The load carrying unit of articulated haulers - Analysis...
Transcript of The load carrying unit of articulated haulers - Analysis...
The load carrying unit of articulated haulers -
Analysis of the welded connections
Växjö June 2009
Thesis no: TD 068/2009
Nermin Dzanic
Martin Lindholm
Metin Uçar
School of Technology and Design
School of Technology and Design, TD
II
Organisation/ Organization Författare/Author(s)
School of Technology and Design Nermin Dzanic, Martin Lindholm and Metin Uçar
Dokumenttyp/Type of document Handledare/tutor Examinator/examiner
Master Thesis Torbjörn Ekevid Anders Karlsson
Titel och undertitel/Title and subtitle
The load carrying unit of articulated haulers - Analysis of the welded connections
Sammanfattning (på svenska)
Detta examensarbete handlar om finita element analys av svetsade förband i korgen på Volvo dumpern A40E. Det genomfördes i samarbete med Volvo CE i Braås. Uppgiften var att ge företaget en lämplig lösning för att minska mängden svetsskarvar på den främre delen av lastenheten. För att uppnå detta har en rad analyser genomförts med hjälp av CATIA och ANSYS på både de befintliga och de justerade (potentiella ersättare) svetsade förbanden. Analyserna visar att utmatningshållfastheten av svetsade förband huvudsakligen beror på inbränningsdjupet. Med andra ord, förstärka svetsförband genom större inbränning är mer fördelaktigt än att använda mer svets på utsidan. Slutsatsen blev att både produktionstid och kostnad kan minskas genom justering av de svetsade förbanden. Eftersom svetsförband på lastenheten är sammankopplade bör mer omfattande studier som inkluderar alla svetsar genomföras för att uppskatta effekterna av liknande justeringar.
Nyckelord
Svetsade förband, svets, notch metoden, dumper, utmattning, Catia, Ansys, Volvo CE, Finita element metoden,
FEM, huvudspänning, 3-D modell, sub-model, mesh, simulering, analys, A40E
Abstract (in English)
The work presented in this master thesis is about the finite element analysis of the welded connections in load carrying unit of the articulated hauler, Volvo A40E. It was performed in cooperation with Volvo CE in Braås. The task was to provide the company with an appropriate solution to reduce the amount of weld used on the front part of the load carrying unit. To accomplish this, a series of analyses utilising CATIA and ANSYS was performed on both existing and adjusted (potential replacement) welded connections. The analyses brought to light the fact that the fatigue resistance of welded connections significantly depends on the penetration depth. In other words, reinforcing the welded connections by deeper penetration is more beneficial than providing support from outside through thicker weld. It was concluded that applying adjusted welds lessens both the production time and cost. Nevertheless, since the welds on the load carrying unit are correlated; more extensive studies covering all welds should be carried out to estimate the impacts of similar replacements.
Key Words
Welded connections, weld, notch method, articulated hauler, fatigue, Catia, Ansys, Volvo CE, Finite element
method, FEM, principal stress, 3-D model, sub-model, mesh, simulation, analysis, A40E
Utgivningsår/Year of issue Språk/Language Antal sidor/Number of pages
2009 English 75
Internet/WWW
III
Abstract
The work presented in this master thesis is about the finite element analysis of the welded
connections in load carrying unit of the articulated hauler, Volvo A40E. It was performed
in cooperation with Volvo CE in Braås.
The task was to provide the company with an appropriate solution to reduce the amount
of weld used on the front part of the load carrying unit. To accomplish this, a series of
analyses utilising CATIA and ANSYS was performed on both existing and adjusted
welded connections
The analyses indicate the fact that the fatigue resistance of welded connections
significantly depends on the penetration depth. In other words, reinforcing the welded
connections by deeper penetration is more beneficial than providing support from outside
through thicker weld.
It was concluded that applying adjusted welds lessens both the production time and cost.
Nevertheless, since the welds on the load carrying unit influence each other; more
extensive studies covering all welds should be carried out to estimate the impacts of
similar replacements.
IV
Preface
The work presented in this master thesis concerns finite element analyses of the welded
connections in load carrying unit of the articulated hauler, Volvo A40E. It was performed
in cooperation with Volvo CE, at the Department of Mechanical Engineering at The
School of Technology and Design, Växjö University, between April and June 2009.
We would like to express our sincere thanks to our supervisor Prof. Torbjörn Ekevid,
Volvo CE and Växjö University, for initiating and excellently supervising the work. We
would also like to thank the engineers and managers at Volvo CE for assisting us
throughout the work.
Finally, thanks to Volvo CE for making possible to perform such an extensive work.
Växjö, June 2009
V
Table of contents
Abstract ............................................................................................................................ III
Preface .............................................................................................................................. IV
Table of contents ............................................................................................................... V
List of figures ................................................................................................................ VIII
List of tables..................................................................................................................... IX
1. Introduction ............................................................................................................ 1
1.1. Background .......................................................................................................................... 1
1.2. Problem formulation ........................................................................................................... 1
1.3. Purpose and aim .................................................................................................................. 2
1.4. The outlines of the thesis ..................................................................................................... 2
1.5. Hypothesis ............................................................................................................................ 3
1.6. Limitations ........................................................................................................................... 3
1.7. Company presentation ........................................................................................................ 3
1.7.1. Volvo group ................................................................................................................. 3
1.7.2. Volvo CE Braås ............................................................................................................ 4
1.7.3. Volvo CE Braås history ................................................................................................ 4
1.8. Articulated haulers A40E ................................................................................................... 5
2. The welding process ............................................................................................... 6
2.1. Welding ................................................................................................................................ 6
2.2. Robot welding ...................................................................................................................... 7
2.3. Robot arc welding ................................................................................................................ 8
2.4. Weld dimensioning ............................................................................................................ 10
3. Fatigue calculations ............................................................................................. 12
3.1. Stress components ............................................................................................................. 12
VI
3.2. Principal stress - eigenvalue approach ............................................................................ 13
3.3. Fatigue ................................................................................................................................ 14
3.4. Fatigue damage .................................................................................................................. 17
3.5. Effective notch stress ......................................................................................................... 18
4. Finite element method ......................................................................................... 20
4.1. One-dimensional analysis ................................................................................................. 21
4.2. Three-dimensional stress analysis .................................................................................... 24
5. Software ................................................................................................................ 27
5.1. ANSYS ................................................................................................................................ 27
5.2. CATIA ................................................................................................................................ 28
6. Method .................................................................................................................. 29
6.1. Preparing the 3-D models ................................................................................................. 30
6.2. Setting up the model for analysis in ANSYS ................................................................... 33
7. Results ................................................................................................................... 38
7.1. Existing welds .................................................................................................................... 41
7.2. Adjusted welds ................................................................................................................... 44
8. Analysis of the results .......................................................................................... 47
9. Discussion and conclusions ................................................................................. 50
10. Further studies ..................................................................................................... 51
11. References ............................................................................................................. 52
11.1. Books ......................................................................................................................... 52
11.2. Articles and theses .................................................................................................... 53
11.3. Electronic sources ..................................................................................................... 53
11.4. Company related sources ......................................................................................... 54
11.5. Pictures ...................................................................................................................... 55
VII
12. Bibliography ......................................................................................................... 56
Appendices Number of pages Appendix A ..................................................................................................................................... 1
Appendix B ..................................................................................................................................... 1
Appendix C ..................................................................................................................................... 2
Appendix D ..................................................................................................................................... 3
Appendix E ..................................................................................................................................... 4
Appendix F ...................................................................................................................................... 1
Appendix G ..................................................................................................................................... 1
Appendix H ..................................................................................................................................... 6
VIII
List of figures
Figure 1: Articulated Hauler A40 ........................................................................................ 5
Figure 2: Fully automate mechanized programmable tools ................................................. 8
Figure 3: Welding torch ....................................................................................................... 9
Figure 4: Wire feeder ........................................................................................................... 9
Figure 5: Weld, a- and s-measure ...................................................................................... 10
Figure 6: Weld, a- and i-measure ....................................................................................... 10
Figure 7: Weld affected area .............................................................................................. 11
Figure 8: Stress element for three-dimensional and two-dimensional (planar) case, ........ 12
Figure 9: Normal stress 𝜎𝜎𝜎𝜎 and shear stress 𝜏𝜏𝜎𝜎 ............................................................... 13
Figure 10: Example of S-N curve ...................................................................................... 15
Figure 11: Stress notations ................................................................................................. 16
Figure 12: Applying the radius of 1 mm on the weld root and weld toe ........................... 19
Figure 13: Continuous domain (left) and group of sub-domains (right) ........................... 21
Figure 14: An axially loaded member ............................................................................... 22
Figure 15: A portion of the member with the length of dx and its axial forces ................. 22
Figure 16 : A tetrahedral element in space defined by x, y, and z coordinates. ................ 24
Figure 17: Flowchart of the structural analysis by ANSYS .............................................. 28
Figure 18: Existing (left) and adjusted (right) welds ......................................................... 29
Figure 19: The gaps between the plates ............................................................................. 30
Figure 20: Closing the gaps by extending the plates ......................................................... 31
Figure 21: Connected plates, welds, notches, and radii ..................................................... 32
Figure 22: Weld specifications .......................................................................................... 32
Figure 23: Sliced basket for z direction ............................................................................. 33
Figure 24: Sliced load for z direction ................................................................................ 34
Figure 25: Sliced load and basket for z direction .............................................................. 35
Figure 26: Boundary conditions: flexible and cylindrical supports ................................... 36
Figure 27: The sub-model for z direction .......................................................................... 37
Figure 28: The highest maximum principal stress concentration areas ............................. 38
IX
Figure 29: The hotspot for acceleration in z ...................................................................... 41
Figure 30: The hotspot for acceleration in y ...................................................................... 42
Figure 31: The hotspot for acceleration in x ...................................................................... 43
Figure 32: The hotspot for acceleration in z ...................................................................... 44
Figure 33: The hotspot for acceleration in y ...................................................................... 45
Figure 34: The hotspot for acceleration in x ...................................................................... 46
Figure 35: An example of existing welds indicating the penetration depth ...................... 48
Figure 36: An example of adjusted welds indicating the penetration depth ...................... 48
List of tables
Table 1: The absolute values of maximum and minimum principal stress ....................... 41
Table 2: The damages ........................................................................................................ 48
Table 3: The comparison of existing and adjusted welds .................................................. 50
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 1 of 56
1. Introduction
This early section of the thesis work intends to provide a sound base for readers. The rationale
behind this study, the formulation of the problem, purpose and aim, and a brief description of
the company where the study was performed are presented.
1.1. Background
The heavy vehicle industry has been a rapidly growing industry for decades. This growth has
been achieved by continuous improvements in terms of products and services provided by
companies. Volvo Construction Equipment (CE) is one of the major companies in this field
and has made extensive contributions to this growth. Regardless of being the market leader,
Volvo CE continually makes investment in development activities in order to assure that its
products have the edge over its rivals. In addition to this, it aims to make sure of contentment
of its customers in all aspects, and reduce the expenditures of development, production,
maintenance etc.
This thesis work is a part of these development activities. It comprehensively covers
production and related phases suchlike development. The major effort will be put on a number
of particular welded connections, which are located on the front part of the load carrying unit.
1.2. Problem formulation
Volvo CE in Braås develops and manufactures heavy off road vehicles used to transport large
volumes of material in terrain difficult to enter. One of their main products is Volvo
articulated hauler A40E. Since the products constantly need to be improved due to both high
competitions in the market and customer contentment, the company requests help for
conducting analyses on the both existing and adjusted (potential replacement) welded
connections of the load carrying unit, i.e. basket. The outcomes of these analyses aim at
guiding the company to choose the best type of welded connections. The task is to provide
the company with an appropriate solution to reduce the amount of weld used to connect the
metal sheets that form the basket.
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1.3. Purpose and aim
The main purpose of this thesis work is to separately analyse existing and adjusted welded
connections and then compare the outcome of both cases. This comparison is intended for
guiding the design team to determine how appropriate and beneficial the adjusted welded
connections will be. The primary objective is to strive for a proper solution and thus minimise
the amount of weld used to connect basket components, and in that sense decrease cost and
time required to produce a basket in a way that is applicable in production. Furthermore, the
design of a weld should be taken into consideration to retain or even improve the fatigue
properties. The results of this work might provide Volvo CE engineers innovative ideas to
apply and/or further examine this matter.
1.4. The outlines of the thesis
The primary aim of this study is to make practical and effective use of the theoretical
knowledge of the thesis team in a skilful manner for the intention of surmounting a real-life
problem. Particularly, to comprehend the industrial implementations of the Finite Element
Method, FEM, on solid mechanics problems using advanced modelling and Finite Element
Analysis, FEA, software suchlike CATIA and ANSYS, respectively, is of importance.
Furthermore, observing the possible impacts of altering partly or entirely design and
production activities on the life-cycle phases and total cost of the product in question, and
certainly on the company’s objectives, is of interest.
The potential forecasted results are as following: significant reduction in the amount of
welding material required for production of the basket, and consequently enabling the
company to reduce production costs and time required for production activities.
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1.5. Hypothesis
The thesis team anticipates that the problem with applied welding, more specifically overuse
of material used for welding, occurs due to the lack of analysis of load types occurring on the
basket, which leads to an excessively high estimation of requisite weld and consequently
welding material to put the basket together.
1.6. Limitations
In order to prevent the thesis to exceed the extent that it will be greater than a master thesis
covering 15 ECTS, a number of limitations were set up. Only welded connections in the front
part of the basket of the articulated hauler A40E will be examined. Likewise, no changing will
be made to the overall design of the basket. In addition to these limitations, the welding
method will not be altered from the method that Volvo CE utilises in the basket today.
1.7. Company presentation
1.7.1. Volvo group
Volvo was officially founded on 14 April 1927 when the first series-manufactured car was
produced in Gothenburg, Sweden, by Assar Gabrielsson and Gustaf Larson. Since then
company expanded into other business areas, today known as the Volvo Group. Other areas
beside Volvo cars are Volvo Trucks, Buses, Construction Equipment, Penta, Aero and
Financial Services. Already from the beginning focus was on safety, which is even today one
of the most important mark in company’s product development. Through the years,
competitors have come and gone, but Volvo Group has developed from a local industrial
company to one of the largest manufacturers. The company have more than 100 000
employees (2007) and production facilities in 19 countries with different kind of operations in
180 countries. Most employees are working in France, Japan, USA, Brazil, South Korea and
Sweden. During 2007 company’s net sales was 285 billion SEK. The Volvo Group vision is
“to be valued as the world’s leading supplier of commercial transport solutions” (Volvo
Group, 2009), (Steen, et al, 2008)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 4 of 56
1.7.2. Volvo CE Braås
Volvo CE in Braås develops and manufactures heavy off road vehicles used to transport large
volumes of material in terrain difficult to enter. The headquarters of Volvo articulated hauler
is in Braås, Sweden where assembly and manufacturing of different components are done.
The production factory in Braås has about 900 employees (2008).
The E series of Volvo articulated haulers was introduced to the market in 2007 proving their
excellence everywhere, with Volvos mission statement “We use our expertise to create
transport-related hardware and software products of superior quality, safety and
environmental care for demanding customers in selected industries” (Volvo 2009a). E series
consisting of four models (A25E, A30E, A35E and A40E) all produced in Braås. 50
articulated haulers were produced per week during 2005, and an increase in volume of 86%
was achieved during period 2001-2007. With 34% of market share Volvo CE Braås holds
market leading position (Steen et al, 2008).
1.7.3. Volvo CE Braås history
Everything started at the end of the 1950’s when the engineering company Livab in Braås
(since 1974 articulated hauler entity) began experimenting in combining driven hauler trailers
and tractors. With some problems in tractors manoeuvrability, principally with tractor’s front
wheels easily sliding in snow, the company started to develop tractor without front wheels,
with articulated steering and drive on the wheels of the load unit.
In 1966, the company presented DR631, the first and unique series-manufactured articulated
hauler with all-wheel drive that could be used in tough and difficult conditions. Since
introduction this type of machine revolutionized mass transport operation, and in the 1980’s
this type of machine had market share of over 50%. By constantly developing and introducing
larger load capacities, six-wheel drive and other innovations Volvo articulated hauler became
world market leader. Today one of Volvo CE’s star products is the articulated hauler. (Volvo
Group, 2009).
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1.8. Articulated haulers A40E
Volvo has been leading the development of articulated haulers since they first introduced the
concept of haulers in the sixties. Articulated haulers are constructed to transport rocks and
ground material in extreme conditions; this is done by means of the rotating hitch and the
frame steering, which makes the tractor and the trailer able to move independently.
The A40E is roughly 11 meters long and have a width and height of approximately 3.5
meters. An A40E has a load capacity of 39000 kg, and volume capacity of 24.0 m3 heaped.
Rising of the body takes 12 seconds when it is fully loaded and 10 seconds to lower the body.
This is done with two powerful double-acting, single-stage hoist cylinders. The specifications
of Articulated Haulers A40E in detail are presented in appendix A. (Volvo Group, 2009)
Figure 1: Articulated Hauler A40E (Volvo Group, 2009)
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2. The welding process
2.1. Welding
Welding is a joining process that connects two work-pieces, with or without added material.
The process is performed by a local heating of the parent material to its fusion temperature,
either by local yielding or atomic diffusion (Weman, 2002).
One of the first welding processes was forge welding, which has been used for centuries.
During the late 1880’s and 1890’s and until today many modern welding methods were
developed such as manual metal arc welding, MMA, metal inert/active gas welding,
MIG/MAG, including continuous wire as electrode and inert/active gas to protect the weld,
submerged arc welding, flux-cored welding (electrode including powder fill material), electro
slag welding, tungsten inert gas welding, TIG, and more modern laser and electron beam
welding. As research and development of welding methods continue, the welding robots,
mechanized programmable tools that are completely automate are becoming more and more
common (Avesta welding, 2005).
Different methods and energy sources are used for welding, such as gas welding, electrical arc
welding, pressure welding consisting of friction, ultrasound, high frequency, resistance
welding etc. Some other types of welding methods are laser welding and electron beam
welding (Weman, 2002). Welding can be performed in many different environments, and is
today most common in industrial processes. It can be very dangerous if not required
precautions are taken. Some of damages that might appear are poisonous, burns, fires,
electrical shocks, overexposure to ultraviolet light, eye damage, skin damages, heat radiations
and other type of damages.
Preventive measures at the working place to observe are as followings; working place shall be
ventilated, work piece shall have effective lagging, person that perform welding shall not take
uncomfortable working posture nor use heavy equipment, etc. (Esab, 2009).
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2.2. Robot welding
In industry, welding is the most efficient and economical way to join materials. To further
decrease cost and increase efficiency, fully automate mechanized programmable tools so
called robots were introduced, see figure 2. Robot welding is mainly used in the processes
where repetitive tasks on similar pieces are common, where the welds in more than one axis
are involved and where pieces difficult to access are present. Automating procedure would be
difficult or impossible to implement if welded joints are too wide or in different position, or
they need adjustment to fit together.
In recent decades, automating a welding process has been rapidly improved, in comparison to
manual welding by increasing the speed and quality. Once a welding robot is programmed
correctly top-notch welds are easily repeatable, hence it performs precisely the same weld
each time on the work pieces with same specifications and dimensions. A fully equipped and
optimized robot can work continuously for 24 hours a day 365 days a year without need for
any breaks. One of the big advantages is safer workplace, reducing the risk of damages by
moving operator away from unhealthy and hazardous environment. Some other important
benefits worth mentioning are greater cycle speed, precision, productivity and increase in
return on investment. (Robots, 2009 and Robot-welding, 2009)
There are two popular types of industrial welding robots; articulating and rectilinear.
Rectilinear robots are moving linearly using any of three axes x, y, and z, with wrist allowing
rotational movements. Working zone of a rectilinear robot is box shaped. On the other hand
articulated robots use arms and rotating joints, with moves similar to those of a human arm,
using rotating wrist integrated at the end. Working zone of an articulating robot is irregularly
shaped. These robot types like others need on a regular basis recalibration or reprogramming
to work properly. In order to set up a robot welding facility numerous of factors are taken into
consideration. Some of these being reliability, number of axes, maintenance, seam tracking
systems, controls, weld monitors, arc weld equipment, part transfer, fixtures etc. (Weld-
engineer, 2009)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 8 of 56
Figure 2: Fully automate mechanized programmable tools (Robot-Welding, 2009)
2.3. Robot arc welding
One of the most popular automated welding processes is the gas metal arc welding (GMAW),
more known by its subtypes as metal inert gas (MIG) and metal active gas (MAG).
Comparing to the manual, automatic arc welding involves high duty cycles and requires
equipment to operate in those conditions. Equipment components must have necessary
controls and features to interface with main control system. Also special power source is
required to perform an arc weld, where it must deliver controllable voltage and current
normally between 10 to 35 V and 5 to 500 A. Automating arc processes utilizes more
complex power source, the welding machine communicates electronically with power source
to control the welding power program for the most optimal performance.
All arc welding processes,, regardless of being automatic or manual, use torch see figure 3 to
transmit current to the electrode, where the torch also works as a shield to the weld area from
surrounding atmosphere. In robot arc welding automatic torch cleaner is used to remove the
spatter. Torch nozzle placed close to the arc gradually picks up the spatter. One of the
available systems is to spray an antispatter agent into the nozzle of the gun. There are
different types of welding torches, and choice depends on welding process, process variation,
current, electrode size and shield medium. Torches can also differ in the way they are cooled,
where water and air cooling are the most common.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 9 of 56
Figure 3: Welding torch, (Robot-Welding, 2009)
For adding filler material during robot welding so called wire feeders are used, see figure 4.
They provide continuous electrode wire into the arc. Normally the wire feeder is mounted on
the robot arm. A control interface is needed between robot controller, the power supply and
wire feeder.
Figure 4: Wire feeder, (Alabama Laser, 2009)
To guarantee that the tip and the tool frame are accurately known with respect to each other,
the calibration process of tool centre point (TCP) is important. In robot arc welding, end of
arm sensing is used to detect the position of the seam on the work piece with respect to the
robot tool frame. Profile data analysis gives the qualified position of the seam to the sensor
reference frame. "If the sensor reference frame pose is known with respect to the end-frame of
the robot, and the tool frame pose is known with respect to the end-frame, then the sensor data
may be used to accurately position the tool centre point (TCP) with respect to the work
piece". (Robot welding, 2009)
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2.4. Weld dimensioning
Figure 5 and 6 below show some general weld notation.
Figure 5: Weld, a- and s-measure (Volvo weld standard booklet, October, 2008)
Figure 6: Weld, a- and i-measure (Volvo weld standard booklet, October, 2008)
In fillet welds a-measure stands for the height of the largest isosceles triangle, between the
weld face and the fusion faces. s-measure represents the distance between the surfaces of the
part to the bottom of the penetration, and is also known as weld depth. It is the minimum
transmitting part of the weld, and cannot be greater than the thickness of the thinnest part. i-
measure stands for the minimum penetration in the gap from the surface of the parent metal.
Figure 7 shows how the work pieces change during welding process, (Volvo weld standard
booklet, October 2008).
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 11 of 56
Figure 7: Weld affected area (Volvo weld standard booklet, October, 2008)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 12 of 56
3. Fatigue calculations
3.1. Stress components
Figure 8: Stress element for three-dimensional and two-dimensional (planar) case, (Marghitu, 2001, p.121)
For the general three-dimensional stress element three positive normal stresses σx, σy and σz,
and six (acting in the positive direction of the reference axis) shear stresses τxy, τyx, τyz, τzy, τzx
and τxz are represented in figure 8. For the static equilibrium to be fulfilled following equation
is required.
,yxxy ττ = ,zyyz ττ = xzzx ττ = (3.1)
For the general two-dimensional stress element, figure 8 illustrates normal stresses σx and σy
as a positive oriented, while τyx is positive and τxy negative oriented.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 13 of 56
3.2. Principal stress - eigenvalue approach
A traction vector t is related to a surface vector with outer normal vector n such that
nSt T= (3.2)
where
=
=
z
y
x
zzzyzx
yzyyyx
xzxyxx
nnn
and nSσσσσσσσσσ
(3.3)
When the traction vector t is divided into a component parallel to n and a component in a
perpendicular direction, the normal stress, σn, and the shear stress, τn, are obtained. That is:
σnntn TTnjijiiin ornntn ==== σσσ (3.4)
and
σnmtm TTnjijiiin ornmtm ==== τστ (3.5)
Figure 9: Normal stress 𝜎𝜎𝜎𝜎 and shear stress 𝜏𝜏𝜎𝜎 , (Ottosen & Ristinmaa, 2005, p. 55)
Eq. (3.4) and (3.5) gives a physical understanding of the eigenvalue problem of the stress
tension. When solving this problem the stress invariants are obtained. If the coordinate system
is chosen by a special method, a particular simple form of the stress tension is obtained.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 14 of 56
This happens when the traction vector t is collinear with the unit vector n (see figure 9), i.e.
the direction of n should be chosen so that:
ii nt λ= (3.6)
where λ is some factor, which with Eq. (3.4) hint that λ= σn. In this situations are ni and mi
orthogonal which leads to that the shear stress τn=0. Combining Cauchy’s formula, see Eq.
(3.7), and Eq. (3.6) results in Eq. (3.8).
𝑡𝑡𝑖𝑖 = 𝜎𝜎𝑖𝑖𝑖𝑖 𝜎𝜎𝑖𝑖 𝑜𝑜𝑜𝑜 𝑡𝑡 = 𝜎𝜎𝜎𝜎 (3.7)
0)(0)( =−=− nIσ λλδσ orn jijij (3.8)
With this and the characteristic equation:
0)det( =− Iσ λ (3.9)
the three principal stresses can be obtained, i.e. σ1=λ1, σ2=λ2 and σ3=λ3. The corresponding
principal direction can be provided by Eq. (3.8).
When the coordinate system is selected collinear whit the principal directions n1, n2 and
n3,the stress tensor will take the form provided by Eq. (3.10).
[ ]321
3
2
1
000000
' nnnAAAσ =
== TT where
σσ
σσ (3.10)
The theory of this chapter was gathered from (Ottosen & Ristinmaa, 2005, p. 53-56).
3.3. Fatigue
When a material/component is exposed to repeated load cycles, it may break down even
though the stress limit has not been reached. Mattson (2005, p. 3) states that metal fatigue is a
process which gradually cases damages to a material component subjected to repeated
loading.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 15 of 56
After a number of cycles a small crack may occur in the material, this crack may then
propagate until it reaches a point where the structure will not be able to carry the load and a
failure due to fatigue will arise. Zahavi and Torbilo (1996, p. 183) declare that it is primary
the surface layer conditions that are responsive for a fatigue failure. The reason is the fact that
the most loads will be in this location, besides the surface layers are also exposed to
environmental effects. Furthermore, Gustafsson and Saarinen (2007, p. 2-5) claim that the
crack will arise in areas with high stress concentrations: these areas can be a change in the
geometry, a weld, etc. There are five major causes that may lead to a crack in a weld or in the
Heat Affected Zone, HAZ, which are undercuts, incomplete penetration, lack of fusion,
porosity and start & stop of weld.
Dahlberg and Ekberg (2002, p. 190) point out that August Wöhler carried out a search on this
matter in the middle of the 19th century. He constructed a machine where a rotated load could
carefully be controlled on various materials; subsequently he plotted the stress attribute as a
function of the number of cycles. Worth mentioning is that when this curve is plotted in a log-
log scale, a curve with straight lines will arise. The resulting plot is a, so called, S-N curve or
Wöhler curve. In this curve(s), it is clear that the higher stress yields lower number of cycles
before failure due to fatigue. During his experiments he also concluded that it is better to use
the stress range, i.e. )( minmax σσ − , in fatigue calculations, rather than maximum stress.
Figure 10: Example of S-N curve (msm, 2009)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 16 of 56
The endurance limit, or Sn, shown in figure 10 is the limit when the material can withstand
"unlimited" number of cycles; this limit is usually between 106 and 107 cycles. However not
all materials have this clear endurance limit as shown above, e.g. aluminium (Juvinalland
Marshek, 2000, p 304-309).
In most real life situations are the stresses not completely reversed, they are instead a mixture
of reversed and static stress. See figure 11 below.
Figure 11: Stress notations (Maintenance world, 2009)
where
σmax:: maximum stress
σmin: minimum stress
σa = (σmax-σmin)/2
σm = (σmax+σmin)/2
Δσ = (σmax+σmin)
R= σmin/σmax
When σm = 0 are the stresses completely reversed, and can therefore withstand the number of
cycles that correspond to Sn. Another case might be, as in figure 11, that σm>0, which means
that the specimen is exposed to tensile mean stress and results into the requirement that the
fluctuating stress must be less than Sn for "infinite life".
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 17 of 56
3.4. Fatigue damage
The stress amplitude is in the most practical cases not constant, instead they vary during a
products life time. These variations are in numerous textbooks referred to as spectrum
loading. This fact makes the direct utilization of an S-N curve, which are designed for
constant stress amplitude, unsuitable in most occasions. Instead another theory is introduced
for this kind of loading, fatigue damage. This idea take care of the total number of cycles and
the number of cycles at a certain stress amplitude, i.e. the damage at each stress amplitude are
summarize to obtain the fatigue damage for a potential failure.
Cumulative damage
As mentioned earlier, an S-N curve shows how many cycles (Ni) that are needed for a failure
due to fatigue for certain stress amplitude (Si). A smaller amount of cycles (ni), i.e. ni<Ni, will
then cause less damage, damage fraction, (di). For a failure due to fatigue to occur the sum of
all damage fractions must be greater or equal to one, see Eq. (3.11).
1... 1321 ≥++++ −idddd (3.11)
One theory for predicting the damages are the Palmgren-Miner theory that was introduced in
1924, and then further developed in 1945. This theory suggests that the damage fraction is
linear proportional to the actual number of cycles and the number of cycles needed for
generating a fatigue failure at a specific stress level, see Eq. (3.12).
∑= Nn
d i (3.12)
Combining Eq. (3.11) and (3.12) gives that failure will occur when:
∑ ≥ 1i
i
Nn
(3.13)
The theory of this chapter was gathered from Collins (1993, p 255-259).
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 18 of 56
With:
m
CNσ∆
= (3.14)
Leads to:
)log(log1)log( NCm
−=∆σ (3.15)
This after some manipulation and simplification gives following formula for the value of the
damage for the construction to withstand fatigue loading:
∑ ∑ <
∆∆
≈= 1m
allow
i
Nn
dσσ (3.16)
3.5. Effective notch stress
In welded joints, the fatigue crack initiation is expected at the notch, i.e. either the weld root
or the weld toe. The total stress at the notch is effective notch stress, ENS, which is attained
by considering linear-elastic material behaviour. An effective contour is employed instead of
the real weld contour so that the non-linear material behaviour at the notch root, and statistical
nature and scatter of weld shape parameters can be taken into account.
The ENS method is applied to welded joints which might fail from the weld root or weld toe.
The effective notch stresses can be obtained by finite element or boundary models, and
compared with a common S-N curve for carrying out fatigue assessment. To acquire accurate
results for structural steels, an effective notch root radius of r = 1 mm is recommended. The
method can also be implemented to aluminium structures.
There are some certain restrictions of the method. For instance, the stress components should
not be parallel to the weld or to the root gap, and the wall thickness should not be smaller than
5 mm (t > 5 mm). In addition, the method is not capable of handling low fatigue cycle.
Therefore, there should be more than 105 cycles (N>105).
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 19 of 56
The tip of the introduced effective notch radius touches the root of the real notch. An
example, applying 1 mm of notch radius on the weld root and weld toe, is illustrated in figure
12.
Figure 12: Applying the radius of 1 mm on the weld root and weld toe (Hobbacher, 1996, p. 29)
The method can handle advanced weld geometries and unusual welded joints. Therefore, it is
a powerful method. The theory of this chapter was gathered from (Hobbacher, 1996, p. 28-
29).
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 20 of 56
4. Finite element method
Engineering studies on physical phenomena cope with formulating physical processes,
establishing mathematical models and performing numerical analyses of mathematical
models. The mathematical formulation of physical phenomena brings forward mathematical
statements suchlike differential equations, which are of importance due to the fact that by
means of these equations physical processes and models can be comprehended. In traditional
variational methods, derivation of approximation functions is carried out with respect to the
entire region. Significant drawbacks for engineering applications can occur on account of the
fact that considering entire region may lead to inaccurate results. Therefore, a new method,
the FEM that offers approximation to the exact solution, has been developed to assist
engineers whilst seeking solutions to problems.
The FEM, unlike traditional variational methods, implements a methodical approach that
considers sub-domains instead of entire domain. The increase of computer power in recent
decades has made possible to carry out complex computations with ease, and hence greatly
contributed to the enlargement of the method. The entire method is characterised by three
basic steps:
1. A continuous geometrically complex domain is represented as a group of sub-
domains, so-called finite elements. Each element is considered as an independent
domain, and has a simple geometrical shape.
2. By utilising the concept of continuous functions that can be represented by a linear set
of algebraic polynomials, approximation functions are derived over each element.
3. In the final stage, governing equations are fulfilled over each element and then an
appropriate method is employed to establish relations among elements. Thereupon, all
sub-domains are located in the global domain, and mathematical relations among
coefficient suchlike nodal values are established.
The difference between continuous domain and sub-domains is illustrated in figure 13.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 21 of 56
Figure 13: Continuous domain (left) and group of sub-domains (right)
The theory of this chapter was gathered from (Reddy, 1993, p. 3-16) and (Martinussen, 2007,
p. 17-18).
4.1. One-dimensional analysis
The equations regulating the motion of structural elements (i.e. bars, beams, and plates) could
be constituted by considering the energy principle. In addition to this, Newton’s second law
and an element of the member with its forces could be considered to establish the governing
equations. Nevertheless, the energy principle is more appropriate for finite element modelling.
Here, the principle of virtual displacements, which is an application of Newton’s second law
and the energy principle, is employed to exemplify the procedure of the FEM for solid
mechanics applications.
First, one can consider an axially loaded bar with the length of L and the cross-sectional area
of A. The material properties of bar are independent of its position, which means that the
material of the body is homogeneous. The cross-section of the bar could be either constant or
vary along length dimension of the bar. In such case, the axial stress in the member of the bar
would be uniform. Here, the only stress component, which is nonzero, is 𝜎𝜎𝑥𝑥 = 𝜎𝜎𝑥𝑥(𝑥𝑥, 𝑡𝑡).
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 22 of 56
dx
f
x
Figure 14: An axially loaded member, (Reddy, 1993, p.124)
dx
Figure 15: A portion of the member with the length of dx and its axial forces, (Reddy, 1993, p.124)
Considering dynamic equilibrium, it is concluded that
𝜕𝜕𝜎𝜎𝑥𝑥𝜕𝜕𝑥𝑥
+ 𝑓𝑓𝑥𝑥 = 𝜌𝜌𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 (4.1)
where the cross-sectional properties of the member are not present. In order to establish the
governing equations for case at hand, all the forces along the x axis should be summed
according to Newton’s second law:
�𝐹𝐹𝑥𝑥 = 𝑚𝑚𝑚𝑚 (4.2)
which leads to
𝐴𝐴𝜎𝜎𝑥𝑥 (𝜎𝜎𝑥𝑥 + 𝑑𝑑𝜎𝜎𝑥𝑥)(𝐴𝐴 + 𝑑𝑑𝐴𝐴)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 23 of 56
−𝜎𝜎𝑥𝑥𝐴𝐴 + (𝜎𝜎𝑥𝑥 + 𝑑𝑑𝜎𝜎𝑥𝑥)(𝐴𝐴 + 𝑑𝑑𝐴𝐴) + 𝑓𝑓𝑑𝑑𝑥𝑥 = 𝜌𝜌[𝐴𝐴 + (𝐴𝐴 + 𝑑𝑑𝐴𝐴)]𝑑𝑑𝑥𝑥2𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 (4.3)
If the terms of Eq. (4.3) are divided by dx, and taking the limit of dx→0, the algebraic
expression in Eq. (4.4) is obtained.
𝜕𝜕𝜕𝜕𝑥𝑥
(𝜎𝜎𝑥𝑥𝐴𝐴) + 𝑓𝑓 = 𝜌𝜌𝐴𝐴𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 (4.4)
where the body for per unit length is denoted by f.
The typical stress-strain relation is given as
𝜀𝜀𝑥𝑥 =𝜎𝜎𝑥𝑥𝐸𝐸
(4.5)
where E denotes the modulus of elasticity. The normal strain in the direction of x is defined
by 𝜀𝜀𝑥𝑥 .
𝜎𝜎𝑥𝑥 = 𝐸𝐸𝜀𝜀𝑥𝑥 = 𝐸𝐸𝜕𝜕𝑢𝑢𝜕𝜕𝑥𝑥
(4.6)
Substituting the terms in Eq. (4.6) into Eq. (4.4) results in
𝜌𝜌𝐴𝐴𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 −
𝜕𝜕𝜕𝜕𝑥𝑥 �
𝐸𝐸𝐴𝐴𝜕𝜕𝑢𝑢𝜕𝜕𝑥𝑥�
= 𝑓𝑓(𝑥𝑥, 𝑡𝑡) (4.7)
One can rearrange this algebraic equation into Eq. (4.8) for static problems
−𝑑𝑑𝑑𝑑𝑥𝑥 �
𝐸𝐸𝐴𝐴𝜕𝜕𝑢𝑢𝜕𝜕𝑥𝑥�
= 𝑓𝑓(𝑥𝑥) (4.8)
which could be employed for determining the displacement u(x). Reddy (1993, p. 125) states
that Eq. (4.8) is derived under the assumption that all material points on the line x=constant
move by the same distance u(x). Thus, it can b e concluded that the stress concentration is
uniform at any cross-section.
The theory of this chapter was gathered from (Reddy, 1993, p. 123-125)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 24 of 56
4.2. Three-dimensional stress analysis
The general finite element procedure can be applied to three-dimensional stress analysis
problems. In fact, three-dimensional problems clearly represent all the practical cases.
Therefore, it is of importance to study this matter.
Triangle is employed as the continuum element for two-dimensional problems. However, in
three-dimensional problems, tetrahedron with four nodes is employed. Since tetrahedron
elements are utilised to represent three-dimensional problems, the total number of equations
required to solve problems can be large. Thereof, one can make use of magnitude of the
problems to overcome this difficulty. Figure 16 below illustrates a tetrahedral element i, j, m,
p.
Figure 16 : A tetrahedral element in space defined by x, y, and z coordinates (Zienkiewicz & Taylor, 2000, p. 128).
The displacement of any point on tetrahedral element can be defined by displacement
components u, v, and w.
𝐮𝐮 = �𝑢𝑢𝑣𝑣𝑤𝑤� (4.10)
In the light of the facts that a linear variation of a quantity can be defined by four nodal
values, and displacement values at the nodes can be equated, one can obtain four equations in
the form of,
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 25 of 56
𝑢𝑢𝑖𝑖 = 𝛼𝛼1 + 𝛼𝛼2𝑥𝑥𝑖𝑖 + 𝛼𝛼3𝑦𝑦𝑖𝑖 + 𝛼𝛼4𝑧𝑧𝑖𝑖 , 𝑒𝑒𝑡𝑡𝑒𝑒. (4.11)
The values of 𝛼𝛼1,𝛼𝛼2,𝛼𝛼3 and 𝛼𝛼4 can then be evaluated in terms of nodal displacements
𝑢𝑢𝑖𝑖 ,𝑢𝑢𝑖𝑖 ,𝑢𝑢𝑚𝑚 and 𝑢𝑢𝑝𝑝 .
𝑢𝑢 =1
6𝑉𝑉�(𝑚𝑚𝑖𝑖 + 𝑏𝑏𝑖𝑖𝑥𝑥 + 𝑒𝑒𝑖𝑖𝑦𝑦 + 𝑑𝑑𝑖𝑖𝑧𝑧)𝑢𝑢𝑖𝑖 + �𝑚𝑚𝑖𝑖 + 𝑏𝑏𝑖𝑖 𝑥𝑥 + 𝑒𝑒𝑖𝑖 𝑦𝑦 + 𝑑𝑑𝑖𝑖 𝑧𝑧�𝑢𝑢𝑖𝑖 +�
�(𝑚𝑚𝑚𝑚 + 𝑏𝑏𝑚𝑚𝑥𝑥 + 𝑒𝑒𝑚𝑚𝑦𝑦 + 𝑑𝑑𝑚𝑚𝑧𝑧)𝑢𝑢𝑚𝑚 + �𝑚𝑚𝑝𝑝 + 𝑏𝑏𝑝𝑝𝑥𝑥 + 𝑒𝑒𝑝𝑝𝑦𝑦 + 𝑑𝑑𝑝𝑝𝑧𝑧�𝑢𝑢𝑝𝑝� (4.12)
The volume 𝑉𝑉 of tetrahedron can now be acquired by rearranging Eq. (4.12), as stated below:
6𝑉𝑉 = 𝑑𝑑𝑒𝑒𝑡𝑡 ��
1 𝑥𝑥𝑖𝑖1 𝑥𝑥𝑖𝑖
𝑦𝑦𝑖𝑖 𝑧𝑧𝑖𝑖𝑦𝑦𝑖𝑖 𝑧𝑧𝑖𝑖
1 𝑥𝑥𝑚𝑚1 𝑥𝑥𝑝𝑝
𝑦𝑦𝑚𝑚 𝑧𝑧𝑚𝑚𝑦𝑦𝑝𝑝 𝑧𝑧𝑝𝑝
�� (4.13)
The displacement components, 𝑚𝑚𝑖𝑖 ,𝑚𝑚𝑖𝑖 ,𝑚𝑚𝑚𝑚 and 𝑚𝑚𝑝𝑝 , constituting the displacement vector 𝑚𝑚𝑒𝑒 , can
be determined with expanding relevant determinants into their cofactors. As each of the
components consists of 3 components, there are thus 12 displacement components defining
the element displacement.
𝑚𝑚𝑒𝑒 = �
𝑚𝑚𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝑝𝑝
� where 𝑚𝑚𝑖𝑖 = �𝑢𝑢𝑖𝑖𝑣𝑣𝑖𝑖𝑤𝑤𝑖𝑖� etc. (4.14)
Consequently, the displacements of an arbitrary point and the shape functions can be
expressed as in Eq. (4.15) and Eq. (4.16), respectively:
𝒖𝒖 = �𝑰𝑰𝑁𝑁𝑖𝑖 , 𝑰𝑰𝑁𝑁𝑖𝑖 , 𝑰𝑰𝑁𝑁𝑚𝑚 , 𝑰𝑰𝑁𝑁𝑝𝑝�𝒂𝒂𝑒𝑒 = 𝑵𝑵𝒂𝒂𝑒𝑒 (4.15)
𝑁𝑁𝑖𝑖 =𝑚𝑚𝑖𝑖 + 𝑏𝑏𝑖𝑖𝑥𝑥 + 𝑒𝑒𝑖𝑖𝑦𝑦 + 𝑑𝑑𝑖𝑖𝑧𝑧
6𝑉𝑉 (4.16)
where I is a 3x3 identity matrix.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 26 of 56
The total strain of a point in three-dimensional analysis can be determined in matrix form by 6
components,
𝜀𝜀 =
⎩⎪⎨
⎪⎧𝜀𝜀𝑥𝑥𝜀𝜀𝑦𝑦𝜀𝜀𝑧𝑧𝛾𝛾𝑥𝑥𝛾𝛾𝑦𝑦𝛾𝛾𝑧𝑧⎭⎪⎬
⎪⎫
(4.17)
By taking account of Eq. (4.12) and Eq. (15), one can attain the relation below,
𝜀𝜀 = 𝑆𝑆𝑁𝑁𝑚𝑚𝑒𝑒 = 𝐵𝐵𝑚𝑚𝑒𝑒 = �𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑚𝑚 ,𝐵𝐵𝑝𝑝�𝑚𝑚𝑒𝑒 (4.18)
where 𝑆𝑆 is a linear operator. The strain displacement matrix 𝐵𝐵 has 4 components 𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑚𝑚 ,
and 𝐵𝐵𝑝𝑝 .
The relation between stresses 𝝈𝝈 and strains 𝜀𝜀 can be established by the elasticity matrix 𝐷𝐷 in
the form of,
𝝈𝝈 =
⎩⎪⎨
⎪⎧𝜎𝜎𝑥𝑥𝜎𝜎𝑦𝑦𝜎𝜎𝑧𝑧𝜏𝜏𝑥𝑥𝑦𝑦𝜏𝜏𝑦𝑦𝑧𝑧𝜏𝜏𝑧𝑧𝑥𝑥 ⎭
⎪⎬
⎪⎫
= 𝐷𝐷 (𝜀𝜀 − 𝜀𝜀0) + 𝜎𝜎0 (4.19)
in which, 𝜀𝜀0 and 𝜎𝜎0 stand for initial strains and initial residual stresses, respectively. Here, the
elasticity matrix can be written in the matrix form considering modulus of elasticity 𝐸𝐸 and
Poisson’s ratio 𝑣𝑣, which are material properties. The theory of this chapter was gathered from
(Zienkiewicz & Taylor, 2000, p. 127-132).
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 27 of 56
5. Software
5.1. ANSYS
ANSYS is a comprehensive general-purpose finite element modelling software utilised to
numerically solve various problems of mechanical engineering. ANSYS is capable of
performing static, dynamic, structural (linear and nonlinear), heat transfer, fluid flow,
electromagnetism, and acoustic analyses (Moaveni, 1999).
There exist two different methods to use ANSYS. These are Graphical User Interface, GUI,
and command files. Occasionally, both methods can be cooperatively used. The GUI method
is more conventional and assists users to perform analyses by means of windows and toolbars,
whereas the second method is advantageous in terms of easy model modifications and
minimal file space requirements (Nakasone, Yoshimoto, & Stolarski, 2006).
As in the FEA, the analysis is in general done in three consecutive stages, pre-processing,
solution, and post-processing. In the course of first stage, the problem is defined, material and
geometric properties are assigned, and, if required, mesh is generated. Loads (point or
pressure) and constraints (translational and rotational) are specified, and then set of equations
are solved in the second stage. In the final, further processing, stage, nodal displacements, and
element forces and moments can be viewed (Nakasone, Yoshimoto, & Stolarski, 2006).
Figure 17 demonstrates the flow of activities of structural analysis by ANSYS.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 28 of 56
Figure 17: Flowchart of the structural analysis by ANSYS (Nakasone, Yoshimoto, & Stolarski, 2006, p.54)
5.2. CATIA
CATIA is a shortening for Computer-Aided Three-dimensional Interactive Application. It is a
3-D modelling software that is used in various industries, (e.g. automotive and industrial
equipment, architecture and construction) all over the world.
CATIA is the flagship of the company Dassault Systèmes, which have been a pioneer in this
area since the company started in 1981. In order to be able to distribute the software
worldwide, they started a partnership with IBM same year as the company where founded.
When CATIA first where developed the founders used technology that was intended for
animated 3D movies, and applied this technology to CAD systems for manufacturing
industries. This first version have since then been improved over the years. Dassault Systèmes
have in total over 100’000 customers in 80 countries. (3DS 2009a and 3DS 2009b)
END
Graphical display of results
Solution
Input boundary conditions
FE discretization of area
Input material constants
Create area
START
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 29 of 56
6. Method
As pointed out above, the purpose of this study is to examine existing weld connections, and
propose adjusted connections which are smaller in size and have deeper penetration, and then
make comparison between them. The part examined is the front part of the load carrying unit.
To fulfil this purpose, first of all the 3-D model of the load carrying unit was built up. A set of
analysis in ANSYS was then performed to obtain required stress results of the existing welds.
Once the results were obtained, numerous adjustments on the welds (according to the data
from production department at the company, see Table 3 in chapter 8) were done so that the
corresponding analyses could be carried out.
Since the load carrying unit is symmetric, it is enough to study only one half of the body. In
figure 18, the right half demonstrates the a- and s-measures of existing and adjusted welds.
The welds of interest are numbered in figure 18. The other welds are included, because they
are in contact with the welds studied.
Figure 18: Existing (left) and adjusted (right) welds
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 30 of 56
6.1. Preparing the 3-D models
The 3-D model of the load carrying unit of the articulated hauler at hand consists of a set of
sheet metal plates with different geometry. These metal plates were located in the correct
position in the global xyz coordinate system. Nevertheless, most of the plates were not in
contact. In order to set up the model for analyses, a solid model of the load carrying unit were
required. Here, it should be noted that since the actual dimensions of the load carrying unit are
fairly big, sample 3-D models below are employed to simplify the setup method of the model.
Figure 19 provides a sample 3-D model to demonstrate the gaps between the plates.
Figure 19: The gaps between the plates (Volvo CE Calculation Models Booklet, 2007)
Through the use of 3-D modelling software CATIA, the gaps between plates were closed by
means of extending them. The holes in the plates, which are utilised to assist positioning of
the plates during production, were also filled. Figure 20 exemplifies how a 3-D model can
look like after the gaps are filled.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 31 of 56
Figure 20: Closing the gaps by extending the plates (Volvo CE Calculation Models Booklet, 2007)
In reality, the plates are connected by welds with different shapes and sizes. These welds were
also included in the 3-D model. Afterwards, in order to accurately simulate the stress
distribution in welds, the notch method was introduced. This method is principally based on
removing material between welded plates. To ease the stress concentrations in the weld,
radiuses are applied on the weld toes and roots. Figure 21 illustrates a 3-D model representing
connected plates, welds, notches, and radii. The dimensions of material to be removed depend
on the weld specifications suchlike a-, s-, and i-measures. Weld specifications and radii are
illustrated in figure 22.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 32 of 56
Figure 21: Connected plates, welds, notches, and radii (Volvo CE Calculation Models Booklet, 2007)
Figure 22: Weld specifications (Volvo CE Calculation Models Booklet, 2007)
As stated earlier, the illustrated examples above provide means for comprehending the
preparation steps of the load carrying unit. The 3-D model of this study is presented in
appendix B.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 33 of 56
Since the existing and adjusted welds were examined and compared throughout this study,
two corresponding 3-D models of the load carrying unit were prepared. In the 3-D model for
adjusted welds, only the welds and notches of interest were modified.
6.2. Setting up the model for analysis in ANSYS
After completing the steps above, the 3-D models were ready for analyses in ANSYS. There
are several steps forming the FEA. Firstly, the mesh was generated to confirm that the global
model of the load carrying unit was correctly built, see appendix C. Next, three global
analysis models were created in order to perform computations in x, y, and z directions,
separately. The reason for creating three individual analysis models is to consider only one
load case at a time. Because, if all load cases are considered together, there might be
interference between different load cases, which might lead to inappropriate results.
Each model was sliced into smaller pieces so that local models, so-called sub-models, could
be built. Sliced basket for z direction is presented in figure 23 whereas corresponding x and y
can be found in appendix D.
Figure 23: Sliced basket for z direction
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 34 of 56
There are numerous ways of applying load on the basket in ANSYS. Some of them are as
following: applying pressure on a certain area, using densities to imitate load or combination
of these two. In this study, the density approach is utilised because it is simpler to accomplish
in ANSYS.
In order to establish load cases for each model, corresponding densities were calculated. The
3-D model representing the load was created with the aim of calculating the density. Load
model was then sliced into smaller pieces, local load models, using the same pattern as for the
load carrying unit. By slicing the load, weight of each piece could be calculated. The weight
of the load pieces with the same density were added to the corresponding local models of the
load carrying unit with the density of structural steel, see appendix E. Figure 24 demonstrates
sliced load for z direction whereas appendix D shows for x and y directions.
Figure 24: Sliced load for z direction
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 35 of 56
With the resulting weights and volumes for each piece of the load carrying unit,
corresponding densities were calculated. The resulting densities were then introduced in
ANSYS assuring that maximum assumed loads were applied on each sliced part of the load
carrying unit. The sliced load carrying unit and load together for z direction are presented in
figure 25. The other directions can be found in appendix D.
Figure 25: Sliced load and basket for z direction
In the following step, various constraints were applied. Load carrying unit was located on the
frame with flexible supports. The front part of the basket was supported by four springs with
stiffness of 190 kN/mm each, while only one spring with stiffness of 2,6 MN/mm supporting
the rear part, see figure 26.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 36 of 56
Figure 26: Boundary conditions: flexible and cylindrical supports
In order to attain different load cases, acceleration of 1,3 g, 1,8 g, and 2,8 g were uniformly
applied on the whole body for x, y, and z directions, respectively. These are experimental
values and were provided by the development department at the company. After that the
analysis was performed to obtain results for maximum and minimum principal stresses. To
acquire more accurate results in the area of interest, denser mesh were required. Since the size
of load carrying unit is fairly big, generating a fine mesh is not possible due to the fact that
today’s computers are not powerful enough. To overcome this dilemma, sub-models were
utilised to ease generating denser mesh. Each sub-model was isolated with the impacts from
global model maintained. There are three sub-models for established load cases. The sub-
model for z direction is presented in figure 27. For other two sub-models, see appendix F.
Cylindrical
support (peg)
Flexible
support in y
direction,
k=190
Flexible supports in z
direction, k=190 kN/mm
Flexible support in z
direction, k=2,6 MN/mm
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 37 of 56
Figure 27: The sub-model for z direction
The denser mesh had the element size of 0,8 mm for weld toe and root whereas the element
size for the rest of the sub-model was 30 mm. The analysis was then performed to locate
stress concentration areas, so-called hotspots. Once these hotspots were located, the mesh was
refined in order to perform further inspections for more accurate values in these areas. Here,
element size was 0,25 mm, see appendix G
Since there were two cases, existing and adjusted welds, to be analysed and their results were
to be compared, the procedure presented in this chapter was performed for each individual
case.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 38 of 56
7. Results
A careful examination of maximum absolute values of principal stresses of both the existing
and adjusted welded connections indicates that there is a similarity between the areas
subjected to high stress concentration.
The areas of highest stress concentrations are pointed out in figure 28. In the case of existing
welded connections, the highest stress concentration areas were on the weld roots. One of
them was in Area 1 when acceleration of 1,8 g was applied in y direction. The other two were
captured in Area 2 when acceleration of 1,3 g and 2,8 g were applied in x and z direction,
respectively.
Carrying out the same analyses for the adjusted welded connections reveals that the pattern of
high stress concentration areas was the same, see figure 28. The weld roots in Area 1 and
Area 2 were the most affected areas in the case of acceleration in y and z direction. However,
for the acceleration in x direction, the most affected area was on the weld toe in Area 2.
Figure 28: The highest maximum principal stress concentration areas
Area 1
The hotspots
B and E
Area 2
The hotspots A,
C, D, and F
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 39 of 56
As pointed out in chapter 6.2, first the stress concentration areas were located and then the
mesh was refined in these areas to obtain more accurate results. In this chapter all results
obtained during simulations are presented. Further discussion about the results can be found
in chapter 8.
Table 1 shows the maximum and minimum principal stress values for each point of interest
and the damage values calculated for these points. The damage was calculated by the
following formula.
∑ ++=
∆∆
= zyx
m
allow
ddddσσ (7.1)
where m is 3 for welds representing the slope of Wöhler curve. The maximum allowable
stress is 368 MPa for welds and represented by allowσ .
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 40 of 56
Existing welded connections Adjusted welded connections
The principal stress values
in the acceleration of Z direction (MPa)
The principal stress values
in the acceleration of Z direction (MPa)
A
Minimum Maximum
D
Minimum Maximum
Z-direction 138 18 Z-direction 109 23
Y-direction 8 133 Y-direction 1 120
X-direction 156 5 X-direction 152 10
Damage d = 0,176 Damage d = 0,131
The principal stress values
in the acceleration of Y direction (MPa)
The principal stress values
in the acceleration of Y direction (MPa)
B
Minimum Maximum
E
Minimum Maximum
Z-direction 98 3 Z-direction 66 2
Y-direction 20 191 Y-direction 24 160
X-direction 2 72 X-direction 2 62
Damage d = 0,166 Damage d = 0,093
The principal stress values
in the acceleration of X direction (MPa)
The principal stress values
in the acceleration of X direction (MPa)
C
Minimum Maximum
F
Minimum Maximum
Z-direction 113 4 Z-direction 117 1
Y-direction 4 127 Y-direction 3 133
X-direction 210 75 X-direction 213 14
Damage d = 0,256 Damage d = 0,273
Table 1: The absolute values of maximum and minimum principal stress
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 41 of 56
7.1. Existing welds
The hotspot A
The maximum absolute value of the principal stress for acceleration in z direction was 138
MPa (see figure 29), whereas the following results for x and y directions in the same point
were 156 MPa and 133 MPa, respectively. See appendix H for other figures.
Figure 29: The hotspot for acceleration in z
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 42 of 56
The hotspot B
The maximum absolute value of the principal stress for acceleration in y direction was 191
MPa (see figure 30), whereas the following results for x and z directions in the same point
were 72 MPa and 98 MPa, respectively. See appendix H for other figures.
Figure 30: The hotspot for acceleration in y
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 43 of 56
The hotspot C
The maximum absolute value of the principal stress for acceleration in x direction was 210
MPa (see figure 31), whereas the following results for y and z directions in the same point
were 127 MPa and 113 MPa, respectively. See appendix H for other figures.
Figure 31: The hotspot for acceleration in x
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 44 of 56
7.2. Adjusted welds
The hotspot D
The maximum absolute value of the principal stress for acceleration in z direction was 109
MPa (see figure 32), whereas the following results for x and y directions in the same point
were 152 MPa and 120 MPa, respectively. See appendix H for other figures.
Figure 32: The hotspot for acceleration in z
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 45 of 56
The hotspot E
The maximum absolute value of the principal stress for acceleration in y direction was 160
MPa (see figure 33), whereas the following results for x and z directions in the same point
were 62 MPa and 66 MPa, respectively. See appendix H for other figures.
Figure 33: The hotspot for acceleration in y
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 46 of 56
The hotspot F
The maximum absolute value of the principal stress for acceleration in x direction was 213
MPa (see figure 34), whereas the following results for y and z directions in the same point
were 133 MPa and 117 MPa, respectively. See appendix H for other figures.
Figure 34: The hotspot for acceleration in x
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 47 of 56
8. Analysis of the results
Once the hotspot for acceleration in a particular direction, for instance x direction, was
captured, the same point was examined in the other two directions to determine the principal
stress values that are to be employed in damage calculations. The underlying reason behind
taking into account the same point in the other two directions is to assure that the impact of
the individual load cases on the same point is considered. The same procedure was repeated
for all directions.
The maximum absolute values of principal stresses obtained by the procedure explained
above were utilised for damage calculations. Consequently, the three damage values for each
case were obtained, see table 2.
Existing Adjusted
z 0,176 0,131
y 0,166 0,093
x 0,256 0,273
Table 2: The damages
For the welded connections at hand, the damage values should be lower than one for the
structure to withstand the fatigue loading. As seen in table 2, the damage values satisfy this
criterion. The damage values for adjusted welded connections are even smaller compared to
the existing ones. It should be noted that the damage in the direction of x for adjusted welded
connections is bigger than existing one. This is because even though highest stress
concentration area, Area 2 as pointed out in figure 28 was the same for both cases; the weld
toe was affected for the adjusted welded connections while the weld root was affected in
existing case.
These results suggest that the penetration depth plays a crucial role in making welded
structures stronger against fatigue loading. It can be concluded that supporting welded
connections from inside, i.e. penetration, rather than outside leads to better fatigue resistance.
Figure 35 and 36 illustrate the difference between penetration depths of existing and adjusted
welds.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 48 of 56
Weld
Notch
Radius
s6 = 6mm
a5 = 5mms6a5 means 1 mm of
penetration (i1)
Penetration i1
Figure 35: An example of existing welds indicating the penetration depth
Weld
Radius
s5 = 5mm
a3 = 3mm
s5a3 means 2 mm of penetration (i2)
i2NotchPenetration
Figure 36: An example of adjusted welds indicating the penetration depth
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 49 of 56
As the damage results indicate, it is possible to replace the existing welds with the adjusted
ones with respect to fatigue. Table 3 represents a comparison between the existing and
adjusted welds in terms of time. By implementing the improved welds, in total 1,09 minutes
of operational time for welding can be saved per unit.
Existing Welds Adjusted Welds
Weld
position
Length
(m)
Weld
specification
Welding time
(min.)
Weld
specification
Welding time
(min.)
Time Saved
(min)
1 0,5 s6a5 0,9 s5a3 0,67 0,23
2 0,5 s6a5 0,9 s5a3 0,67 0,23
3 1,25 s6a5 2,3 s6a3 1,67 0,63
Total 1,09
Table 3: The comparison of existing and adjusted welds
The welding operation of the front part costs 1242 SEK per hour. With reduction of 1,09
minutes, approximately the cost of 23 SEK per unit can be saved.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 50 of 56
9. Discussion and conclusions
This thesis work was initially limited to analyse the welds in the front part of the load carrying
unit. Nevertheless, as the work progressed, it was discovered that carrying out required
analyses for every weld would exceed the time set for the work, approximately ten weeks.
Therefore, the focus was put upon only three particular welds instead. Since the analysis
procedure applied can be implemented on other welds, the created 3-D models, and the
analysis routine developed in ANYS can be used as a base and modified for analysing the
other welds in the load carrying unit.
As it was predicted earlier, the overuse of welding material occurs due to the excessive
estimation of the forces that the load carrying unit are subjected to. This conclusion can easily
be drawn, if the outcome of the analyses of existing and adjusted welds is compared. In detail,
there were mainly two areas where the highest fatigue damage occurs. However, detailed
inspections of these areas indicate that the damage potential is much smaller than the
requirement, d<1. This was the case for both the existing and adjusted welds. Besides,
evaluating the fatigue damages of both cases reveals that implementing adjusted welds would
not cause any problem with respect to fatigue, see table 2.
Applying the adjusted welds in production results in 1,09 minutes of time reduction, which
leads to 23 SEK decrease in cost per unit. Though these outcomes may seem insignificant,
their significance of these numbers would be obvious if long term and large production
volumes are considered.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 51 of 56
10. Further studies
In this thesis work only one part of the load carrying unit was examined, which is the result of
lack of time to perform a more extensive research. To get a better understanding how the
welds in the basket are subjected to fatigue, more studies should be done covering all of them.
To be able to make the changes on the welds in the load carrying unit, more load cases should
be established, covering most of the situations that may arise in reality. This would assure that
the basket would withstand the employment over its entire lifetime.
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 52 of 56
11. References
11.1. Books
Zahavi, Eliahu & Torbilo, Vladimir. 1996. Fatigue Design – Life Expectancy of Machine
parts. USA. CRC Press
Dahlberg, Tore & Ekberg, Anders. 2002. Failure Fracture Fatigue – An Introduction.
Lund. Studentlitteratur
Juvinall, Robert C. & Marshek, Kurt M. 2000. Fundamentals of Machine Component
Design. John Wiley & Sons, USA
Moaveni, Saeed .1999. Finite Element Analysis-Theory and Application with ANSYS.
Prentice-Hall
Nakasone, Y., Yoshimoto, S., & Stolarski, T. 2006. Engineering Analysis with ANSYS
Software. Elsevier Butterworth-Heinemann
Reddy, J. N. 1993. An Introduction to the Finite Element Method. McGraw-Hill
Zienkiewicz, O. C., & Taylor, R. L. 2000. The Finite Element Method (5th Edition upp1.,
Vol.I: The Basis). Butterworth-Heinemann
Weman, Klas. 2002. Karlebo-Svetshandbok. Liber.
Engfeldt, Jan. 2005. Avesta Welding Manual.Avesta
Marghitu, Dan B. 2001. Mechanical Engineer's Handbook. Academic Press Series in
Engineering. San Diego, CA: Academic Press. Department of Mechanical Engineering,
Auburn University, Auburn Alabama
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 53 of 56
Collins, Jack A. 1993. Failure of Materials In Mechanical Design – Analysis, prediction,
prevention. Canada. JohnWiley & Sons, Second Edition
Hobbacher, A. 1996. Fatigue Design of Welded Joints and Components:
Recommendations of IIW Joint Working Group XIII-XV. Woodhead Publishing
Ottosen, Niels Saabye & Ristinmaa, Matti. 2005. The Mechanics of Constitutive
Modelling. (1st Edition). Elsevier. Division of Solid Mechanics. Lund University
11.2. Articles and theses
Steen, J. & Bartsch, S. 2008. Master thesis, School of Management and Economics, Växjö
University -Internal Material Handling At Volvo Construction Equipment Braås.
Mattson, Henrik. 2005. Evaluation of Fatigue Procedures for Welds and Rotating axes.
Luleå
Gustafsson, Johannes & Saarinen, Juha. 2007. Multi-axial fatigue in welded details – An
investigation of existing design approach. Göteborg
Martinussen, M. 2007. Numerical Modelling and Model Reduction of Heat Flow in
Robotic Welding. Norwegian University of Science and Technology – Department of
Engineering Cybernetics. Trondheim. Norway
11.3. Electronic sources
Volvo Group 2009
http://www.volvogroup.com (accessed on 2009.03.07)
Volvo 2009a
http://www.volvo.com/group/global/en-gb/volvo+group/mission_vision/our_mission.htm
(accessed on 2009.03.07)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 54 of 56
Volvo 2009b http://www.volvo.com/constructionequipment/global/engb/AboutUs/history/history+track
/1966/introduction.htm (accessed on 2009.03.07)
Volvo 2009c
http://www.volvo.com/constructionequipment/global/engb/products/articulatedhaulers/intr
oduction.htm (accessed on 2009.03.07)
Volvo 2009d
http://volvo.com/dealers/sv-se/Swecon/products/articulatedhaulers/A40E/introduction.htm
(accessed on 2009.03.07)
Esab 2009
www.esab.se (accessed on 09.03.05)
3DS 2009a
http://www.3ds.com/fileadmin/PRODUCTS/CATIA/PDF/CATIAbd.pdf
(Accessed on 09.05.28)
3DS 2009b
http://www.3ds.com/se/plm-glossary/(Accessed on 09.05.28)
Robots 2009
www.robots.com (Accessed on 09.05.24)
Robot-welding 2009
www.robot-welding.com, 2009 (Accessed on 09.05.24)
Weld-engineer 2009
www.weldengineer.com, 2009 (Accessed on 09.05.24)
11.4. Company related sources
Volvo weld standard booklet, October, 2008
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 55 of 56
11.5. Pictures
Figure 1: http://www.volvogroup.com (accessed on 2009.03.06)
Figure 2 & 3: www.robot-welding.com, 2009 (Accessed on 09.05.24)
Figure 4: www.alspi.com/wirefeed.htm (accessed on 09.05.24)
Figure 5-7: Volvo weld standard booklet, October, 2008
Figure 8: Marghitu, Dan B. 2001. Mechanical Engineer's Handbook. Academic Press
Figure 9: Ottosen, Niels Saabye & Ristinmaa, Matti. 2005. The Mechanics of Constitutive
Modelling. (1st Edition). Elsevier. Division of Solid Mechanics. Lund University
Figure 10: http://www.msm.cam.ac.uk/phasetrans/2006/SI/8.jpg (accessed on 2009.05.29)
Figure 11: http://www.maintenanceworld.com/Articles/material-engineering/Fatigue-
Failures/stress.jpg (accessed on 2009.05.29)
Figure 12: Hobbacher, A. 1996. Fatigue Design of Welded Joints and Components:
Recommendations of IIW Joint Working Group XIII-XV. Woodhead Publishing
Figure 14 & 15: Reddy, J. N. 1993. An Introduction to the Finite Element Method.
McGraw-Hill
Figure 16: Zienkiewicz, O. C., & Taylor, R. L. 200. The Finite Element Method (5th
Edition. Vol.I: The Basis). Butterworth-Heinemann
Figure 17: Nakasone, Y., Yoshimoto, S., & Stolarski, T. 2006. Engineering Analysis with
ANSYS Software. Elsevier Butterworth-Heinemann
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 56 of 56
Figure 19-22: Volvo CE Calculation Models Booklet, 2007
12. Bibliography
Rao, Singiresu S. 1999. The Finite Element Method in Engineering. Butterworth-
Heinemann
Ellyin, Fernand. 1997. Fatigue Damage, Crack Growth and Life Prediction.
Chapman&Hall
Cook, Robert D. 1995. Finite Element Modelling for Stress Analysis. John Wiley&Sons
Martinsson, Johan. 2005. Fatigue Assessment of Complex Welded Steel Structures. Royal
Institute of Technology-Department Aeronautical and Vehicle Engineering
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar A1
Appendix A
Figure A.1: Volvo articulated hauler A40E specifications (Volvo, 2009d)
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar B1
Appendix B
Figure B.1: The 3-D model of the load carrying unit
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar C1
Appendix C
Figure C.1: Generated mesh for load case z
Figure C.2: Generated mesh for load case y
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar C2
Figure C.3: Generated mesh for load case x
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar D1
Appendix D Sliced basket
Figure D.1: Sliced basket in x direction
Figure D.2: Sliced basket in y direction
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar D2
Sliced load
Figure D.3: Sliced load for x direction
Figure D.4: Sliced load for y direction
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar D3
Sliced basket and load
Figure D.5: Sliced basket and load for x direction
Figure D.6: Sliced basket and load for y direction
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar E1
Appendix E Since the left and right parts of the basket are symmetric, only one half was used during
analysis and calculations. Therefore the max basket load and the volume were divided by two.
Max basket load: m=39000/2=19500 kg
Basket volume: V=18,85/2=9,425 m3
Load density: 33 /2069
425,919500 mkg
mkg
volumemass
==
=ϕ
Load case 1: Z-direction
Sliced load parts: L [kg] Load density: φ=2069 kg/m3
L11 96,76 L21 299,31 L31 520,37
L12 965,54 L22 3384 L32 7232,8
L13 311,46 L23 1090,8 L33 2115,7
L14 374,4 L24 1183,1 L34 1923,9
Sliced basket parts (steel): B1 [kg] Steel density: φ=7850 kg/m3
B111 87,67 B121 84,42 B131 176,17
B112 443,15 B122 210,22 B132 365,62
B113 147,85 B123 69,6 B133 197,29
B114 243,39 B124 119,35 B134 241,83
Adding load L to corresponding B1 resulting in B2 [kg]
B211 184,44 B221 383,73 B231 696,54
B212 1408,69 B222 3594,22 B232 7598,42
B213 459,31 B223 1160,4 B233 2312,99
B214 617,79 B224 1302,45 B234 2165,73
Sliced basket parts volume: B3 [m3]
B311 1,12E-02 B321 1,08E-02 B331 2,24E-02
B312 5,65E-02 B322 2,68E-02 B332 4,66E-02
B313 1,88E-02 B323 8,87E-03 B333 2,51E-02
B314 3,10E-02 B324 1,52E-02 B334 3,08E-02
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar E2
New densities computed for each sliced part of the basket representing different materials.
Computed densities are to be used during analysis in ANSYS.
43
23 B
BB
mkg
volumemass
==
=ϕ
B411 1,12E-02 B421 1,08E-02 B431 2,24E-02
B412 5,65E-02 B422 2,68E-02 B432 4,66E-02
B413 1,88E-02 B423 8,87E-03 B433 2,51E-02
B414 3,10E-02 B424 1,52E-02 B434 3,08E-02
Load case 2: Y-direction
Sliced load parts: L [kg] Load density: φ=2069 kg/m3
L11 214,16 L21 296,63 L31 354,94 L41 50,71
L12 1979,4 L22 3071,9 L32 4776,4 L42 1754,7
L13 611,44 L23 979,36 L33 1534 L43 393,18
L14 697,93 L24 1165,9 L34 1489,2 L44 128,44
Sliced basket parts (steel): C1 [kg] Steel density: φ=7850 kg/m3
C111 111,43 C121 72,22 C131 97,39 C141 67,22
C112 399,12 C122 119,73 C132 180,05 C142 319,2
C113 132,55 C123 38,62 C133 77,7 C143 165,86
C114 189,72 C124 110 C134 209,89 C144 94,94
Adding load L to corresponding C1 resulting in C2 [kg]
C211 325,59 C221 368,85 C231 452,33 C241 117,93
C212 2378,52 C222 3191,63 C232 4956,45 C242 2073,9
C213 743,99 C223 1017,98 C233 1611,7 C243 559,04
C214 887,65 C224 1275,9 C234 1699,09 C244 223,38
Sliced basket parts volume: C3 [m3]
C311 0,014195 C321 0,0092 C331 0,012406 C341 0,008563
C312 0,050844 C322 0,015252 C332 0,022936 C342 0,040663
C313 0,016885 C323 0,00492 C333 0,009898 C343 0,021129
C314 0,024168 C324 0,014013 C334 0,026738 C344 0,012094
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar E3
New densities computed for each sliced part of the basket representing different materials.
Comuted densities are to be used during analysis in ANSYS.
43
23 C
CC
mkg
volumemass
==
=ϕ
C411 22936,95 C421 40091,63 C431 36460,5 C441 13772,44
C412 46780,74 C422 209259,8 C432 216099,2 C442 51002,14
C413 44062,19 C423 206902,9 C433 162826,1 C443 26458,42
C414 36728,32 C424 91051,17 C434 63545,89 C444 18470,32
Load case 3: X-direction
Sliced load parts: L [kg] Load density: φ=2069 kg/m3
L11 15,93 L21 46,88 L31 65,66
L12 135,99 L22 459,85 L32 645,67
L13 198,68 L23 946,6 L33 1598,9
L14 975,61 L24 4925,9 L34 9482,5
Sliced basket parts (steel): A1 [kg] Steel density: φ=7850 kg/m3
A111 27,829 A121 30,72 A131 38,35
A112 87,19 A122 37,3 A132 45,17
A113 113,42 A123 61,95 A133 99,95
A114 646,1 A124 403,83 A134 805,93
Adding load L to corresponding A1 resulting in A2 [kg]
A211 43,76 A221 77,6 A231 104,01
A212 223,18 A222 497,15 A232 690,84
A213 312,1 A223 1008,55 A233 1698,85
A214 1621,71 A224 5329,73 A234 10288,43
Sliced basket parts volume: A3 [m3]
A311 0,003545 A321 0,003913 A331 0,004886
A312 0,011106 A322 0,004751 A332 0,005754
A313 0,014448 A323 0,007891 A333 0,012733
A314 0,082306 A324 0,051444 A334 0,10267
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar E4
New densities computed for each sliced part of the basket representing different materials.
Computed densities are to be used during analysis in ANSYS.
43
23 A
AA
mkg
volumemass
==
=ϕ
A411 12343,23 A421 19829,05 A431 21289,04
A412 20095,08 A422 104636,1 A432 120056,5
A413 21601,61 A423 127806,4 A433 133421,4
A414 19703,42 A424 103602,6 A434 100208,7
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar F1
Appendix F
Figure F.1: The sub-model for x direction
Figure F.2: The sub-model for y direction
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar G1
Appendix G
Figure G.1: The generated mesh with different element sizes
Figure G.2: The denser mesh
The element size
of mesh is 30 mm
for the rest of the
model.
Denser mesh
with the element
size of 0,25 mm
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar H1
Appendix H Existing welds - z acceleration
Figure H.1: The same point for acceleration in x
Figure H.2: The same point for acceleration in y
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar H2
Existing welds - y acceleration
Figure H.3: The same point for acceleration in x
Figure H.4:The same point for acceleration in z
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar H3
Existing welds – x acceleration
Figure H.5: The same point for acceleration in y
Figure H.6: The same point for acceleration in z
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar H4
Adjusted welds – z acceleration
Figure H.7: The same point for acceleration in x
Figure H.8: The same point for acceleration in y
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar H5
Adjusted welds – y acceleration
Figure H.9: The same point for acceleration in x
Figure H.10: The same point for acceleration in z
Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar H6
Adjusted welds – x acceleration
Figure H.11: The same point for acceleration in y
Figure H.12: The same point for acceleration in z
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