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Department of Mechanical Engineering
Mechanics and Materials (MCEN30017)
Part 2: Finite Element Analysis (FEA)
Semester 2, 2024
Assignment
Objective:
This assignment aims to evaluate students’ ability to use an analytical FEA approach to solve
1D/2D structural problems (see examples in lecture notes_ and utilize both Matlab and a
commercial FEA package to give a flavor of conducting research to students and prepare them
for structural integrity of a modern world engineering problem.
Assessment:
This assignment constitutes 25% of your total grade. You are required to submit an individual
report addressing all the questions. The report must be submitted online through the LMS by
Friday, October 18, 2024, at 23:59.
The report should be at least 15 pages long, including figures, in a word or pdf document format.
Alternatively, you may submit a written report of at least 10 to 12 pages, including figures,
accompanied by a 4 to 6-minute video presentation (e.g., a voice-over PowerPoint), explaining
your steps for conducting the FEA simulations required for Question 3.
We recommend using an equation editor for writing mathematical equations and formulas.
However, you may also use clear and legible handwritten equations if preferred. Section 1: FEA analytical approach
Question 1. (20 marks)
For the plane truss shown in figure 1, determine the horizontal and vertical displacement of node
1 and node 2, and calculate the stresses on rods A, B, C. Let Young’s modulus = 210 &
uniform cross-section area = 4 × 10
−4
2
for all elements. You should demonstrate:
a) Calculation of the stiffness matrix for each rod in this figure
b) Calculation of displacements on nodes 1 and 2 in both horizontal and vertical directions
Figure 1
Question 2. (20 marks)
Most of the engineering problems fall into a category of solution of a partial differential equation
(PDE). There are analytical, experimental, and numerical methods to solve these PDEs. Read
the following documentation (only the uniaxial tension section) on analytical stress analysis of a
circular hole in an infinite plate (you can search for “stress concentrations at holes”).
https://www.fracturemechanics.org/hole.html
Download the Matlab code for assignment on LMS, or alternatively go through the following
MATLAB help center which guides you through simulation of a circular hole in a rectangular
strip.
https://au.mathworks.com/help/pde/ug/stress-concentration-in-plate-with-circular-hole.html
B (4m)
C (3m)
F (4m)
E (4m)
(3m)
4000 N
3000 N
5Following the instructions, instead of a rectangle, design a square with a circular hole in the
middle of it. Call circular hole diameter “d” and square width “w” and use only fine mesh. We
know that the analytical solution is not valid anymore if “d/w” parameter is not small enough.
a) This is the analytical method to the solution of a PDE. Write a maximum of 2 paragraphs
on your understanding of the nature of the problem. (4 marks).
b) Iterate multiple times and report the minimum “d/w” in which maximum stress is three
(3) times higher than the average stress at the edge of the square. Hint: you can find the
average stress on one edge and on the centerline similar to the way stress is defined on
the circle (a few lines of code). (8 marks)
c) Make a similar geometry in SolidWorks and conduct an FEA analysis. Present both results
(8 marks)
Section 2: FEA numerical approach
Question 3 (60 marks)
During the tutorial sessions, we have learned how to design and analyze an FEA model. Try to
design the model below in SolidWorks and report the required steps to perform a valid simulation
for a prosthetic hip joint replacement. You are supposed to generate the backbone of your model
first. Subsequently, add fillets and cut-extrudes to the model to generate the final model as
proposed in the next page. Keep the 10 mm bottom edge of the model, and its midpoint as a
reference to start your design. Each fillet size is simply written as 5 as an example to convey a
5 mm fillet.
The common practice is to use a dynamic load on the joint; however, we simplify the modeling
with a 1500 Newtons of load applied to the spherical part of the joint.
In your report/video presentation:
i) Show how you construct your model (use revolve feature), select your material
(Titanium alloy- Titanium (Ti-6Al-4V)). (15 marks)
ii) Present the boundary conditions that you use to initiate your simulation. In order not
to have a rotation in your model, what type of B.C. you would use, and on what
edges/faces? Justify your boundary conditions. (10 marks)
iii) Perform a mesh sensitivity analysis and demonstrate the regions of high stress on your
model, which require further refinement of mesh. Explain your strategy to refine mesh
on high stress/ critical zones and report the appropriate mesh size. (10 marks)
iv) Present the regions of high stress in your model based on Von-mises stress.
Demonstrate a graph for the region with the highest stress. Are you able to reduce
this stress in your model? (10 marks).
v) A design engineer has recommended reducing the weight of implant considering a few
holes inside the model. Apply a 1 mm fillet for each hole. Develop your model based
on the suggested design and conduct a design study to investigate the most appropriate
size of the holes in your model. Try holes with a diameter of 6, 8, 10, 12 mm. (15
marks)