΨΨ

NIE NPN NI J NIE

I J I iI iIE 1 I 1NIE

J

Ψ ( ) AΨ ( ) Ψ ( )X X

Awhere NIE is the number of surrounding projected planes evaluated at X

= =

•= ⇒ =∑ ∑∑

% %XX X

Meshfree Shell Surface II -- with Local Approach局部法

Z,w

X,u

Y,v

Iz

I J K

Iy

IxM-plane

iy

ix

iz

IJ K

M-plane

-1M M 1 Criticalcos ( , ) θ+ ≤n n

Mn

1M +n

/0 plate∀ ∈ EX

60



Constructed Meshfree Surface无网格的壳结构中心面

Meshfree Global ApproachMeshfree Local Approach

Meshfree Global ApproachMeshfree Local Approach Meshfree Local Approach

61



( ) ( ) bottomI

topII3I3

NP

1II

refI

NP

1III ;

2x)(x xxVV,,x −=+≈ ∑∑

==

ςηξΨηξΨ

Meshfree Shell Formulation无网格壳的公式形式

First-order shear deformable shell theory with 5/6 –parameter approach 满足精确的一阶剪切变形，采用壳原理

( ) ( ) ( )

β∆α∆∆

ζηξζηξφζηξ

123

3 2h,

2hwithttt:

VVV

,,V,,,,,xx

+−=

+−∈+=∈= 3RB

A co-rotational coordinate system is embedded at each in-plane integration zone and defined by the convectedcoordinates

ξ

η

sx

sysz

x

yz3V

1V

2V

x

yz

Two approximations for local velocity

[ ] ( ) n3iij

1n3i

NP

1I I

I1iI2iI

II

NP

1IiIIi V∆θRV

βα

VV2tΨζvΨv =

−+= +

==∑∑ ;~ˆ~ˆ &

&

∑∑==

+=NP

1IyI

xI

II

NP

1IiIIi

0θθ

2tΨζvΨv ˆ

ˆ~ˆ~ˆ &

&

ˆ3with | v z | 0.01⋅ < (Belytschko’s element)

62



Lagrangian smoothed strains in co-rotational system [Chen and Wu 1998] 拉格朗日平滑化的应变

Meshfree Shell Formulation (cont.) 无网格壳的公式形式

∑∑∑ ===I

IsI

s

II

bI

b

II

mI

m ζ dB~ε~dB~ε~dB~ε~

LΓ

lΓ

LΩ

lΩ

ξη

ζ

LX

lX

( )

( ) ( ) ( ) ( ) ΓςηξΨςηξΨ

Ωεε

Γ

Ω

dn]VV,[n]VV,[A

dA

X~

iIjIjIjIiIi

NP

II

L

lij

LLij

L

L

hh

22II11II22II11II1

1

θtθt2

θtθt22

1

1

+++−

=

=

∑ ∫

∫

=

63

∫

∫

∫

⋅=

⋅=

⋅=

L

l

l

ΓL

LsI

Γl

lbI

Γl

lmI

dΓA1)(

dΓA1)(

dΓA1)(

nBxB~

nBxB~

nBxB~

sI

bI

mI

iX

0X

0 X

XX)(~~

)(~~

W)(~~

1I

2iII

1II

J1J

I

=∇

=∇

=∇

∑

∑

∑

=

=

=

Ψ

Ψ

Ψ

where



tΦfd)K(K ∆ttNL −=+ +∆

( ) ( ) ( ) ( )∑=

++=NP

1LLL

1JL

0Jε

TεL

1IL

0I A][]([

TT

ζζζζ BBCTTBBK L

Equilibrium Equation

( ) ( ) ( ) ( )∑=

++=NP

1LLL

1NJL

0NJε

TεL

1NIL

0NI A][]([

TT

ζζζζ BBSTTBBK N

( ) ( )∑=

′+=NP

1LL

TεL

1IL

0I A]([

TT

σζζΦ TBB

• Internal nodal force

dΩdΩζdΩΩ

TsIΩ

TbIΩ

TmI

intI ∫∫∫ ⋅⋅+⋅⋅+⋅⋅= σB~σB~σB~f ΦΦΦ

Summary• Thin to moderate thick shell适用于薄到中等厚的壳

• Show advantages in membrane and bending-dominant problems在薄膜和弯曲占主导的问题中有一定的优势

64

Meshfree Shell Formulation (cont.) 无网格壳的公式形式



Belytschko-Tsay (1983)

S/R Hughes-Liu (1981)

Belytschko-Leviathan (1994)

Assumed Strain (1990)

Meshfree Local Projection

Meshfree Global Approach Explicit Analysis

Clamped Shallow Cap Under Inflation四周夹住的浅帽盖



Clamped Shallow Cap四周夹住的浅帽盖

66



Explicit mesh-free shell formulation

67



Simulation Model Coupled FEM/Mesh-free Discretization

FEM

FEMMesh-free

ο40.16

Meshfree Experiment

16.4 17.1

Springback Angle

Workpiece Angle Change

Spring-back Analysis (Explicit-Implicit Switch): NUMISHEET 93 回弹分析

Coupled FEM/Mesh-free (movie)

68



Effective Stress during Springback 等效应力

Spring-back Analysis (cont.)回弹分析

69



Mesh free shells

• Based on the mesh-free surface representation and the mesh-free shell formulation

l First-order shear deformable shell theory is adoptedl An assumed strain method is utilized

• Works well for the membrane and bending-dominant problems with highly irregular meshes

• Full car crash models from NCAC with 100% EFG shells have reached normal termination

70



Constant stress solid (default)单点积分六面体单元

8-node brickOne point integrationValid for wedge and tetrahedron

Solid Element Formulations 体单元

Fully integrated S/R solid完全积分六面体单元

8-node brick2x2x2 integrationNo locking

Fully integrated quadratic with nodal rotations

8-node brick14 integration points

Tetrahedron element四面体单元

1 point tetrahedron1 point nodal pressure tetrahedronS/R quadratic tet. with nodal rotation (5 integraion points)

Meshfree EFG element 无网格的EFG 单元

8-node brick 六面体

4-node tetrahedron 四面体

ALE elementALE 单元

8-node brick

71

* More formulations please refer to user manual



eΩ

eΩ

eΩ

• Define the physical domain 定义物理边界• Provide the mass computation 计算质量• Impose boundary conditions 施加边界条件• Create stress points 创建应力点• Can not go beyond Lagrngian description

Background Mesh 背景网格“ Valid within Lagrangain description “

non-overlapping ‘mesh’不重叠

Usually in solid and structure !

72

*SECTION_SOLID_EFG



• Momentum equation 动量方程

• Continuity equation 连续方程

vx∇−= ρρ&

bσv x +⋅∇=& ρ ( ) sssII

II

Ω ΓΩΩ

VΦm

ΓddΩdΩvdΩ

σxv

τvbv σvv

x ⋅∇−=

⋅+⋅+∇−=⋅

∑

∫ ∫∫∫&

& δδδρδ :

( )sII

Iss Φ xv x∑ ∇⋅−= ρρ&

Particle 粒子

Stress point 应力点

I

( )t ,xr I

EFG Fast Transformation Method快速转换EFG方法

∑∑∑∈∈∈

∈∈

≡⋅=

ΩΩI

I[m]

IΩJ

JI[m]J

ΩΩI

[n]I

hΩ )(Ψ)(Ψ)(Φ)(u

xx

xxxxxx ˆ

73

Particles Stress points

AccelerationVelocityPosition

DensityStrain rateStressesInternal energy

Direct variables computation

用转换法施加边界条件



EFG无网格法FEM 有限元

74

Go further ?

Foam Compression Simulation泡沫材料的压缩

能否模拟得更远 ?



Lagrangian Kernel: 1.support is defined in the initial configuration

拉格朗日 2.support covers the same set of material points throughout time

Eulerian Kernel:欧拉 1.support is defined in the current configuration

2.support covers the different material points throughout time

Semi-Lagrangian Kernel: 半拉格朗日 1.support is defined in the current configuration

2.support covers same number of material points throughout time

EFG

EFG

)](),(),()()()()([),(),(),(),( ][][ tx

ttvttt

(t)tvx

tut

tutv iIj

xI

jI

iIxIiI

xI

jj

iii ξξξ

∂Ψ∂

+Ψ+∂

Ψ∂=

∂∂

+∂

∂= ∑ xxxhx;xxxx xx

&

44 344 21EFG

EFG Kernels EFG核函数

75



Negative Volume in EFG ?负体积在EFG

)det(Jddt

FXFx

Xx

=⋅=

= ),(φ •Is continuously differentiable•Is one-to-one•J>0•F is invertible 变形梯度可逆

No material overlappingNo gapNo negative volume

Lagrangian拉格朗日

76

Negative Volume in EFG ?“Beyond Lagrangian Description ! ”

超出了拉格朗日描述的范围

物质不重叠没有间隙



0Ω

tΩ J>0

Particle

Stress point

Improve EFG Negative Volume改善EFG中的负体积

Interactive mesh-free adaptivity无网格的自适应

Severe material deformation物质大变形

Incorporates with Eulerian description引入欧拉描述

Material separation物质分离

Introduce strong discontinuity引入强的不连续

77



EFG + Semi-Lagrangian KernelEFG无网格法+ 半拉格朗日核函数

78

Foam Compression Simulation泡沫材料的压缩

EFG无网格法FEM 有限元



Foam Compression Simulation

79



Adaptive Mesh-free Method自适应的无网格方法

Adaptive Mesh-free Method = EFG Fast Transformation Method 自适应的无网格方法快速转换EFG方法

+ Adaptive Lagrnagian Particles with Eulerian Kernel 用欧拉核函数的自适应拉格朗日粒子

+ Consistent Mesh-free Interpolation for State Variable Transfer对状态变量采用连贯的无网格插值

80

Motivation 目的Improve the large deformation analysis that is beyond the Lagrangian description.改善超出了拉格朗日描述的范围的大变形分析.

Current Practice 应用Solving the forging and extrusion problems.主要解决锻造，挤压问题.

Formulation 方案



Adaptive Lagrangian Particles with Eulerian Kernel 用欧拉核函数的拉格朗日粒子

fCf

f

vv C

)t

∇⋅+∂

∂=

−= +−

(χ&

)(),(

)(),(

1

1

frametimereferencett

frametimematerialt

t

n

n

χx

v

Xx

v X

χ∂

∂=

∂

∂=

++

+−

( )n[m]

I tΨ ( )1n[m]

I tX,Ψ +

( )1n[m]

I t,xΨ +−

Lagrangian Kernel

Eulerian Kernel Particle

Stress point

• Momentum equation

• Continuity equation

j

j

jj x

vx

Ct ∂

∂−=

∂∂

+∂∂ ρρρ

χ

ij

ij

j

ijχ

i bxσ

xvρC

tv ρ +

∂

∂=

∂∂

+∂∂

Convective velocity C due to Eulerian kernel由欧拉核函数引起的相对速度



Operator Split 分步运算

( ) ( )−+=

+ −∆+=∂∂

⋅∆+≈ ∑ vvxxx fx

Cff nxx

- ttΦt n-

JJ

JθJ

θθ ,;~

1. Lagrnagian phase : 拉格朗日阶段

2. Transport phase : 传送阶段

0( =∇⋅+∂

∂fC

f)

t χ

: Ponthot and Belytschko 1998

A

B

: TB stress recovery scheme – conservative– consistent

is [m] order accurate; Currently m=1

Nodal valueRemapped value

-[m]Jn

[m]J Ψ)t,(Ψ =x

( )∑∑ =∂

∂=∇

JJnI

[m]JI

JI

[m]J tΨΨ fxffx

f ~, ;~

( ) ( )

( ) JJ

[m]J

[m]J[m]

J[m]J

Ψ

ΨΨΨ

fxf

xxxxx

x--

~

)(

∑ ++

++

≈

+∂

∂⋅−−= − Λ

Adaptive Lagrangian Particles with Eulerian Kernel 用欧拉核函数的拉格朗日粒子

82



Mesh-free Interpolation for Data Transfer连贯的无网格插值

Current variable update :

( )J[m]

IIJ

nns

ns

ns

xΦA

fAAfAf

=

=≈ −+++ −

βαβααα

1111 ~

( )1n[m]

I t,xΨ +−

Particle

Stress point

( )1n[m]

I t,xΨ ++

Old Particle

Old Stress point

New Particle

New Stress point

( )1n[m]

S t,xΦ ++

I I

S

83

Stress recovery scheme is conservative, consistent and monotonic !应力的插值是守恒的，连贯的，和单调的。



Analytical SolutionEFG SolutionInterpolation Solution

fudxdu

dxd

=+− )( )1,0(∈x

0)1()0( == uu4sinh

4sinh2 xxu −=

Interpolation of the State Variable in 1-D

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-3 -2.5 -2 -1.5 -1 -0.5 0

Log (Nodal space)

Log

(Err

or n

orm

)

EFG solution

Interpolation solution

Slope 1.68

Convergence in derivative of solution

4sinh4sinh1522 xxf +−=

84



VEFG

EFG Adaptivity

ForceVolume change (1.7%)

13661 nodes

Wheel Forging Simulation锻造模拟

85

5827 nodes



Wheel Forging Simulation (Explicit)锻造模拟

86

(courtesy Alcoa)



Final Background MeshFinal Nodes Distribution

Wheel Forging Simulation

87



Extrusion Simulation (Implicit)(Courtesy of JRI)

*MAT_POWER_LAW_PLASTICITY*CONTACT_SURFACE_SURFACE*SECTION_SOLID_EFG

Final Plastic Strain

88



Extrusion Simulation (Implict and Explicit)

Local RefinementGlobal Refinement

Final Plastic StrainFinal Plastic Strain

89



Extrusion Simulation(Courtesy of JRI)

Local Refinement

90



Extrusion Simulation: Results Comparisons

Force Volume change (4.0%)

Results Comparisons for Implict and Explicit EFG Adaptivity

91



ALE Applied to Modeling of AirbagsALE用于气囊的模拟



Out-of-Position Capabilities处理OOP的功能

Modeling Out-Of-Position occupants requires the ability to compute the early time evolution of the airbag deployment before the uniform pressure, control volume, approach is valid. An approach using Arbitrary Lagrangian Eulerian techniques, ALE, and Particle Method are used in LS-DYNA.

模拟OOP的乘客需要计算气囊展开中达到均匀气压以前的展开过程。

用控制体积法会有较大的误差。LS-DYNA利用ALE (任意拉格朗日欧

拉法) 和颗粒法技术来实现这个关键功能.

93



Gas mixture 混合气体

Moving point sources 移动的点源

Automatic expansion of the ALE mesh ALE网格的自动扩

ALE mesh moves along with vehicle ALE网格随汽车移动

Robust contact algorithm for fabric-to-fabric contact有效的纤维材料同纤维材料的接触计算

Fabric porosity for ALE 纤维材料的渗透

Discrete venting for ALE 分散的出气孔

Blockage considered for porosity and ventingALE supported in SMP and MPP 可用于并行版

94

ALE Applied to Modeling of AirbagsALE用于气囊的模拟



*MAT_GAS_MIXTURE

95

The burning propellant in an airbag inflator produces several different gases. 燃烧的助推器产生不同性质的气体.

Allows a mixture of up to 8 different gases. 允许混合8种不同气体.

Cp and Cv inputs required for each gas

*INITIAL_GAS_MIXTUREl Initialize the density and temperature of a material (gas)l Initialize air inside a tank for a tank test simulation



ALE Mesh Expansion and MovingALE网格扩展和移动

Provides a method to have a fine ALE mesh during the initial stages of airbag deployment. 在气囊展开的初始阶段有比较细的ALE网格.

ALE mesh automatically expands ensuring the airbag parts are within the ALE mesh.

网格的扩展保证气囊在 ALE网格内.

Automatic expansion and moving can be used together.

ALE网格扩展和移动可同时使用.

Ale mesh moving is cost effective compared to a large ALE domain.与一个整个的 ALE网格相比，有效地减少ALE单元数量.

96



Fabric Shells Coupled to ALE Gas纤维壳与ALE气体的耦合

97



Fabric Shells Coupled to ALE Gas纤维壳与ALE气体的耦合



ALE Physical Venting ALE 通气孔

99



ALE-Control Volume SwitchingALE法转成控制体积法

100

*AIRBAG_ALERun control volume only 只用控制体积法

Run ALE only 只用ALE方法

Start with ALE and switch to control volume 先用ALE法然后转成

控制体积法



050

100150200250300

Elap

sed

time

(min

utes

)

ALE CV ALE-CV30 MS RUN

LINUX 1CPU

101

ALE-Control Volume SwitchingALE法转成控制体积法



• Very similar input as Control volume input 与体积控制法的输入相似

• Venting and Porosity supported 支持开孔和渗透l Blocked and unblocked

• Internal baffles defined through sid2l Flow through internal baffles can be monitored

• Multiple inflators 多个进气孔

• Switching from Particle method to CV 从颗粒法转换成体积控制法

• 2 step procedurel Extract mdot and Temp. from gasguide stationsl Use of extracted data in step 1 as input to individual chambers.

• Tank test simulation – resident gas in the tank/bag can be considered

• 3 unit systems currently supported for ease of input. 支持三个单位体系

Particle method 颗粒法

102



multi-material Eulerian and fluid-structure interaction

uniform pressure

particle method

Example: flat bag after 5ms compared to results from Eulerian and uniform pressure models

扁平气囊袋打开5ms后的结果比较


103



UP

particle

Eulerian

time (ms)

bag

cen

ter

def

lect

ion (

mm

)

Example: airbag center deflection compared to resultsfrom Eulerian and uniform pressure models


104



Particle method tank test

105



Particle method tank test

106



0 50 100 150

Controlvolume

ParticleMethod

ALE

CPU minutes for 3 methods

107



Particle airbag method

• Gas mixtures• Moving point sources and multiple inflators• Airbag deployment in moving vehicle• Robust contact algorithms for tightly folded bags• Fabric porosity • Treat external and internal vents• Blockage considered for porosity and venting• Switch from particle method to control volume to save CPU time• Serial, SMP, and MPP support



Particle method-new features

Dynamic radius - IRDP

• Particle size is adjusted automatically based on potential collision rate to keep reasonable mean free path

• Particle moves easier in tight space to give reasonable flow rate (gas guide tube)

• Particle collision rate higher in open spaces

*AIRBAG_PARTICLE

SID1 STYPE1 SID2 STYPE2 BLOCK HCONV FRIC IRDP

ndl

..21

2π=

IRDP: Eq.0 off (Default)Eq. 1 on



Inside guide tube particle size reduced

Larger particles in bag




Inflator gas flow and momentum transfer

• More realistic inflow condition using flow speed• Particles carry thermal velocity to avoid artificial jet in the inlet• The cone angle (CAi) is hence obsolete from release 4• New option is available to measure and apply reaction forces to

inflator from inlet gas impulse (IMOM)

*AIRBAG_PARTICLE

…….

NORIF cards

NIDi ANi VDi CAi INFOi IMOM

BoltzmannMaxwellflowinlet EEE −+=

IMOM: Eq.0 off (Default)IMOM: Eq.0 off (Default)

Eq. 1 onEq. 1 on




Particle method curtain bag

112



Particle method with curtain bag with switch to cv at 20ms

113




LS-DYNA introduction LS-DYNA介绍

New Features in LS971 LS971新功能

New Element Technology 新的单元技术



114




Numerical Solution Errors

Source Numerical Solution Errors

Discretization Finite element interpolation for geometry and solution variables

Linear,isoparameter

Numerical Integration in space

Finite element matrices using numerical integration

Evaluation of constitutive relation

Nonlinear material models Metal, ploymer

Solution of dynamic equilibrium equation

Direct time integration

Solution of FE equation by iteration

Gauss-Seidel, Newton-Raphson Convergence tolerance

Round off computers

115



Accuracy Efficiency Robust 精度效率鲁棒

116



Mesh Convergence

1. mesh convergence means that the simulation result no longer changes as the mesh is further refined.

2. the numerical result is then mesh independent and thus reliable.

3. too coarse meshes allow only low curvature buckling modes.

4. using FE methodology, convergence is achievable for elements of finite size.

118



Mesh Convergence

Mesh convergence can be checked by refining the mesh and comparing results or by judging the smoothness of the deformed mesh.

How fine the mesh should be in order to reach convergence depends upon the structure, the loadcase, and other aspects.

Convergence for the folding automotive structure (car body) is in the neighborhood of 1-3mm characteristic meshlength.

Usually mesh convergence seems a sufficient condition to predict intrusions.

119



Mesh quality reflects the suitability of a global mesh under a certain loadcase.

Element size should be uniform whenever possible.

Contact, damping

Maintain a smooth transition from coarse to fine mesh.

noise

The element mesh should be orthogonal to the centerline of the part.

Use a minimum of 3 rows of elements to get a good in-plane bending.

Use a minimum of 5 elements for a buckle.

Limit the number of tri’s. (<10%) 三角形单元数量不超过10%

Mesh Quality

120



Element quality is referred to a single element such as warp angle, skew angle, aspect ratio, Jacobian .

Element Quality

121



Mass scaling

122



In-Plane Bending 平面内弯曲

Shell 2 shell 41shell 16

123



Out-of-Plane Bending 平面外弯曲

Shell 2 shell 41shell 16

124



• Tri’s are used for mesh transition regions 用于网格过渡

• Tri’s are good for curved geometry 用于弯曲的几何

• Tri’s do not need hourglass control 无须沙漏控制

• Tri’s are stiffer 三角形单元很硬

• Avoid using degenerate quad’s (Use C0 tri’s) 避免用退化的四边形单元

• Limit the number of tri’s (<10%) 三角形单元数量不超过10%

Triangular Shell 三角形壳单元

125




Shell 2四边形单元

tri’s三角形壳单元

degenerate quad’s退化的四边形单元

126




127




128



Mats Larsson’s tables show that the BT element istheoretically not convergent : the energy absorptiondecreases as long as we refine the mesh

However from an engineering point of view we reachconvergence since the influence of a change in themeshsize becomes small compared to the influence ofother parameters in the input

Alternatively, theoretical convergence can be achievedwith element type 16 in LS-DYNA

However type 16 element will overstiff for large element sizes

133



1. Numerical dispersion must be minmizied to compute accurate acceleration peaks.

2. A uniform and orthogonal mesh is required throughout the entire structure.

3. Active mass

4. Contact thickness

Predicting Acceleration Peaks

134



NCAC reports



Papers in LS-DYNA users conference



Conclusions 结论

Version 971 has become a major release with many new capabilities that focus on the automotive industry.971版包括许多用于汽车工业的新功能。

MPP implicit 并行处理的隐式解法

ALE is at production level for out-of-position occupant analysisALE 用于OOP乘客的分析(气囊)EFG is reaching production level无网格EFG的应用

Significant progress has been made to include most crash capabilities within the implicit solver.

大部分的汽车碰撞功能已有相应的隐式求解器。

Full compatibility with linear structure models leading to a one model environment.完全与线性结构模型协调，迈向共同维护和共同享用一个模型的开发环境。

138



LSTC is committed to be the leader in large scale numerical simulationsLSTC继续致力于在大型数值模拟的领先地位

l LSTC has been actively working on the most challenging issuesLSTC将继续从事于解决有挑战的问题

l Many of LSTC’s innovations have been well accepted by industrial users

许多 LSTC的创新已经得到工业界接受

LSTC is not content with what has been achievedLSTC不满足于现有的成就

l New features and algorithms will be continuously implemented to handle new challenges and applications

将继续实现新的功能和算法来解决新的挑战和应用

Conclusions 结论

139



Thank You

谢谢 !!!!

140

lsdyna 2009 5 2 - · pdf file1 ls-dyna 以及它在汽车行业中的应用 ls-dyna and its...

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