finite element analysis and optimisation of egg–box energy absorbing structures

213 Pages·2013·3.27 MB·English

ANGLIA RUSKIN UNIVERSITY

FINITE ELEMENT ANALYSIS AND
OPTIMISATION OF EGG–BOX
ENERGY ABSORBING STRUCTURES

MARYAM SANAEI

A Thesis in partial fulfilment of the requirements of Anglia Ruskin University for the
degree of Doctor of Philosophy

Submitted: December 2013
AKNOWLEDGMENT

On top of all, I thank God for giving me the opportunity to discover, study and grow.
I would like to present my gratitude to my supervisory team, Prof. Shirvani, Dr.
Nwaubani and Dr. Shirvani at the Faculty of Science and Technology at Anglia
Ruskin University, and Dr. Miraj at the Department of Civil and Environmental
Engineering at UCI, for their invaluable advice and support along the journey of this
research. My appreciation also goes to Cellbond Composites Ltd. for offering their
time and information to assist the initiation of this project.
I am also grateful to Prof. Mosallam at UCI for his kind consideration and guidance
and Mr. Cartillieri, Mr. Metzner, Mr. Rutz and Mr. Kim for offering their facilities
and advice as well as Mr. Becerra for his novel ideas.
I also take this opportunity to thank my family (my parents, parents in law, husband,
sister, brother and son), without whose continuous moral encouragement and
financial support, starting and completing this research would not have been
possible.

i
ii
DEDICATIONS

To my Parents;
for their infinite love, unconditional support and invaluable advice.

To my Husband;
for understanding, caring and standing by me along the way.

And last but certainly not least,

To my Sister and Brother;
for always being there and completing my life.

iii
ANGLIA RUSKIN UNIVERITY
ABSTRACT

FACULTY OF SCIENCE AND TECHNOLOGY
Doctor of Philosophy

MARYAM SANAEI
December 2013

This study investigates the mechanical and geometrical attributes of egg–box
energy absorbing structures as crash safety barriers in the automotive industry. The
research herein was originated from the earlier work of Prof. Shirvani, patented and
further investigated by Cellbond Composites Ltd. who has invested in further
research, for developing an analytical tool for geometric optimisation as an enhanced
resolution to various shapes and materials. Energy absorption in egg-box occurs
through plastic deformation of cell walls, examined through non–linear finite
element simulations using ANSYS® and ANSYS/LS–DYNA® FE packages.
Experimental dynamic crash tests have been designed to verify the validity of the FE
simulations. Geometrical models are defined as 3D graphical representations,
outlined in detail. Further, the impact behaviour of commercially pure aluminium
egg-box energy absorbers is studied to identify the optimum design parameters
describing the geometry of the structure. A simulation-based multi-objective
optimisation strategy is employed to find a set of Pareto-optimal solutions where
each solution represents a trade-off point with respect to the two conflicting
objectives: the maximum impact force and the energy absorption capacity of the
structure. The aim is to simultaneously minimise the former and maximise the latter,
in the attempt to find purpose–specific optimal egg–box geometries. In light of the
associated outcomes, it is shown that egg–box geometries with
< ω
), thin walls (t < 1mm), short inter–peak distances and small peak diameters.
M –
< ω ), thin walls (t < 1mm), lengthy inter–peak distances and
smaller peak diameters. It is concluded that, egg–box structures combined in the
form of sandwich panels can be designed per application to act as optimised energy
absorbers. Results of the proposed optimised sandwich structure are verified using
analytical techniques.
iv
CONTENTS
AKNOWLEDGMENT ................................................................................................. i
DEDICATIONS .......................................................................................................... iii
ABSTRACT ................................................................................................................ iv
CONTENTS ................................................................................................................. v
NOMENCLATURE ................................................................................................. viii
LIST OF FIGURES .................................................................................................... xi
LIST OF TABLES ................................................................................................... xvii
1. INTRODUCTION AND THEORETICAL BACKGROUND .............................. 1
1.1. Characteristics of Cellular Egg–box Energy Absorbing Structures................. 4
1.1.1. Geometrical Configuration of Egg–box ............................................. 5
1.2. Why Egg–box as an Energy Absorbing Module? ............................................ 6
1.3. Evaluation of the Performance of Egg–box Structure ..................................... 8
1.4. ANSYS® and ANSYS/LS–DYNA® as Tools for Numerical Analysis ....... 10
1.5. Aims and Objectives of the Research ............................................................ 11
1.6. Scope of the Thesis ........................................................................................ 12
1.7. Research Methodology .................................................................................. 13
1.8. Research Questions and Contribution to Knowledge .................................... 14
1.9. Thesis Outline ................................................................................................ 15
2. LITERATURE REVIEW .................................................................................... 18
2.1. Energy Absorption and Crashworthiness ....................................................... 18
2.1.1. Energy Absorbing Structures ........................................................... 19
2.1.2. Deformation Modes .......................................................................... 28
2.1.3. Experimental Testing........................................................................ 29
2.1.4. Analytical Modelling ........................................................................ 31
2.1.5. Numerical Simulation and Analysis ................................................. 33
2.2. Optimised Energy Absorption ....................................................................... 35
2.3. Optimisation of Egg–box Structures .............................................................. 38
3. EXPERIMENTAL STUDIES ............................................................................. 40
3.1. Introduction .................................................................................................... 40
3.2. Material Details and Sample Preparation....................................................... 40
3.3. Impacting System and Data Recording Devices ............................................ 43
3.4. Dynamic Impact Experiments on Egg-box Specimens.................................. 47
3.5. Results of Flat and Oblique Impact Experiments .......................................... 48
4. THEORETICAL CONSIDERATION ................................................................. 56
4.1. Introduction .................................................................................................... 56
4.2. Analytical Modelling ..................................................................................... 57
4.3. Finite Element Modelling .............................................................................. 62
4.3.1. Geometrical Model ........................................................................... 62
4.3.2. Material Properties ........................................................................... 64
4.3.3. Mesh Generation .............................................................................. 65
4.3.4. Boundary Conditions ........................................................................ 65
4.4. Verification and Critical Analysis of the Results........................................... 67
v
5. ANALYSIS AND OPTIMISATION OF MODIFIED EGG-BOX ..................... 74
5.1. Introduction .................................................................................................... 74
5.2. Geometrical Alterations ................................................................................. 74
5.3. Simulation Configurations ............................................................................. 76
5.4. Systemised Assessment ................................................................................. 77
5.4.1. Geometrical Variations at ω ....................................................... 78
5.4.2. Geometrical Variations at ω ....................................................... 83
5.4.3. Geometrical Variations at ω ....................................................... 88
5.4.4. Geometrical Variations at ω ....................................................... 93
5.4.5. Geometrical Variations at ω ....................................................... 98
5.5. Observation and Discussion of Results ........................................................ 103
5.6. Evaluation of the Effects of Geometrical Variations ................................... 106
5.7. Optimised Egg–box Structure ...................................................................... 107
5.8. Optimum Sandwich Structures .................................................................... 109
5.9. Critical Analysis of Optimised Sandwich Panel .......................................... 115
5.9.1. Case Study 1 ................................................................................... 115
5.9.2. Case Study 2 ................................................................................... 117
5.9.3. Evaluation against Optimised Sandwich Structure ........................ 118
5.10. Analytical Validation of Sandwich Panel................................................... 120
6. DISCUSSION .................................................................................................... 124
7. CONCLUSIONS ................................................................................................ 128
7.1. Recommendations for further Investigation ................................................ 132
REFERENCES ........................................................................................................ 134
BIBLIOGRAPHY .................................................................................................... 147
APPENDIX A .......................................................................................................... 162
A.1. Introduction .................................................................................................. 162
A.2. Safety Evaluation in the Automotive Industry ............................................. 162
A.3. Structural Crashworthiness and Impact Mechanics ..................................... 163
A.3.1 Quasi–static and Dynamic Loads ................................................... 165
A.3.2 Strain Rate Sensitivity .................................................................... 167
A.3.3 Inertia Effect Characteristics .......................................................... 168
A.4. Energy Absorption by Structural Collapse .................................................. 170
A.4.1. Energy Absorbed Per Unit Volume ................................................ 171
A.4.2. Energy Absorbed Per Unit Mass .................................................... 171
A.4.3. Energy Absorbed Per Unit Length ................................................. 172
A.5. Energy Absorbing Structures ....................................................................... 173
A.5.1. Egg–box Structure .......................................................................... 174
A.6. Analysis of Energy Absorbing Structures .................................................... 176
A.6.1. Experimental Methods.................................................................... 176
A.6.1.1. Static Loading of Egg–box Structures ......................................... 177
A.6.1.2. Egg–box Structures under Dynamic Impact................................ 178
A.6.2. Mathematical Approach ................................................................. 180
A.6.3. Finite Element Numerical Analysis................................................ 183
vi
A.7. Finite Element Software and Commercial Packages ................................... 185
A.7.1. ANSYS® and LS–DYNA® Numerical Analysis Packages .......... 186
A.7.2. ANSYS/LS–DYNA® Numerical Analysis Package ..................... 187
A.8. Finite Element Modelling of Energy Absorbers .......................................... 188
A.8.1. Material Models.............................................................................. 190
A.9. Structural Optimisation ................................................................................ 191
A.9.1. Optimising Energy Absorbing Structures ...................................... 192
A.9.2. Crashworthiness Optimisation of Application–specific Egg–box
Models ....................................................................................................... 194
A.9.3. Application of FEA in Structural Optimisation.............................. 195

vii
NOMENCLATURE
Abbreviation Description Units
Al Aluminium
CP Commercially Pure (99% Al Alloy)
EA Energy Absorber
FE Finite Element
KE Kinetic Energy
LCS Local Coordinate System
PE Potential Energy
ɛ Nominal Axial Strain
Strain Rate s-1
ɛ Densification Strain
D
Ө Cone Angle with Horizontal degree
ρ Density of Crushed Structure ton/mm3
ρ Density of Commercially Pure Aluminium Sheet ton/mm3
a
Ratio of Egg–box Mass to Mass of Solid Block
σ Nominal Axial Stress MPa
σ Stress due to Impact MPa
i
σ Material Yield Strength MPa
Y
ω Epical Angle (Cell Wall Angle to the Vertical) degree
A Cross Sectional Area of Impacted Structure mm2
viii
a Acceleration mm/s2
a Crush Acceleration mm/s2
crush
d Diameter at Top of Cell mm
D Base Diameter of Frusta mm
E Energy Absorber per Unite Length N.mm/mm
L
E Total Crush Energy Absorbed N.mm
total
Favg Average Value of Total Load Applied N
Fi Applied Impact Load N
g Gravitational Acceleration mm/s2
h Egg–box Cell Cone Height mm
H Egg-box Total Cell Height = 2h mm
k Geometrical Constant
m Impacting Mass kg
P Applied Load N
p Inter–peak Distance in between Egg–box Cells mm
r Fillet Radius at Wall to Peak Transition Egg–box mm
R Radius of Peak/Base Curvature mm
SEA Specific Energy Absorption N.mm/ton
t Cell Wall Thickness mm
t Total Time of Deformation s
crush
V Velocity mm/s
ix