MCEN30017 Finite Element Analysis

Department of Mechanical EngineeringMechanics 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 solve1D/2D structural problems (see examples in lecture notes_ and utilize both Matlab and acommercial FEA package to give a flavor of conducting research to students and prepare themfor structural integrity of a modern world engineering problem.

Assessment:

This assignment constitutes 25% of your total grade. You are required to submit an individualreport addressing all the questions. The report must be submitted online through the LMS byFriday, 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 代 写MCEN30017  Finite Element Analysis   to 6-minute video presentation (e.g., a voice-over PowerPoint), explainingyour 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 node1 and node 2, and calculate the stresses on rods A, B, C. Let Young’s modulus 𝐸 = 210 𝐺𝑃𝑎 &uniform cross-section area 𝑆 = 4 × 10−4 𝑚2 for all elements. You should demonstrate:

1. a) Calculation of the stiffness matrix for each rod in this figure
2. b) Calculation of displacements on nodes 1 and 2 in both horizontal and vertical directionsFigure 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. Readthe following documentation (only the uniaxial tension section) on analytical stress analysis of acircular hole in an infinite plate (you can search for “stress concentrations at holes”).https://www.fracturemechanics.org/hole.htmlDownload the Matlab code for assignment on LMS, or alternatively go through the followingMATLAB help center which guides you through simulation of a circular hole in a rectangularstrip.https://au.mathworks.com/help/pde/ug/stress-concentration-in-plate-with-circular-hole.htm(3m)Following the instructions, instead of a rectangle, design a square with a circular hole in themiddle of it. Call circular hole diameter “d” and square width “w” and use only fine mesh. Weknow that the analytical solution is not valid anymore if “d/w” parameter is not small enough.

1. a) This is the analytical method to the solution of a PDE. Write a maximum of 2 paragraphson your understanding of the nature of the problem. (4 marks).

1. 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 theaverage stress on one edge and on the centerline similar to the way stress is defined onthe 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 todesign the model below in SolidWorks and report the required steps to perform a valid simulationfor a prosthetic hip joint replacement. You are supposed to generate the backbone of your modelfirst. Subsequently, add fillets and cut-extrudes to the model to generate the final model asproposed 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 𝑅5 as an example to convey a5 mm fillet. The common practice is to use a dynamic load on the joint; however, we simplify the modelingwith a 1500 Newtons of load applied to the spherical part of the joint.In your report/video presentation:

1. i)Show how you construct your model (use revolve feature), select your material(Titanium alloy- Titanium (Ti-6Al-4V)). (15 marks)

1. ii)Present the boundary conditions that you use to initiate your simulation. In order notto have a rotation in your model, what type of B.C. you would use, and on whatedges/faces? Justify your boundary conditions. (10 marks)iii)Perform a mesh sensitivity analysis and demonstrate the regions of high stress on yourmodel, which require further refinement of mesh. Explain your strategy to refine meshon high stress/ critical zones and report the appropriate mesh size. (10 marks)

1. 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 reducethis stress in your model? (10 marks).

1. v)

A design engineer has recommended reducing the weight of implant considering a fewholes inside the model. Apply a 1 mm fillet for each hole. Develop your model basedon the suggested design and conduct a design study to investigate the most appropriatesize of the holes in your model. Try holes with a diameter of 6, 8, 10, 12 mm. (15marks)