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Finite Element Methods for Stress Analysis (Ver. 2021/22)

MECH0059: Advanced Computer Applications in Engineering

Finite Element Analysis - Assignment

THE PROBLEM

Use finite element method to carry out a strain/stress analysis of the 2D structure shown in Figure 1A (under plane stress condition). Assume E=100 GPa, ʋ=0.3 and plate thickness is 2 mm.

Part 1: Write a MATLAB program to determine the displacement and strain in the thin plate, consisted of three (i) three-noded and (ii) six-noded triangular elements (see Figure 1B), under uniform tension as shown in Fig 1A.

Part 2: Re-run your program in Part 1 to determine the displacement and strain, based on at least three six-noded triangular elements, (i) for three additional elastic modulus (ii) for three additional loading conditions i.e. changing the loading direction from θ=90° . Keep other variables constant. Here compare the results of the additional simulations performed.

Part 3: use ANSYS Mechanical APDL to: (i) validate the MATLAB program, (ii) carry out mesh convergence, for a specific configuration of your choice (in terms of elastic modulus and loading condition).

Use the element arrangement that you think is most appropriate, a 3 elements configuration is suggested in Figure 1A.

Figure 1: (A) thin plate under tension; (B) three-noded and six noded elements [1].

REPORT OUTLINE AND MARKING SCHEME

Prepare your report in the format of a journal article based on the following guidelines: Title page

title of report, your name, affiliation, email address and word count

Abstract -------------------------------------------------------------------------------------------------------------------

Introduction ---------------------------------------------------------------------------------------------------------------

describe the problem; review previous studies/literature; describe the aim of the study …

Materials and Methods---------------------------------------------------------------------------------------------------

model description; material properties; boundary conditions and loads; element type and mesh

convergence; simulations, sensitivity tests and measurements (computer models & theory)...

Results ---------------------------------------------------------------------------------------------------------------------

results of the simulations in the same order that mentioned in the method...

Discussion ----------------------------------------------------------------------------------------------------------------

discuss the results of each simulation in the same order as in the Results section; comparison

between different models, with theory and/or experiments; comment on the validity and limitations of the model; summary/conclusion...

References

Figures and Tables

Appendix ------------------------------------------------------------------------------------------------------------------

MATLAB code must be included here

See marking rubric.

REPORT REQUIREMENTS AND SUBMISSION DATELINE

Your report must be submitted online on the relevant moodle page.

The main text (excluding title page, abstract, references, equations, tables, figure captions and

appendices) must not exceed 2500 words. Word count must be included on the first page.

Total number of Figures plus number of Tables must be less than 10.

Do not include the Figures and Tables in the main text. Include all the Figures and Tables at

the end of the text after References. Figures and Tables must be cross-referenced in the text.

Include page and continuous line number.

Your report including all sections (i.e. including signed cover-sheet) must not exceed 15 pages. Use font Arial 11, line spacing 1. 15, margins 25.4 mm on all sides, continuous line and page

number. The formatting does not apply to the Appendix.

International System of Units (or SI units) must be adopted throughout the report. Note up to 20 marks penalty will apply if you do not follow the guidelines. All students are reminded of the UCL plagiarism policies given in the following webpage, viz.