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日期：2024-10-17 09:07

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)