universiti putra malaysiapsasir.upm.edu.my/51516/1/fk 2009 107rr.pdf · 2017-03-16 · universiti...

UNIVERSITI PUTRA MALAYSIA

REZA AFSHAR HOSSEINABADI

FK 2009 107

CRASH DEFORMATION SIMULATION OF TUBULAR STRUCTURE TO DETERMINE AUTOMOTIVE CENTRE OF GRAVITY

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Crash Deformation Simulation of Tubular Structure to Determine Automotive

Centre of Gravity

By


Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfilment of

the Requirements for the Degree of Master of Science

September 2009

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DEDICATION

To my dear parents

and

lovely wife

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ABSTRACT

Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfilment

of the requirement for the degree of Master of Science

Crash Deformation Simulation of Tubular Structure to Determine Automotive

Centre of Gravity

By


September 2009

Chairman: Aidy Ali, PhD

Faculty: Engineering

In this study, the effects of crush behaviour of tubular structures have been

investigated throughout simulation work. The axial crush was performed to predict

the behaviour of tubular structures in terms of displacement of centre of gravity

(COG) and mass moments of inertia (𝐼𝑦𝑦 𝑎𝑛𝑑 𝐼𝑥𝑧).

Crush simulation includes two sections; close and open cross-sections respectively.

In the case of close cross-sections, a displacement of COG of tubular structures with

various polygonal cross-sections is numerically investigated under axial crush using

program code of ANSYS/LS-DYNA. A subroutine is developed using this code to

calculate the COG of deformed shape, during and after crush condition. The effect of

wall thickness on displacement of COG is also investigated. Subsequently, a

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procedure to find real time COG of tubular structure during and after crush is

developed. Base on this procedure, a macro is added in the frame work of

ANSYS/LS-DYNA to study the deformation behaviour of tubular structure by the

accurate criteria of COG, 𝐼𝑦𝑦 𝑎𝑛𝑑 𝐼𝑥𝑧. Furthermore, the optimum number of edge of

polygonal cross-section to have a reasonable symmetric deformed shape during crush

is determined. It is found that the effect of number of polygonal edges on symmetric

deformation of COG becomes more prominent as wall thickness of tubular structure

decreases. The higher number of edges stabilizes the deformation shape.

To examine the open cross-sections, the tubular structures with various Cee-shaped

cross sections are numerically investigated. The subroutine used for the first section

is performed again. Yet, the effect of wall thickness was also studied. Subsequently,

the effect of opening angle of Cee becomes more prominent as the wall thickness of

the structure decreases. As the thickness increases, displacement of the COG in crush

direction almost stabilizes for all opening angle of Cee in the range of 100 −

900 degrees. Furthermore, variation of 𝐼𝑦𝑦 of structure with thicker wall for different

cases of applied mass is approximately identical. As a contribution to real

application, Cee-shaped cross-sections with higher wall thicknesses can be used in

the form of frame structures in automotive industry in order to reduce the overall

weight of the structure and therefore, to save more energy.

The study is the continue by incorporating a developed subroutine that added in the

pre-processing module, in the frame work of ANSYS, distribution of the extra mass

according to specific assigned COG and calculation the first bending and torsional

natural frequencies of the simplified model in order to maximize these frequencies

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with final mass constraint was successfully investigated. It was found that adding the

extra mass symmetrically about longitudinal axes of Body In White (BIW), higher

values for first bending and torsional natural frequency is achieved.

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ABSTRAK

Abstrack tesis yang dikemukakan kepada Senat Universiti Putra Malaysia

sebagai memenuhi keperluan untuk ijazah Master of Sains

Simulasi Deformasi Remuk Struktur Berongga Bagi Penentuan Pusat Graviti

Automotif

Oleh


September 2009

Pengerusi: Aidy Ali, PhD

Fakulti: Kejuruteraan

Didalam kajian ini, kesan sifat remukkan struktur berongga dikaji dengan

menggunakan kaedah simulasi. Remukkan arah menegak dijalankan bagi menjangka

anjakan pusat gravity (COG) dan momen inersia (𝐼𝑦𝑦 𝑎𝑛𝑑 𝐼𝑥𝑧).

Simulasi remuk kesan hentaman ini dibahagikan kepada dua bahagian: tertutup dan

terbuka. Bagi kes tertutup, COG untuk struktur dengan polygonal keratin rentas

dikaji secara berangka. Menggunakan program kod ANSYS/LS-DYNA. Sebuah

pengatur caraan program di talis untuk mengukun COG bagi perubahan bentuk,

ketika dan selepas hentaman. Kesan ketebalan struktur berongga ini juga dikaji.

Seterusunya, kaedah mentukan COG secara seuanasa juda dibangunkan. Berasaskan

kaedah ini, makro ditambah didalam rangka ANSYS/LS-DYNA untuk mengkaji

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sifat deformasi tiub COG, 𝐼𝑦𝑦 𝑎𝑛𝑑 𝐼𝑥𝑧 . tambahan lagi, segi optimum poligonal

keratan rentas memiliki remukkan bentuk simetri. Di dalam kajian ini, didapati

jumlah segi poligonal adalah signifikan apabila ketebalan meningkat. Semakin tinggi

jumlah segi, semakin stabil keadaan remukkan.

Untuk mengkaji kes keratin rentas terbuka, tiub dengan beberapas bentuk Cee

terbuka diuji. Pengatucaraan yang sama untuk kes tertutup digunakan sekali lagi.

Kesan tebelatan juga dikaji. Kesan ketebales semakin jelas, anjakan COG disetuap

arah semakin stabil untuk setiap sudut 100 − 900 darjah. Tambahan lagi, variasi 𝐼𝑦𝑦

dengan beban yang seragan ditemui serupa. Sebagai sumbangan applikasi, bentuk

Cee dengan ketebalan tinggi boleh digunakan untuk struktur automotive bagi

mengurangkan berat seteterusnya tenaga.

Kejuan ini diteruskan dengan menanbahkan pengatucaraan didalam per proses

modul, didalam ANSYS, taburan lebihan beban mengikut keperluan spesifik COG,

dengan mengira lenturan dan puntiran frekuensi asli, didalam model yang diubah

suai, bagi memaksimumkan kekangan beban. Didapti, penanbahan beban secara

simetri di ats poksi memanjang di badan automotif, lenturan dan puntiran frekuensi

dicapai.

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ACKNOWLEDGEMENT

First and foremost I would like to express my deep gratefulness to my supervisor Dr.

Aidy Bin Ali for his support, encouragement and suggestions during the study and

preparation of this thesis. I truly appreciate the time he devoted in advising me and

showing me the proper directions to continue this research.

I would also like to express my gratitude towards my co-supervisor Professor Ir. Dr.

Barkawi Bin Sahari. I am grateful for his supervision, help, helpful advice and

knowledge that made an invaluable contribution to this dissertation. Many ideas

originate in our frequent discussion and his constant support and patience have been

of invaluable help.

I wish to express my special thanks and appreciation to my beloved parents, my wife

and specially my dear uncle Isa for their unconditional supports and good cheer.

Last but not least the deepest appreciation goes to my very close friends, Amirreza

and Ayyoub for their contentious support and encouragement. Another thank goes

for Guru for the translation of abstract into Malay language.

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APROVAL

I certify that a thesis Examination Committee has met on 8 September 2009 to

conduct the final examination of Reza Afshar Hosseinabadi on his thesis entitled

“Crash Deformation Simulation of Tubular Structure to Determine Automotive

Centre of Gravity” in accordance with Universities and University Colleges Act 1971

and Constitiuation of the Universiti Putra Malaysia [P.U.(A) 106] 15 March 1998.

The Committee recommends that the candidate be awarded the Master of Science.

Members of the Examination Committee are as follows:

Chairman, PhD

Dr. Mohd Khairol Anuar Mohd Arifin

Department of Mechanical and Manufacturing Engineering

Faculty of Engineering

Universiti Putra Malaysia

(Chairman)

Examiner 1, PhD

Associate professor Datin Dr. Napsiah bt. Ismail




(Internal Examiner)

Examiner 2, PhD

Associate professor Dr. Tang Sai Hong




(Internal Examiner)

External Examiner, PhD

Associate professor Dr. Shahrum Abdullah

Department of mechanics and material

Faculty of engineering

University Kebangsaan Malaysia

(External Examiner)

BUJANG KIM HUAT, PhD

Professor and Deputy Dean

School Of Graduate Studies

University Putra Malaysia

Date:

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This thesis submitted to the Senate of Universiti Putra Malaysia and has been accepted

as fulfillment of the requirement for the degree of Master of Science. The members of

the Supervisory Committee were as follows:

Aidy Bin Ali, PhD

Senior Lecturer




(Chairman)

Barkawi Bin Sahari, PhD

Professor

Institue Advanced Technology


(Member)

HASANAH MOHD GHAZALI, PhD

Professor and Dean

School Of Graduate Studies

University Putra Malaysia

Date: 16 November 2009

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DECLARATION

I hereby declare that the thesis is based on my original work except for quotations and

citations which have been fully acknowledged. I also declare that it has not been

previously or concurrently submitted for any other degree at UPM or other institutions.


Date: 23 November 2009

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TABLE OF CONTENTS

Page

DEDICATION ii

ABSTRACT iii

ABSTRAK vi

ACKNOWLEDGEMENT viii

APROVAL ix

DECLARATION xi

LIST OF TABLES xvi

LIST OF FIGURES xvii

LIST OF ABBREVIATIONS xxiv

1 INTRODUCTION 1

1.1. Introduction 1

1.2. Research Problem 2

1.3. Research Objectives 3

1.4. Scope of the Study 4

1.5. The Layout of this Thesis 4

2 LITERATURE REVIEW 6

2.1 Introduction 6

2.2 Previous Works on Crushing of Tubular Structures 6

2.2.1 Experimental and Theoretical Method 7

2.2.2 FEM and Experimental Method 10

2.3 Centre of Mass, centre of gravity and geometric centre 20

2.3.1 Centre of Mass (COM) 20

2.3.2 Application of COM 21

2.3.3 COM calculation of discrete system 21

2.3.4 COM calculation of continuous systems 22

2.3.5 COM and centroid 23

2.3.6 COM and symmetry 23

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2.3.7 COM of composite objects 24

2.3.8 Geometric centre (centroid) 25

2.3.9 Centre of Gravity (COG) 25

2.3.10 COG for a System of n Particles 27

2.3.11 COG of lines, areas and volumes 29

2.4 Experimental methods of determining COG 30

2.4.1 Pendulum test method 30

2.4.2 Frequency Response Function (FRF) method 30

2.5 Inertia properties of a structure 31

2.5.1 Why inertia properties are needed 31

2.6 COG and weight distribution 31

2.7 Body in white of an automotive 32

2.7.1 Unitized and frame constructions 33

2.7.2 Space frame technology 38

2.7.3 BIW and COG 39

2.8 Static analysis of body structure 41

2.8.1 Modal analysis 42

2.8.2 Natural frequency 42

2.8.3 FEA eigensystems 45

2.8.4 Methods of solution 47

2.9 Mode shapes of a structure 48

2.9.1 Introduction 48

2.9.2 Modal analysis of automotive body by FEM 49

2.10 Discussion 55

3 METHODOLOGY 58

3.1 Introduction 58

3.2 Numerical simulation of xial crush of tubular structure 61

3.2.1 The Finite Element Method - Analysis Stages 61

3.2.2 FEM commercial package 63

3.3 Pre-processing 63

3.3.1 Modelling 63

3.3.2 Meshing 66

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3.3.3 Material properties 67

3.3.4 Applying boundary conditions 71

3.4 Processing 75

3.4.1 Computational Processing 75

3.5 Post-processing 76

3.5.1 Reading the result and implementing the

subroutine 76

3.6 Implementing COG auto generation subroutine 77

3.7 Methodology of COG auto adjust 78

3.8 Pre-processing 79

3.8.1 Modeling 79

3.8.2 Meshing 80

3.8.3 Material Properties 81

3.8.4 Applying Boundary Conditions 82

3.9 Implementing subroutine 82

3.9.1 Step 1: Obtain the COG and total mass of the

initial model 84

3.9.2 Step 2: Define desired COG on X-direction (the

model is symmetric about X-axis) 85

3.9.3 Step 3: Define Co-ordination of extra mass

(according to the centrioad of the extra mass) 85

3.9.4 Step 4: Obtain the value of extra mass on X-axis

and the COG of new model on Y-axis 86

3.9.5 Step 5: Overlap added parts with the initial

model 87

3.9.6 Step 6: Define material properties of added parts,

meshing the new model (consisting of the initial

model and the added parts) 88

3.9.7 Step 7: Apply boundary conditions and solve 88

3.10 Processing 88

3.10.1 Computational Processing 88

3.11 Discussion 88

4 RESULTS AND DISCUSSION 90

4.1 Introduction 90

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4.2 Result of axial crushing of tubular structure with various

polygonal cross-sections 90

4.2.1 Reading result in each increment of time 90

4.2.2 Verification of simulation work 92

4.2.3 Displacement of COG in every computational

condition 108

4.2.4 Calculation of mass moments of inertia 111

4.2.5 Displacement of COG by different wall thickness 112

4.3 Conclusions of axial crush of tubular structure with

different polygonal cross-sections 113

4.4 Result of axial crushing of tubular structure with various

Cee-shaped cross-sections 114

4.4.1 Reading result in each increment of time 114

4.4.2 Deformed shapes of tubular structures 115

4.4.3 Displacement of COG in every computational

condition 118

4.4.4 Calculation of mass moments of inertia 123

4.5 Conclusions of axial crush of tubular structure with

different Cee-shaped cross-sections 129

4.6 Results of applying COG auto adjust subroutine in order to

find the desired COG and calculation of first bending and

torsion natural frequencies. 129

4.7 Parameters used for second subroutine 134

4.7.1 Extra mass 135

4.7.2 COG on Y-axis 135

4.7.3 First bending natural frequency 138

4.7.4 First torsional natural frequency 138

5 CONCLUSIONS AND RECOMMENDATIONS 140

5.1 Conclusions 140

5.2 Recommendations for further work 141

REFRENCES 142

APPENDICES 150

BIODATA OF STUDENT 163

LIST OF PUBLICATIONS 164

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LIST OF TABLES

Table Page

2.1 ID number and properties of candidate material [63]. 54

2.2 Optimized first bending frequencies [64]. 55

3.1 Material Properties of tubular structures with normal polygonal

cross-sections [65]. 68

3.2 Material Properties of tubular structures with normal polygonal

cross-sections [65]. 69

3.3 Material Properties of shell structure of simplified BIW. 81

4.1 Comapring simulated results with predicted model and errors in the

case of tubular structure with thickness of 1.5 mm. 104

4.2 Comapring simulated results with predicted model and errors in the

case of tubular structure with thickness of 2.5 mm. 104

4.3 COG properties and first bending and torsional natural frequencies

of initial model. 130

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LIST OF FIGURES

Figure Page

2.1 A typical load-displacement trace for PVC square tube under

quasi-static compression [13]. 7

2.2 Elastic buckling modes of thin PVC square tubes with (a) t/d =

0.034, l/d =3 and (b) l/d = 4 [13]. 8

2.3 Load-displacement curve [31]. 9

2.4 Crush deformation by different number of corners with different

wall thicknesses [34]. 11

2.5 Effect of crush strength versus number of corners and thicknesses

[34]. 11

2.6 Different bulge height [39]. 14

2.7 Simulated and experiment of crush [17]. 15

2.8 Comparison of simulation and experimental of force-displacement

[17]. 16

2.9 Comparison between crush load–displacement of empty and foam-

filled [28]. 17

2.10 Interaction effect in foam-filled tube [28]. 18

2.11 and experimental crash pattern and crash load-displacement curve

of empty tube [29]. 19

2.12 A comparison between crash load-displacement of empty and

foam-filled tubes [27]. 20

2.13 COM of a system consisting of two masses [46]. 22

2.14 The COM and geometric centroid share the symmetries of the

object [46]. 24

2.15 COM of composite system [45]. 24

2.16 Geometric centre of triangle. 25

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2.17 System of n particles [47]. 27

2.18 System of n particles (rotated 90 about x axis) [47]. 29

2.19 A sample BIW [50]. 33

2.20 (a) body-over-frame and frame structure. (b) unibody structure

[51]. 33

2.21 A unibody of automotive structure [51]. 34

2.22 Half-ton 2002 Dodge Ram pickup truck [52]. 34

2.23 BIW of Honda Acura MDX 2007 and different possible impact

situation [53]. 35

2.24 Different construction of BIW of Honda Acura MDX 2007 [53]. 35

2.25 Cross-section used in side construction [53]. 36

2.26 Cross-section used in rear construction [53]. 37

2.27 Distributed load pattern in the case of frontal impact in frontal

construction [53]. 37

2.28 Cross-sections used in frame construction [53]. 38

2.29 Modern space frame of a vehicle construction [55]. 39

2.30 BIW and different attached part of automotive body [55]. 40

2.31 The developed front platform with developed of side and center

member assembly front floor [39]. 41

2.32 Spring-Mass system and free body diagram [56]. 43

2.33 Tacoma Narrows bridge disaster [59]. 48

2.34 Modal analysis of a automotive body [59]. 49

2.35 Modal analysis of automotive body by FEM [60]. 51

2.36 Average of first torsional and first bending frequencies

maximization results from topology optimization (a) and sizing

optimization (b) [61]. 52

2.37 Mode density of BIW [62]. 53

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2.38 First bending frequency maximization results: (a) 1% added mass

(b) 3% added mass [64]. 55

3.1 Overall project flowchart of COG auto generation. 59

3.2 Overall project flowchart of COG auto mass adjust. 60

3.3 Procedure of implementing COG auto generation, during and after

crush deformation of tubular structure in ANSYS. 62

3.4 Various polygonal cross-sections. 64

3.5 Various Cee-shaped cross-sections. 66

3.6 Shell 163 geometry [65]. 67

3.7 Stress-strain curve of material with polygonal cross-section. 68

3.8 Stress-strain curve of material with Cee-shaped cross-section. 70

3.9 Procedure of defining model behaviour in ANSYS. 71

3.10 Two components used for simulation of crush and boundary

conditions, in the case of regular polygonal cross-sections. 72

3.11 Geometric modeling and boundary conditions of regular polygonal

cross sections. 73

3.12 Two components used for simulation of crush and boundary

conditions, in the case of Cee-shaped cross-sections. 74

3.13 Geometric modeling and boundary conditions of Cee-shaped cross

sections. 75

3.14 Selecting the specific substep and reading the results. 76

3.15 Calling the subroutine through ANSYS command line. 77

3.16 Procedure of subroutine to calculate the COG of deformed shape of

tubular structure. 78

3.17 Procedure of implementing COG auto adjust subroutine in the

finite element model of tubular structure. 79

3.18 Shell structure of BIW developed in Solidworks. 80

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3.19 Shell 63 geometry [66]. 81

3.20 Applying boundary conditions on BIW to obtain first bending and

torsional natural frequency. 82

3.21 Regions for adding the mass according to desired COG. 83

3.22 Procedure of COG auto adjusts subroutine of tubular structures. 84



4.3 Deformed shapes of tubular structure with octagonal cross section

for thickness of 1 mm. 92

4.4 Displacement of COG vs. time during the crush of tubular structure

with octagonal cross section for thickness of 1 mm. 93

4.5 Mass moment of inertia vs. time during the crush of tubular

structure with octagonal cross section for thickness of 1 mm. 94














with octagonal cross section for thicknesses of 1, 2 and 3 mm. 101

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for thickness of 1.5 mm. 102


for thickness of 2.5 mm. 103


with octagonal cross section for thicknesses of 1.5 and 2.5 mm and

comparison with the predicted model. 105

4.16 Deformation shapes (initial, 100 ms and 150 ms after crush), initial

wall thickness: (a) 1 mm; (b) 2 mm; (c) 3 mm. 106

4.17 The effects of increasing the number of corners and thickness on

behaviour of deformed shapes at 150 ms after crush. 107

4.18 Displacement of COG for various cross-sections with thickness=1

mm. 108


mm. 109


mm. 110

4.21 Mass moments of inertia about COG for various polygonal cross-

sections with different thicknesses. 112

4.22 Displacement of COG for various cross-sections with different

thicknesses. 113



4.25 Deformed shapes of different cross sections with thickness of 1

mm. 116


mm. 116


mm. 117

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4.28 Deformed shapes of different cross sections by applying 10 (1)

and 20 Kg (2) on the structure, (a) with thickness of 2 mm. (b) with

thickness of 3 mm. 118

4.29 Displacement of COG versus opening angle of Cee in the case of

applying 10 kg on the structure with thickness of 1 mm. 119






applying 10 kg on the structures with thicknesses of 1, 2 and 3mm. 122

4.33 Displacement of COG on Y axis versus opening angle of Cee with

thickness of 2 and 3 mm. 123

4.34 Variation the Mass moment of inertia about the COG by various

opening angle of Cee in the case of applying 10 kg on the structure

with thickness of 1 mm. 124








opening angle of Cee in the case of applying 10 kg on the

structures with thicknesses of 1, 2 and 3 mm. 127


opening angle of Cee in the case of applying 10 kg (1) and 20 kg

(2) on the structures with thicknesses of 2 and 3 mm. 128

4.39 Applied Boundary conditions to obtain the first bending and

torsional natural frequencies. 130

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4.40 Different position of the extra mass along X-axis. 131

4.41 Variation of first bending natural frequency by different position of

extra mass along Z-axis (XC=8.0 cm). 132

4.42 Variation of first torsional natural frequency by different position

of extra mass along Z-axis (XC=8.0 cm). 133

4.43 Different positions of the extra mass along Z-axis. 134

4.44 Variation of extra mass by displacing the COG along X-axis. 135

4.45 Variation of the COG along Y-axis by displacing the COG along X-

axis for different position of extra mass at X=80 cm (symmetric

about X-axis and at the middle of platform). 136

4.46 Variation of the COG along Y-axis by displacing the COG along X-

axis for different position of extra mass at X=80, 85, 90 and 95 cm

(symmetric about X-axis and at the middle of platform). 137

4.47 Variation of the first bending natural frequency by displacing the

COG along X-axis for different position of extra mass at

extra_mass=80 cm (symmetric about X-axis and at the middle of

platform). 138

4.48 Variation of the first torsional natural frequency by displacing the

COG along X-axis for different position of extra mass at

extra_mass=80 cm (symmetric about X-axis and at the middle of

platform). 139

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LIST OF ABBREVIATIONS

BIW Body In White

COG Centre Of Gravity

COM Centre Of Mass

CAE Computer Aided Engineering

FEM Finite Element Method

FE Finite Element

MDO Multi Design Optimization

APDL Ansys Parametric Design Language

NGV Natural Gas Vehicle

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CHAPTER 1

1 INTRODUCTION

1.1. Introduction

The performance of vehicle in the event of collision is one of the most prominent

areas that must be considered at the design stage. For instance a dangerous situation

resulting in injury of the occupants can occur if the deformation of vehicle body

members extends into the passenger compartment. To ensure adequate occupant

protection, the crash energy must be absorbed through a deformation of front-end of

automotive body structure.

All of the members, including the front-end and side members, particularly, play a

major role in absorbing crash energy. Therefore, rising up their energy absorption

efficiency is an important key point in improving the crashworthiness of the

vehicle’s front-end. The side members are generally structured as thin-walled

components which have square, rectangular or hat-shaped cross-sections. It is

generally curved positioned below the passenger compartment due to their positional

relationship with the suspensions and other parts. However its front portion needs to

be kept as straight as possible in order to make them capable to withstand greater

loads. It is evident that the ability of side members to absorb energy is efficiently

increased by proper design so that the collapse will be in predicted manner with

preventing their side walls collapse in bending. This type of collapse mode can be

engineered through several innovative techniques such as placing beading or

reinforcements at appropriate place along the side members.

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Furthermore, it was found that aluminium columns are also connected to the vehicle

bumpers as a crush boxes to protect the passengers and the structure itself under

impact loading. The aluminium columns are used to absorb the initial kinetic energy

and keep the force level sufficiently low, so that lead to prevent from damage to the

front-end compartment. Generally, the energy absorption will take place by extensive

folding and bending collapse of the column wall. A specific characteristic of such a

deformation mechanism is obtained when the rate of energy dissipation is located

over the narrow zones, while the rest of the structure experiences a rigid body

motion. At present, an increased of interest on vehicle safety have led to a

comprehensive research [1] of the crash response of aluminium tubes from all

aspects, experimental, analytical and numerical means. In this study, the Finite

Element Method (FEM) was used to locate the centre of gravity (COG) of such

tubular structures during and after axial crush deformation in order to have an

accurate situation of deformed shape concerning the COG. Further more it will lead

to come out with proper criteria to decide on the behaviour of tubular structure in

term of deformation shape.

1.2. Research Problem

Thin-walled tubular structures are commonly used as the strengthening members in

an automotive Body In White (BIW). Many researchers [2-20] have paid

considerable attention on the crush behaviour of tubular structure for the past two

decades. There have been a lot of activities on dynamic crush of tubular structures

during recent years and most of them have been concerned with the energy absorbing

systems of vehicles [21-29].

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Assessing the general deformed shape of tubular structure during crush has been

performed based on visual observation. However, this deformation is accessible in

finite element simulation, having an accurate situation of deformed shape concerning

the COG of structure was the lack of studies. Hence having a subroutine in FEM will

help the researchers to obtain the inertia properties of arbitrary tubular shapes during

and after crush deformation, and evaluate the accuracy of phenomenon of deformed

shape of tubular structure during and after crush.

A number of automobile manufacturers have developed and produced all-aluminum

bodies as a means of weight reduction [67]. Hence, examining the deformation

behavior of various tubular structures made of aluminum by means of variation of

their COG during and after crush deformation will help to extend the application of

light materials for automotive BIW.

Furthermore, the correct location of COG is prominent for engineers in Computer

Aided Engineering (CAE) analysis, when it comes to vehicle yaw, moment and

rotation due to impact. Yet again, at design stage, mass in CAE model should be

evenly distributed in order to obtain the correct COG. For instance, by having some

extra parts in new designs such as adding fuel tanks in Natural Gas Vehicle (NGV),

having the correct COG is a very prominent issue.

1.3. Research Objectives

The objectives of the study are:

1. To develop an algorithm that can auto adjust the location of COG of

deformed shape, during and after crush.

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2. To simulate the real time location of COG of the tubular structure during and

after axial crush.

3. To develop a subroutine to distribute the extra mass according to specific

assigned COG and access the first bending and torsion natural frequencies of

the simplified model in order to maximize these frequencies with final mass

constraint.

1.4. Scope of the Study

The study involves finite element simulation of crushing the tubular structures with

different polygonal and open cross-sections, incorporating the subroutine integrated

to the post processing module, in the framework of ANSYS/LS-DYNA. The

experimental determination of COG location during deformation is not covered in

the scope. The verification of the developed modelled was carried out based on

analytical establish calculation.

1.5. The Layout of this Thesis

This thesis consists of five chapters including the introduction in Chapter 1, followed

by literature review on Chapter 2. The literature review is covered from the previous

works have been performed by many researchers on analysis of tubular structures

subjected to crushing using different approaches, including: experimental, theoretical

and FEM. The COG definition and different methods used in determining COG also

discussed in this chapter.

Chapter 3 discusses the methods used and finite element analysis procedure

involved. In addition the procedures of subroutines that added in the post-processing

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and pre-processing module of ANSYS/LS-DYNA code to calculate COG of

deformed shape and adjust the COG in specified location are also discussed. Chapter

4 presents the results and discussion of the results. Chapter 5 highlights the

contribution to new study, conclusions and recommendations for future work.

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