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Finite Element Methods for Stress Analysis (Ver. 2020/21) A2 - 1 MECHGM0059: Advanced Computer Applications in Engineering Finite Element Analysis - Assignment 2 THE PROBLEM Develop a finite element program based on 4 noded quadrilateral elements, using MATLAB to estimate the deformation of the structure shown in Figure 1A. Part 1: Write a MATLAB program to calculate the stiffness matrix of a two-dimensional plane stress 4 noded quadrilateral element as shown in Figure 1B. Assume E=200 GPa, ʋ=0.3 and plate thickness is 2 mm. Part 2: Use your program in Part 1 to determine the displacement and strain in Figure 1A, consisted of 2 and 4 quadrilateral elements. Assume E=200 GPa, ʋ=0.3 and plate thickness of 2 mm. Note do not change the dimensions in Figure 1 and use the element arrangement that you think is most appropriate. Part 3: Re-run your program in Part 2 to determine the displacement and strain, (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. Your report must compare/comment on the: • displacement and strain results obtained from different elements, material properties and loading conditions • validity of your program, here you are expected to model the same structure using a commercial program and compare your results against it. Figure 1: (A) A thin plate loaded. (B) a single four-noded element. University College London Finite Element Methods for Stress Analysis (Ver. 2020/21) A2 - 2 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, include a sketch/drawing of the problem; 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 Presentation [20 marks]; technical content [50 marks discussion and critical analysis [30 marks] Part 1; 10marks; Part 2; 25 marks; Part 3; 15 marks]; REPORT REQUIREMENTS AND SUBMISSION DATELINE • Your report must be submitted online on the relevant moodle page 1300 (UK time) on 8th February 2021. • The main text (excluding title page, abstract, references, equations, tables, figure captions and appendices) must not exceed 1500 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 the References. Figures and Tables must be cross-referenced in the text. • Include page and continuous line number. • Your report including all sections must not exceed 14 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. REFERENCE [1] Seshu P. Textbook of finite element analysis. PHI Learning Private Limited 2003. Dr M Moazen 7th December 2020 University College London ...
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