Usama Abdul Matin
FEA Report
BEng Mechanical Engineering
ME2502 - Engineering For Industry
STATIC FINITE ELEMENT ANALYSIS OF AN E-CARGO BIKE
FRAME FOR TAXI PURPOSES
Usama Abdul Matin
332968
abdulmau@aston.ac.uk
To the attention of: ME2502 (2021) Supervisors and Lecturers
SUMMARY
A static finite element analysis of the e-cargo bike frame, to be manufactured with 6082 aluminium and designed by
Group 25 was undertaken in Solidworks 2019 for a load case investigating the ability to transport two adults and a
young child as part of a taxi service in the 500 litres of cargo provided. The analysis has been made to assess the
structural strength of the frame and to ensure it is suitable for manufacturing, thereby ensuring its reliability. The
results which were achieved for a total of 81.3k elements, with 95.4% having an aspect ratio lesser than 3, showed up
a factor of safety greater than the intended value of 2.6 throughout the entire frame (with the extra margin of error
taken as a precautionary measure for enhanced fatigue life). Thus it can be proven that the frame design is fit for its
purpose and even though refinements in design or alternatives in material may be considered to reduce the cost and
weight, the only recommendations that should be made are:
a) Investigate the stress singularity identified at the rear end of the design (results neglected in this instance).
b) Additional load cases, should a wider range of operations be intended, should be tackled as appropriate.
c)
An estimate of fatigue life through SolidWorks could be undertaken
This report is accompanied with the associated SolidWorks 2019 file:
2.FEA_Group_25_AbdulMatin_Usama_332968
17/03/2021
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FEA Report
TABLE OF CONTENTS
TABLE OF FIGURES
2
Table of tables
2
NOMENCLATURE
2
1. INTRODUCTION
3
2. DESIGN AND ANALYSIS
3
2.1 Cargo Bike Design and Material
3
2.2 Finite Element Analysis Setup
3
2.3 Meshing and Convergence Study
4
3. RESULTS AND RECOMMENDATIONS
4
3.1 Results
4
3.2 Recommendations
5
4. CONCLUSION
5
5. REFERENCES
6
TABLE OF FIGURES
Figure 1: (a) the design of the cargo bike and (b): simplified frame model (Group 25, 2021)
3
Figure 2: FEA setup with fixtures and loads applied to the simplified frame
4
Figure 3: Convergence study for the Von Mises stress and displacement
4
Figure 4: Overall Von Mises results
5
Figure 5: (a) Results for the displacement and (b): factor of safety greater than 2.6.
5
TABLE OF TABLES
Table 1: Main specifications, retrieved from Group 25, 2021
NOMENCLATURE
h - Number of elements
s - Global average element size (mm)
AR - Aspect Ratio
FEA - Finite Element Analysis
LCG - Longitudinal Centre of Gravity
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FEA Report
1. INTRODUCTION
The need for taxi services via electric vehicles have increased at a fantastical rate since 2019, clocking in at an increase
of 25% each year, seeing a particular increase over the covid-19 lockdown during 2020 (Gregson, 2021). Following the
design of a new generation of e-cargo bikes with extra focus placed on the frame, as introduced in Section 2.1, the finite
element analysis setup and convergence study can be obtained in Section 2.2 and 2.3 respectively, which aims to assess
the suitability for having a taxi service carrying two adults and a young child. Lastly, the results of the structural
assessment and recommendations will be presented in Section 3.1 and 3.2, before drawing conclusions in Section 4.
2. DESIGN AND ANALYSIS
2.1 CARGO BIKE DESIGN AND MATERIAL
The design presented in Figure 1 (a) (Group 25, 2021) is aimed at providing a frame that is both minimal in design and
has reductions in both weight and cost (materials as well as manufacturing); the main specifications being listed in
Table 1. For the purpose of the finite element analysis (FEA), a simplified frame was modelled (Group 25, 2021), which
shows the primary structural members that contribute to the strength of the frame but for ease of purpose has the finer
details and the non-structural components removed. This allows for a faster solving time, also pointing to the notion that
the potential contribution of the suppressed elements to the overall structural strengths is neglected. 6082 aluminium
was chosen as the designated alloy of choice for Group 25 with consideration of many factors including yield strength
and affordability being taken into account.
Figure 1: (a) the design of the
cargo bike
Figure 1: (b) simplified frame model
(Group 25, 2021)
Table 1: Main
Specifications
2.2 FINITE ELEMENT ANALYSIS SETUP
A static analysis of the frame was undertaken in SolidWorks 2019 (Dassault Systemes, 2019) to model a specific load
case, namely the bike being used to carry two adults and a young child as part of a taxi service for the total cargo
volume available. The FEA setup, as can be seen in Figure 2, features a rack with two fixtures and is able to carry the
three loads stated:
- A 100kg rider, approximated as 1000N, applied to the seat post. The figure used is in compliance with the ISO 15194
(International Organisation for Standardisation, 2017), and makes sure it can be ridden by most riders since it
comfortably exceeds that of the 50th percentile for adult American men (Fryer, et al, 2012).
- A 25.41kg bike, approximated as 410N, the mass being derived from the original design of the bike (Group 25, 2021)
and being applied at the approximate longitudinal centre of gravity (Group 25, 2021). This comes from the
assumption that in beam theory the distributed load can be assumed to be a point load acting on a specific point i.e.
the centre of gravity (Budynas & Young, 1938).
- 228kg of cargo, approximated at 2300N (the load evenly distributed along the frame), corresponding to the average
weight of two adults and a young child in the 500L cargo volume. The weight of an adult male is taken as 84kg
(Centers for Disease Control and Prevention, 2018) and the weight of a 16 year old child is taken as 60kg
(OnAverage). The load of these individuals is then assumed to be spread evenly and laterally along the frame. It is
assumed that their combined weight is spread along the bottom of the frame with the head support assumed to be not
carrying any of the load.
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FEA Report
Rider 1000N
Fixed points
Cargo 2300N
Figure 2: FEA setup with fixtures and loads applied
to the simplified frame
2.3 MESHING AND CONVERGENCE STUDY
A standard mesh with automatic transition was created, with the entire frame besides the rack having a global average
element size (s) of 10.52mm while the rack was meshed at a finer 4mm, for a total of 81.3k elements (h) where it was
found that 95.4% had an aspect ratio (AR) lesser than 3, an indicator that a suitable mesh was indeed chosen
(AbdulMatin, 2021). A convergence study was then undertaken from a slightly coarser mesh than the one used
(s=11mm; h=91737) to a finer mesh of 7mm, to demonstrate that converge had indeed been reached and thus
confirming the FEA outputs had been accurate. The results then yielded a good convergence for the displacement, as
can be seen in Figure 3. There seems to be an outlier in both the displacement and Von Mises for the 9mm meshing, the
reasons for which is further discussed in Section 3.1, did not allow for a fully satisfactory convergence result, although
the fact that the other points seem to be following a trend and the AR being less than 3 for 95.4% allows for being fairly
confident in the accuracy of the results.
Figure 3: Convergence Study for the Von Mises stress
and displacement
3. RESULTS AND RECOMMENDATIONS
3.1 RESULTS
As noted above, there seems to be an outlier in the results in the 9mm meshing of the frame. This may have
been caused due to the mesh not being setup correctly, the results being recorded wrong or simple human
error. The error is depicted in Figure 3 while the overall Von Mises stress is in Figure 4.
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Figure 4: Overall Von Mises results
From the results that are shown in Figure 5(a), the displacements seem to be as expected, there is no
deflection towards the rear end of the frame and it gradually increases as it nears the unsupported seat,
culminating in a maximum reading where the rider is located, and yielded sensible and converging results.
Figure 5(b) has then been placed to demonstrate how compliant the bike frame with the desired factor of
safety (2.6) and it points to the conclusion that the design is indeed suitable.
Figure 5(a): Results for the
displacement
Figure 5(b): Factor of safety greater than 2.6
3.2 RECOMMENDATIONS
The frame complies with the factor of safety target of 2.6 across the whole frame. Since it complies so well with the
intended target, an argument could be made to reduce costs by using a cheaper aluminium alloy or by reducing the
weight however it may be unwise to do so. This is because the added safety margin in the factor of safety is a beneficial
thing as it ensures there is no structural failure due to fatigue and it prolongs the longevity of the bike, something which
is highly desirable in the industry.
4. CONCLUSION
A static finite element analysis of an e-cargo bike frame dedicated to being a taxi service for two adults and a young
child by carrying them as part of a 500L cargo space has been undertaken in SolidWorks 2019 (Dassault Systemes,,
2019). The accuracy of the results was demonstrated by the converge study conducted and showed the trend between
the Von Mises stress and the displacement, even though the 9mm mesh seemed to be an outlier - the reasons for which
were discussed in the results. Since the intended target of safety margin greater than 2.6 has been achieved, and
increasing longevity of the frame being one of the main goals, the current design is deemed suitable and no further
alterations can be recommended.
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5. REFERENCES
Electroheads. 2021. How Have E-bikes Become So Popular? - Electroheads. [online] Available at: <https://
electroheads.com/how-have-e-bikes-become-so-popular> [Accessed 8 April 2021].
Dassault Systèmes, 2019. SolidWorks, Paris: Dassault Systèmes.
International Organisation for Standardisation, 2017. ISO 15194: 2017 Cycles - Electrically power assisted cycles EPAC Bicycles, Geneva: International Organisation for Standardisation.
Group 25, 2021. E-Cargo Bike Group Assessment (ME2502), Birmingham, Aston University, Mechanical, Biomedical
and Design Department.
Fryar, C., Gu, Q. & Ogden, C., 2012. Anthropometric Reference Data for Children and Adults: United States,
2007-2010, Washington D.C.: US Department of Health and Human Services.
Budynas, R. G. & Young, W. C., 1938. Roark’s Formulas for Stress and Strain. 1st ed. New-York: McGraw-Hill
Companies.
AbdulMatin, U., 2021. 7.1 ME2502 FEA Background, Birmingham: Aston University, Mechanical, Biomedical and
Design Department.
Medicalnewstoday.com. 2021. What is the average weight for men?. [online] Available at: <https://
www.medicalnewstoday.com/articles/320917#average-weight-of-men-in-the-us> [Accessed 8 April 2021].
Weight, A., COVID-19, A., Manchester, A., Walk, A. and Cup, A., 2021. Average Child Weight | Onaverage.co.uk.
[online] Onaverage.co.uk. Available at: <https://www.onaverage.co.uk/body-averages/average-child-weight> [Accessed
8 April 2021].
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