Faculty of Mechanical Engineering,
Universiti Teknologi Malaysia
SEMM3033: Finite Element Methods
Semester 2 - 2024/2025
Name
Matric Number
SHERWIN ARON SMITH
A22EM0016
DIVITHA A/P KESAVAN
B23KM0017
NAZRULHANIF BIN MUHAMAD JAYATUAH
A21EM0171
Table Of Contents:
1.​ Introduction
……………………………3
2.​ Methodology
..………………………4 - 9
●​ Load Cases
………………………………4
●​ Theoretical Analysis
…………………………..5 - 6
●​ FEM Model Preparation
………………………….7 - 9
3.​ Result
………………………….10
4.​ Discussion
…………………….11 - 12
5.​ Conclusion
…………………… 13 - 14
6.​ Reference
………………………….15
7.​ Appendix
…………………….16 - 21
2
Introduction:
The Finite Element Method (FEM) is a widely used simulation technique in engineering
that helps predict how structures will behave under various types of loads. It allows engineers to
break down complex geometries into smaller elements and analyze stress, strain and deformation
throughout the model. In this project, FEM was used to evaluate the structural performance of a
bicycle frame under distributed loading conditions.
The aim of the study was to understand how mesh density affects the accuracy and
reliability of FEM results. Three different mesh configurations were analyzed the standard, low
density and high density while keeping the same loading conditions for consistency. Key results
such as von Mises stress, equivalent strain and overall displacement were observed and
compared across the different mesh types.
By comparing these outcomes, the project highlights the importance of choosing the right
mesh density in FEM analysis. It also provides insights into how simulation settings can
influence the quality of the results. The findings from this study can help improve the design
process and ensure that structures like bicycle frames are both safe and efficient for real world
use.
3
Methodology:
Load Cases:
To ensure a reliable structural assessment of the bicycle frame, a variety of load cases were
selected based on realistic and critical operating conditions. The first considered scenario is the
static vertical load caused by the rider’s body weight. In this case, vertical forces are applied at
the seat tube to simulate the rider sitting in a stationary position. This load case represents the
most common everyday condition and is essential to verify the frame’s ability to support the
user's weight under normal operation.
The second load case involves pedalling, which introduces both torsional and axial forces. A
tangential force is applied at the bottom bracket area to replicate the torque generated by the rider
during active pedalling. This case is crucial as it results in significant stress concentration at the
bottom bracket shell, down tube, and chainstays. It also contributes to evaluating the frame’s
torsional stiffness and its ability to handle repeated load cycles.
The third case simulates braking, where longitudinal forces are applied at the front fork and rear
stays to replicate the deceleration forces experienced during sudden braking. This scenario is
critical because it introduces large axial and shear loads, particularly in the head tube and rear
triangle regions of the frame. It helps assess how well the structure copes with emergency or
high-speed braking situations.
The fourth scenario represents lateral loading, which can occur during cornering, side impacts, or
riding over uneven terrain. Sideways forces are applied to the top and down tubes to simulate the
resulting side loads. Although typically lower in magnitude, this load case is important for
identifying lateral flex and potential buckling, which affects both handling and rider safety.
The final case simulates an impact or drop, where a high vertical force is suddenly applied at the
bottom bracket or rear frame to represent the bike being dropped or involved in a collision. This
is a worst-case scenario involving transient but potentially severe stress, especially at joints and
welds, and is vital for understanding failure mechanisms under accidental conditions.
4
Theoretical Analysis:
To do a theoretical analysis, we evaluate the bending moment and resulting stress at critical
frame sections (typically at the down tube, seat tube, and bottom bracket area).
σ = M⋅c​/ I
Where:
●​ σ = normal stress due to bending​
●​ M = bending moment at the critical section​
●​ c = distance from neutral axis (half the tube outer diameter)​
●​ I = second moment of area of the tube cross-section
Assume:
Rider weight W=400 N
Pedalling force Fp = 300 N applied at crank (pedal offset ~0.17 m)
Tube diameter D = 40 mm, thickness t = 2 mm
1. Seat Loading
Scenario: Rider sits on the saddle, load applied vertically downward on the seat tube and top
tube junction. Reaction forces at the bottom bracket and rear axle.
Let’s assume:
●​ Horizontal top tube length = 0.55 m​
●​ Load applied at midpoint = 400 N​
5
●​ Moment at the base of seat tube:
Mseat ​= W ⋅ L / 2 ​= 200 ⋅ 0.55 / 2 ​= 110 Nm
σseat​= M ⋅ c / I ​= 110 ⋅ 0.02 / 2.62 × 10 ^ − 8​ ≈ 84MPa
2. Pedaling Load
Scenario: Crank torque is applied via pedals.
●​ Pedaling force: Fp=300 ​
●​ Crank length r = 0.17 m​
●​ Torque at bottom bracket:​
T = Fp ⋅ r = 300 ⋅ 0.17 = 51 Nm
This torque causes torsional shear, not bending. For comparison, convert to equivalent bending
stress (approximate using thin-wall assumption):
J = 32π ​(D^4 − (D−2t)^4 ) ≈ 2 ⋅ I = 5.24×10−8
τ = 51 ⋅ 0.02 / 5.24×10^−8 ​≈ 19.5MPa
Following the theoretical analysis of the major load cases, it is evident that seat loading has the
highest stress. Therefore, the study will be based on seat loading to help save computational
power.
6
FE Model Preparation:
Model name: Bicycle Frame
Solid Bodies
Document Name and
Reference
Treated As
Volumetric Properties
Bicycle Frame
Solid Body
Mass:13.4406 kg
Volume:0.00171174 m^3
Density:7,852.01 kg/m^3
Weight:131.718 N
Analysis type
Static
Mesh type
Solid Mesh
Thermal Effect:
On
Thermal option
Include temperature loads
Zero strain temperature
298 Kelvin
Include fluid pressure effects from
SOLIDWORKS Flow Simulation
Off
Solver type
Automatic
Inplane Effect:
Off
Soft Spring:
Off
Inertial Relief:
Off
Incompatible bonding options
Automatic
Large displacement
Off
Compute free body forces
On
7
Friction
Off
Use Adaptive Method:
Off
Unit system:
SI (MKS)
Length/Displacement
mm
Temperature
Kelvin
Angular velocity
Rad/sec
Pressure/Stress
N/m^2
Properties
Name:
AISI 4130
Steel,
normalized at
870C
Model type:
Linear Elastic
Isotropic
Default failure
criterion:
Max von Mises
Stress
Yield strength:
4.6e+08
N/m^2
Tensile
strength:
7.31e+08
N/m^2
Elastic
modulus:
2.05e+11
N/m^2
Poisson's ratio:
0.285
Mass density:
7,850 kg/m^3
Shear
modulus:
8e+10 N/m^2
8
Fixture name
Fixture Image
Fixture Details
Fixed-1
Entities:
3 face(s)
Type:
Fixed
Geometry
Resultant Forces
Components
X
Y
Z
Resultant
Reaction force(N)
-0.000933886
365.419
-162.701
400.003
Reaction Moment(N.m)
0
0
0
0
Load name
Load Details
Torque-1
Load name
Load Details
Force-1
Entities:
1 face(s)
Reference:
Face< 1 >
Type:
Apply
torque
Value:
10 N.m
Entities:
1 face(s)
Type:
Apply
normal
force
Value:
400 N
9
Result:
1)aDistributed Forces ( on the frame where the bicycle seat is connected with the frame).
Name
Type
Min
Max
Stress1
VON: von Mises Stress
1.154e+02N/m^2
4.131e+05N/m^2
Node: 5238
Node: 280
0.000e+00mm
6.295e-04mm
Node: 39
Node: 86
1.461e-09
1.195e-06
Element: 13183
Element: 12778
Displacement1
Strain1
URES: Resultant Displacement
ESTRN: Equivalent Strain
2) Low mesh Density (Distributed Force)
Name
Type
Min
Max
Stress1
VON: von Mises Stress
3.757e+03N/m^2
3.150e+06N/m^2
Node: 2903
Node: 484
0.000e+00mm
4.953e-03mm
Node: 39
Node: 24786
1.607e-08
9.676e-06
Element: 8111
Element: 2092
Displacement1
Strain1
URES: Resultant Displacement
ESTRN: Equivalent Strain
3) High Mesh Density- Distributed Force:
Name
Type
Min
Max
Stress1
VON: von Mises Stress
2.686e+03N/m^2
3.263e+06N/m^2
Node: 41048
Node: 275
0.000e+00mm
4.955e-03mm
Node: 39
Node: 14232
1.896e-08
9.508e-06
Element: 9581
Element: 18376
Displacement1
Strain1
URES: Resultant Displacement
ESTRN: Equivalent Strain
10
Discussion:
The high-density mesh configuration is the most suitable for this structural analysis.
While it slightly increases computational time, the benefits of greater result accuracy and mesh
quality significantly outweigh the cost. This makes it the best choice for engineering applications
where detail, safety, and performance validation are critical.
a)​ Total Elements: 23,340
b)​ Maximum Element Size: 18.3781 mm
c)​ Minimum Element Size: 2.25005 mm
The table is taken data from the high meshing density
1. Highly Stressed Region
The analysis identified the region of maximum stress through the von Mises stress distribution.
The maximum von Mises stress was recorded as 3.263 × 10⁶ N/m², located at Node 275. The
minimum stress value was 2.686 × 10³ N/m², indicating a wide distribution but very low
magnitude of stress across the component.
According to the simulation, the stress values remain well below the material yield strength,
which is 4.6 × 10⁸ N/m² for AISI 4130 steel. This implies that no yielding or permanent
deformation is expected under the applied load. The stress distribution is localized and does not
raise any immediate concerns regarding structural failure.
2. Maximum Deflection
The displacement result shows that the maximum resultant displacement is 4.955 × 10⁻³ mm,
observed at Node 14232. The minimum displacement recorded is 0 mm, indicating that parts of
the structure remain fully constrained or barely affected by the loading.
11
This level of deflection is extremely small and suggests that the component is very stiff. Such
behavior is expected when using high-strength materials like AISI 4130, especially under
relatively low loading conditions. From a design standpoint, this minimal deformation ensures
dimensional stability and service reliability during operation.
3) The safety factor is calculated using the definition:
8
𝑆𝐹 =
2
4.6 𝑋 10 𝑁/𝑚
6
2
3.263 𝑥 10 𝑁/𝑚
= 141
This result shows that the component can withstand stresses up to 141 times higher than the
current applied load before reaching the yield point. Such a high safety factor indicates a very
conservative design. From an engineering perspective, this level of overdesign may be
appropriate for critical safety components or to account for uncertain loading conditions.
However, it also suggests an opportunity for material optimization if weight or cost reduction is
desired.
4. Failure Criterion Justification
The default failure criterion used in this study is the Maximum von Mises Stress. This is defined
as a scalar stress value used to predict yielding of materials under any loading condition based on
the distortion energy theory. It is especially suitable for ductile materials, such as AISI 4130
steel, because it provides a reliable indication of when the material will start to deform.
By applying this criterion, the analysis ensures that any regions experiencing combined stress
states are accurately evaluated for potential failure, rather than simply looking at principal or
directional stresses. The choice of von Mises stress, therefore, is both theoretically sound and
practically relevant for assessing ductile metal components.
12
Conclusion:
In conclusion, the finite element analysis conducted under three different mesh
configurations are standard mesh, low mesh density, and high mesh density. It reveals significant
insights into the structural performance of the bicycle frame. Among these, the high mesh
density model proved to be the most accurate and critical for assessing stress distribution and
displacement behavior. Each load case simulated the force acting on the part of the frame where
the bicycle seat connects to the rest of the structure, which is a critical region due to its exposure
to rider weight and dynamic forces during use.
The comparison of results among the three load cases shows clear differences in the
precision and accuracy of the output values particularly in the stress, strain, and displacement
distributions. The high mesh density configuration provided the most refined and reliable data,
revealing a maximum von Mises stress of 3.263 × 10⁶ N/m² at Node 275, which is notably higher
than that recorded in the standard and low mesh configurations. Additionally, this configuration
yielded a maximum displacement of 4.955 × 10⁻³ mm at Node 14232 and an equivalent strain of
9.508 × 10⁻⁶. These values reflect the effectiveness of the high mesh density in capturing
localized effects and stress concentrations. That is typically missed or underestimated in lower
resolution meshes. In contrast, the standard mesh configuration recorded a significantly lower
maximum stress of only 4.131 × 10⁵ N/m². It underrepresents the critical stress areas due to its
coarser discretization. The low mesh density case showed similar displacement values to the high
mesh model but the quality and resolution of stress distribution were inferior, indicating that
finer mesh density leads to more accurate representation of physical behavior.
Even though the results varied between the different mesh types all of them showed that
the structure is very safe and far from reaching the material breaking point. The material used,
AISI 4130 steel has a yield strength of 4.6 × 10⁸ N/m². The highest stress found in the analysis
was much lower than that by over 100 times. This gives a very high safety factor of about 141
which means the frame is much stronger than it needs to be for the current load. While this
shows the design is very safe and reliable, it also suggests that the frame might be overbuilt.
There is room to improve the design by making parts thinner, switching to lighter materials or
adjusting the shape to reduce weight and possibly lower production costs. This could be
especially useful for racing bikes or performance models where every gram counts.
13
To improve the model, further refinements can be introduced such as localized mesh
enhancement in regions with high stress gradients. It is to maintain accuracy without
significantly increasing computational cost. Exploring additional boundary conditions including
dynamic or point loading scenarios could provide a more realistic representation of in service
performance. Given the conservative safety margin, there is an opportunity to optimize the
design by considering thinner materials or alternative lightweight alloys. Which could reduce
weight and cost without compromising safety. Incorporating experimental validation and fatigue
analysis in future studies would also enhance the reliability and applicability of the model for
long term use.
14
References:
●​ ISO 4210-6:2015, Cycles – Safety requirements for bicycles – Part 6: Frame and fork test
methods, International Organization for Standardization, 2015.​
●​ J. Zhao, Z. Xu, and Q. Yu, “Structural analysis of bicycle frames based on finite element
method,” Procedia Engineering, vol. 15, pp. 3023–3028, 2011.​
●​ R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II:
Mainly Electromagnetism and Matter, Addison-Wesley, 2005.​
●​ Hibbeler, R. C., Mechanics of Materials, 10th ed., Pearson, 2020.​
●​ S. Rao, The Finite Element Method in Engineering, 5th ed., Butterworth-Heinemann,
2011.​
●​ A. Shabana, Computational Dynamics, 2nd ed., Wiley, 2009.​
●​ ANSYS, Inc., ANSYS Mechanical APDL Theory Reference, Canonsburg, PA, USA, 2023.
[Online]. Available: https://www.ansys.com
15
Appendix:
Bicycle Frame Model
16
Seat Loading (Distributed force at the face)
Torsional Loading (Torsion at the face shown)
Results:
1)​ Distributed Forces ( on the frame where the bicycle seat is connected with the frame).
Von Misses Stress
17
Displacment
Strain
2) Low mesh Density (Distributed Force)
Von Mises Stress
18
Displacment
Strain
3) High Mesh Density- Distributed Force:
19
Von Mises Stress
Displacment
Strain
20
Graph;
The graph shows the node vs displacement for high density meshing
The graph shows the node vs Von Mises Stress for high density meshing
21