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MENG30011 Applied Solid Mechanics
AY 2022/23 coursework assessment
This assessment is designed to test your attainment of the Intended Learning Outcomes for
MENG30011 Applied Solid Mechanics. The assessment is a single piece of coursework which carries
20 credits. The deadline for this coursework is 12:00 noon on Thursday 15th December 2022.
This coursework has three parts. In Part A, you will analyse a mechanical component design using FEA
and report on its suitability for service. In Part B you will answer questions about finite element theory.
In Part C you will answer questions about the failure of materials. The three parts contribute
separately to your overall unit mark; the weighting is Part A: 40%, Part B: 20%, Part C: 40%.
You should hand in your work via Turnitin on the unit Blackboard page. There are separate page limits
for each part. These must include all figures, references and appendices. If you exceed the page limit
for any part, your response for that part will not be accepted. You should put your responses together
and submit them as a single .pdf document without a cover sheet.
This coursework must be done individually. You may discuss the coursework with other students but
all work that you hand in, and any underlying analysis, must be entirely your own1
.
Harry Coules & Alexander Velichko, 07/10/2022
Part A: FEA Investigation and Report
Introduction
Liquified Natural Gas (LNG) carriers are tanker vessels that move LNG between major ports(see Figure
1). Natural gas is an important source of energy, and its large-scale transport allows the international
energy market to operate efficiently while reducing the need for intercontinental pipelines. For
transport by LNG carrier, natural gas is liquified by cooling in a special plant. The cold LNG is then
pumped into large tanks onboard the carrier vessel. As the vessel sails between ports, gradual
warming of the stored LNG inevitably causes some of it to boil off. To prevent a build-up of boil-off
gas from over-pressurising the tanks, it must be re-liquified or gradually released. Any released boiloff gas is either: a.) diverted to the ship’s engines, or b.) simply burned off so that only combustion
products are released into the environment, rather than the more environmentally-damaging gas
itself. LNG carriers use a large Gas Combustion Unit (GCU) to burn boil-off gas that cannot be either
consumed by the engines or re-liquified and returned to the tanks. GCU modules are constructed in a
factory and then lifted into place during fitting-out of the LNG carrier.
You are a stress analyst on the design team of a major supplier for GCUs to the marine LNG transport
industry. Your team is a part of a company project which aims to design a new low-cost type of large
GCU for bulk LNG carriers and bring it to market. The new design is almost complete, and your team
are now finalising the design of its lifting attachments. Other team members have suggested a design
for a lifting lug to support the GCU as it is lifted into place on the ship. The lugs are used during lifting
operations only: different attachments secure the GCU to the ship. The Team Leader asks you to
perform stress analysis on the part and produce a written report that the team can use to justify their
proposal to the Project Lead.
1 As in any summative assessment, all instances of suspected plagiarism will be reported to the Exam Board.
2
Figure 1: The Japanese-flagged Energy Innovator is an example of a modern LNG carrier. The GCU is installed in the blue
exhaust stack towards the stern.
Design details
The lifting lug design is designed to keep the GCU stable as it is lifted, while avoiding a set of hydraulic
control lines and instrumentation cables on the side of the unit. The lug designed by the team is shown
in Figure 2. This shape will be fabricated from S355JR structural steel of a uniform thickness and
welded to the rigid sidewall of the GCU using two welds. The integrity of the welds will be considered
by a separate team and does not need to be included in your analysis. The dimensions a, b and c shown
in Figure 2 and the thickness of material used to fabricate the lifting lug are given in Table 2 below.
a. b.
Figure 2: Proposed design of the GCU lifting lug. a.) Overall design showing loading and attachments to the GCU body. b.)
Dimensions of the lifting lug (in mm). The values of dimensions a and b can be found in Table 2.
The lifting arrangement used to install the GCU is shown in Figure 3. The GCU is roughly cylindrical and
six lifting lugs of the type shown in Figure 2 are positioned around its circumference so that the load
is shared roughly equally between them. The overall mass of the GCU is 36,000 kg. It is essential that
the GCU can be lifted safely during installation, and that the lifting lugs will not break. For lifting
equipment of this type, a typical safety factor is:
???????????????????????????????? ????????????????????????????? ???????? ????????? ????????????????????????????????????
???????????????? ???????????????????????????? ???????????????? ≈ 5
3
The breaking strength of a component is the maximum load that it will support (e.g. when tested to
destruction). The safe working load is the load below which a component is intended to be used
normally without fear of it breaking.
Table 1: Ambient-temperature mechanical properties of the structural steel which will be used for the lifting lugs (Steel, EN
10025-2 – S355JR).
Property Value
Young’s modulus 209 GPa
Poisson’s ratio 0.3
Yield strength2 355 MPa
Ultimate tensile strength 630 MPa
Elongation at failure 22%
Density 8010 kg m-3
Figure 3: Vertical lifting arrangement to be used for installing the GCU. Six lugs are spaced equally around the circumference
of the object. It can be assumed that all cables, shackles and harnesses used in the lifting operation will be appropriate for
the loads involved.
Report
You must produce a report on your analysis. This report will be delivered to the Project Lead, who will
make the final decision on whether to go ahead with this design. In your report, you should:
? Briefly outline the problem that you are aiming to solve.
? Explain and justify any analysis methods that you have used.
? Use appropriate methods to demonstrate that your stress analysis results are valid3
.
? Clearly present and interpret the results of your stress analysis.
2 Specifically, this refers to the minimum allowable 0.2% offset yield strength.
3 For example, these might include mesh sensitivity studies or comparisons to analytical solutions.
4
? Give a clear and well-justified recommendation on whether the lifting lug design is adequate
or whether there is a potential safety hazard.
Additionally, the Team Leader has asked you to include two specific pieces of information in the
report and highlight them in yellow:
? The maximum vertical deflection of the end of the lifting lug (i.e. the furthest point from the
GCU wall) that would be expected during the lifting operation.
? The maximum value of von Mises’ stress anywhere on the lug, excluding the contact region
between the lug and lifting shackle, that would be expected during the lifting operation.
You may use any format or structure for the report – there is no set template. However, it must not
exceed 4 sides of A4 and you must use 11-point font or larger. Any figures, tables, equations,
references and appendices must be included within this limit. You can assume that the Project Lead
has a good knowledge of stress analysis, FEA and mechanics of materials.
You must decide what sort of FEA to perform and what software you use. You could use Abaqus4
,
MATLAB5
, any of the FEA packages suggested in the formative coursework information, or any other
software that you want. However, in the report you must carefully explain and justify any analysis that
you have performed.
Part A report marking
Your Part A report will be marked on three criteria:
? Accuracy (30%) – The numerical accuracy of the results presented.
? Credibility (50%) – The overall persuasiveness of your report and its conclusions. This includes
the quality of the analysis and how well-justified it is, the credibility of any arguments that you
make, and how well these arguments are explained in relation to the boarder context of the
work (e.g. any existing literature).
? Presentation (20%) – The quality of presentation seen in the written report, including figures
etc. Sensible formatting and margin sizes should be used.
Each report will be marked individually. Marking will follow the University’s standard 21-point scale.
Marks for each of the criteria with be weighted and then summed together. This total mark will be
converted to an overall percentage for Part A.
4 This assessment is designed so that it can be done using the Learning Edition of Abaqus rather than the full
version if necessary. However, for practical reasons this is discouraged. Although you will not be marked down
for using Learning Edition, the fact that this version of Abaqus only supports a very limited number of nodes will
put a severe and unnecessary limitation on your model design. 5 The example MATLAB functions given on the unit Blackboard can be used and/or modified as you wish.
5
Part B: Theory of FEA
Introduction
Part B of this coursework comprises a single theory task. You should answer it using no more than
3 sides of A4 with 11-point font or larger. You may use equations and/or figures if you want to; they
are included in the page limit. You may use any layout you like for your response to Part B so long as
it is clear; there is no fixed template.
Task
Download the Part B.zip file. Extract it and then run the enclosed .p code in MATLAB using6
:
>> PartB(*my_student_code*)
replacing * my_student_code* with your own 7-digit student code. You do not need to run the
contents of the folder named Mesh2d v24; these are functions that are called by PartB.p
When you run PartB.p, you will see two figures: Figure 1 shows a 2D domain which has been
discretised using a mesh made up of Constant Strain Triangle elements. Figure 2 shows a particular
element from that mesh. The domain in Figure 1 represents a piece of isotropic linear-elastic material.
You will also see information on the material’s Young’s modulus, its Poisson’s ratio and whether it
should be considered in plane stress or plane strain.
Now answer the following questions in your Part B report:
1. How many: a.) elements, b.) nodes and c.) degrees-of-freedom does the mesh in Figure 1
have?
2. What is the stiffness matrix of the element shown in Figure 2? You do not need to show a
derivation of formulae for the stiffness matrix, but you should show your working.
3. Consider the element in Figure 2 alone. Imagine the situation where:
? Nodes 2 & 3 are restrained against movement in both the x and y directions. Node 1
remains unrestrained.
? Forces ????1???? and ????1???? are applied at Node 1 in the x and y directions. The values of these
forces per unit thickness of material are given by the MATLAB script.
What is the magnitude of the reaction force at Node 2? Show your working.
4. Consider the domain shown in Figure 1 again. If you knew:
? The distribution of mass in the domain.
? Its boundary conditions.
? That any material damping was negligible.
describe how you could find its natural frequencies of vibration. You do not need to determine
these frequencies.
Part B marking
Your response to Part B will be marked based on:
6 If this doesn’t work, you may need to add the unzipped folder to your MATLAB path by right clicking on it in
MATLAB and selecting Add to path>Selected folders and subfolders.
6
? The accuracy of your answers (primary criterion).
? Your use and explanation of methods (secondary criterion). Is an appropriate method being
used/proposed? Is any working clear and straightforwardly explained?
? Presentation (secondary criterion). Your response must be clear and legible.
Your responses will be marked individually. Marking will follow the University’s standard 21-point
scale. The mark will be converted to a percentage for Part B.
7
Part C: Failure of Materials
Introduction
You are asked to complete two research investigations, related to the structural integrity of service
systems on board the LNG carrier. To complete these tasks, you may need to perform some numerical
calculations. You can use any software (for example, you can write a program in MATLAB). You do not
need to show your code. However, you need to clearly describe all formulas and methods you are
using. During your analysis you can use any reasonable approximations. It is important to clearly
describe and justify them. You may use any layout you like for your response to Part C so long as it is
clear; there is no fixed template.
Part C questions
Question 1
One of the load-bearing structural components represents a large plate with rectangular crosssection. The material is aluminium and has a yield stress of 400 MPa, an elastic modulus of 70 GPa, a
Poisson’s ratio of 0.3 and a fracture toughness of 20 MPa √m . The plate is loaded by (unknown)
normal stresses ???????? and ???????? as shown in Figure 4. In order to measure these stresses a test is performed.
The stresses are calculated from strains, which are measured by strain gauges bonded to the plate. It
is assumed that these stresses are not sufficient to cause yielding.
Q1a. What is the smallest number of strain measurements required to determine ???????? and ?????????
Q1b. Calculate applied stresses ???????? and ???????? from strain measurements.
1) Define the orientations of the necessary strain gauges.
2) The relevant strain values can be obtained using the MATLAB function provided.
In order to ensure the structural integrity of the component during the service an additional stress ????????
must be taken into account. It is assumed the magnitude of this stress |????????| ≤ 400 MPa and its
direction is defined by the angle ???????? = 300 as shown in Fig.4. It is also assumed that a central crack of
an arbitrary orientation can be developed due to environmental and loading conditions (see Fig. 4).
The crack can be identified by ultrasonic non-destructive testing, however, the minimum detection
size is 5 mm.
Q1c. Provide analysis of the possible component’s failure mechanisms as a function of stress ???????? and
crack orientation.
You can consider the following points:
1) Analyse safety factors, corresponding to different failure mechanisms.
2) Define the range of stress ????????, which is safe for the structural integrity of the component.
3) Find the most dangerous orientation of the crack.
4) The results can be presented using diagrams, graphs, or tables.
5) Try to give a physical explanation of obtained results where it is possible.
In order to calculate strain gauge measurements for Q1b run the enclosed fn_strain.p code in MATLAB
using
>> strain = fn_strain(my_student_code,theta)
8
and replacing my_student_code with your own 7-digit student code. The variable theta is a strain
gauge orientation angle ???? in degrees (see Fig.4) and can be a scalar or vector.
Figure 4: Stressed plate containing an inclined crack with a strain gauge attached.
Question 2
The LNG carrier has a complicated pipework which is required to support its service systems. It is very
important to maintain structural integrity of the pipework, therefore, routine inspections must be
performed in certain time intervals. One section of the pipework represents a steel pipe with closed
ends, an outer diameter of D = 200 mm and a wall thickness of t = 10 mm. The pipe works in cycling
loading with internal pressure varying from zero to p = 40 MPa and back. Additionally, there is a
possibility of a valve fault which can cause a sudden short-term increase of the maximum working
pressure by a factor of 2. It is assumed that during the service a semi-circular crack can occur in a pipe
weld as shown in Figure 5. The pipe is regularly inspected, and the crack can be detected with
probability of detection described by the function ????????????????(????), where ???? is the crack radius (the function
????????????????(????) corresponds to the probability that all cracks with the radius greater than a are
detected).
The steel has a fracture toughness of KIC = 90 MPa √m. The fatigue crack growth is described by Paris’
law with constants C = 10-12 m/cycle
?MPa√m?
???? and m = 4. The geometry correction factor for the semi-circular
crack of radius a is given by:
???? = 0.728 + 0.373 ?
????
????
?
2
? 0.029 ?
????
????
?
4
, ???? ≤ ????.
Q2a. How does the pipe’s probability of failure depend on the interval between pipe inspections?
Q2b. Find the inspection interval, corresponding to the probability of failure equal to 0.01.
In order to calculate the probability of detection function ????????????????(????) run the enclosed fn_pod.p code in
MATLAB using
>> p = fn_pod(my_student_code,a)
9
replacing my_student_code with your own 7-digit student code. The variable a is a crack radius in
millimetres and can be a scalar or vector.
Tips:
1) Determine the failure mechanism first.
2) The inspection interval can be measured in terms of the number of cycles.
Figure 5: Service pipework containing a crack in the radial-circumferential plane.
Part C marking
Your responses to Part C will be marked based on:
? The correctness of your answers.
? The understanding of the methods involved.
? Presentation. Your explanations must be clear and legible.
Your responses will be marked individually. Marking will follow the University’s standard 21-point
scale. The mark will be converted to a percentage for Part C.
10
Appendix: Lifting lug dimensions for Part A
In Part A, each candidate will analyse a lug of unique design. The lug dimensions that should be used
by each candidate are given in Table 2, ordered by student code. Use your 7-digit student code to
determine the values of a, b, c and t (thickness) that you should use.
Table 2: Dimensions of the lifting lug to be considered by each candidate.
Student code a (mm) b (mm) c (mm) thickness (mm)
1531251 70 40 30 30
1800708 70 40 30 32.5
1805922 70 40 30 35
1820499 70 40 32.5 30
1839288 70 40 32.5 32.5
1839815 70 40 32.5 35
1847047 70 40 35 30
1857219 70 40 35 32.5
1859176 70 40 35 35
1900444 70 45 30 30
1901327 70 45 30 32.5
1903913 70 45 30 35
1904306 70 45 32.5 30
1904894 70 45 32.5 32.5
1904930 70 45 32.5 35
1907015 70 45 35 30
1907378 70 45 35 32.5
1909131 70 45 35 35
1913974 70 50 30 30
1914413 70 50 30 32.5
1915056 70 50 30 35
1915370 70 50 32.5 30
1915577 70 50 32.5 32.5
1915585 70 50 32.5 35
1915835 70 50 35 30
1922384 70 50 35 32.5
1929936 70 50 35 35
1932179 70 55 30 30
1932286 70 55 30 32.5
1934756 70 55 30 35
1935805 70 55 32.5 30
1936285 70 55 32.5 32.5
1936453 70 55 32.5 35
1936945 70 55 35 30
1937669 70 55 35 32.5
1937850 70 55 35 35
1938848 75 40 30 30
1940730 75 40 30 32.5
1943414 75 40 30 35
11
Student code a (mm) b (mm) c (mm) thickness (mm)
1944637 75 40 32.5 30
1946274 75 40 32.5 32.5
1958722 75 40 32.5 35
1972250 75 40 35 30
1973031 75 40 35 32.5
1973074 75 40 35 35
1974620 75 45 30 30
2000284 75 45 30 32.5
2000683 75 45 30 35
2000863 75 45 32.5 30
2002632 75 45 32.5 32.5
2002667 75 45 32.5 35
2002695 75 45 35 30
2002820 75 45 35 32.5
2003420 75 45 35 35
2003879 75 50 30 30
2003933 75 50 30 32.5
2005902 75 50 30 35
2006664 75 50 32.5 30
2006679 75 50 32.5 32.5
2006847 75 50 32.5 35
2007122 75 50 35 30
2007824 75 50 35 32.5
2008767 75 50 35 35
2008918 75 55 30 30
2008959 75 55 30 32.5
2009028 75 55 30 35
2010407 75 55 32.5 30
2010521 75 55 32.5 32.5
2010683 75 55 32.5 35
2011110 75 55 35 30
2011644 75 55 35 32.5
2011745 75 55 35 35
2011809 80 40 30 30
2011862 80 40 30 32.5
2012109 80 40 30 35
2012800 80 40 32.5 30
2012804 80 40 32.5 32.5
2012815 80 40 32.5 35
2013500 80 40 35 30
2013640 80 40 35 32.5
2014459 80 40 35 35
2014606 80 45 30 30
2015242 80 45 30 32.5
2015329 80 45 30 35
12
Student code a (mm) b (mm) c (mm) thickness (mm)
2015454 80 45 32.5 30
2016852 80 45 32.5 32.5
2016955 80 45 32.5 35
2017124 80 45 35 30
2017408 80 45 35 32.5
2017620 80 45 35 35
2017949 80 50 30 30
2017962 80 50 30 32.5
2018122 80 50 30 35
2018717 80 50 32.5 30
2022281 80 50 32.5 32.5
2022947 80 50 32.5 35
2023463 80 50 35 30
2030919 80 50 35 32.5
2031587 80 50 35 35
2032425 80 55 30 30
2034182 80 55 30 32.5
2034223 80 55 30 35
2034933 80 55 32.5 30
2039183 80 55 32.5 32.5
2039711 80 55 32.5 35
2040966 80 55 35 30
2042634 80 55 35 32.5
2042710 80 55 35 35
2043303 85 40 30 30
2043623 85 40 30 32.5
2044316 85 40 30 35
2044449 85 40 32.5 30
2044546 85 40 32.5 32.5
2046106 85 40 32.5 35
2046826 85 40 35 30
2047448 85 40 35 32.5
2047474 85 40 35 35
2048600 85 45 30 30
2049040 85 45 30 32.5
2049155 85 45 30 35
2050825 85 45 32.5 30
2050899 85 45 32.5 32.5
2051568 85 45 32.5 35
2051713 85 45 35 30
2051796 85 45 35 32.5
2051988 85 45 35 35
2052844 85 50 30 30
2054100 85 50 30 32.5
2054379 85 50 30 35
13
Student code a (mm) b (mm) c (mm) thickness (mm)
2055371 85 50 32.5 30
2055707 85 50 32.5 32.5
2055745 85 50 32.5 35
2055792 85 50 35 30
2055853 85 50 35 32.5
2059727 85 50 35 35
2059728 85 55 30 30
2059811 85 55 30 32.5
2060463 85 55 30 35
2061182 85 55 32.5 30
2062153 85 55 32.5 32.5
2063472 85 55 32.5 35
2064398 85 55 35 30
2064558 85 55 35 32.5
2064844 85 55 35 35
2065424 90 40 30 30
2065759 90 40 30 32.5
2066239 90 40 30 35
2066245 90 40 32.5 30
2067728 90 40 32.5 32.5
2068178 90 40 32.5 35
2068409 90 40 35 30
2068656 90 40 35 32.5
2071528 90 40 35 35
2074204 90 45 30 30
2074754 90 45 30 32.5
2075340 90 45 30 35
2081747 90 45 32.5 30
2087849 90 45 32.5 32.5
2090671 90 45 32.5 35
2337888 90 45 35 30
2341547 90 45 35 32.5
2342316 90 45 35 35
2343120 90 50 30 30
2343636 90 50 30 32.5
2345139 90 50 30 35
2053620 90 50 32.5 30