Assignment Problem: Solid mechanics and finite elements
For this coursework you are required to select a 2D planar (either plane stress or plane strain) problem of your choice, and to use the ABAQUS programme to analyse your problem, and to produce a report of your findings. This will require you to select a problem of interest (example listed below) with appropriate dimensions, realistic material properties, force loadings and boundary conditions, and to formulate this within the ABAQUS program for analysis. The analysis should centre on 1) the findings of the calculations, e.g. locating areas of high stress and strains that would most likely cause structural issues, and perhaps looking at the maximum stress/strains as a function of force; and 2) convergence analysis of your results and performance of the various FEM formulations, e.g. how is solution convergence affected with respect to mesh refinement, element types (quadrilateral or triangles) and polynomial order (ABAQUS has linear and quadratic basis functions available). The report must be a maximum of 7 page (you probably require less so don't waffle to fill space) including figures and tables, and should consist of the sections listed below.
1) Abstract: A short and concise description of the whole report detailing the conducted work and its findings.
2) Introduction: Problem definition
Detail your problem fully, and clearly. It should be presented in a way that someone else can reproduce the exact same problem. I.e. all dimensions, material properties, boundary conditions, forces should be defined. If you have used sources of information to get your problem specifications then make sure you reference your sources.
3) Results & Discussion:
Provide a detailed discussion of how the problem has been analysed and demonstrate you have found numerically converged results. That is, don't just perform one calculation and assume that is your answer, you will need to calculate many solutions with increasing mesh resolution and demonstrate the results are trustworthy, e.g. though graphs comparing the stresses/strains/deformations, at a number of points of interest, against mesh resolution. These will need to show that your solutions have converged to their true solution. Your analysis should also look at how convergence is affected by changing the mesh type (e.g. triangles or quadrilaterals) and polynomial order of the basis functions. You should also provide a discussion of where your problem is subjected to areas of high stress and strain, thus indicating where structural failures are most likely to occur. You may also wish to discuss computational times that are required to obtain numerically converged results (although not necessary here).
Hint: Whilst you will need to perform several computations, e.g. when increasing mesh resolution, do not show all solutions in the report graphically (it is both unnecessary and your space is quite tight). Show only a few solutions of stresses/strains/deformations for 2-3 of your results, but the rest will be used to form the data in the graphs you present.
4) Conclusion:
This should contain a summary analysis of the findings of the report and results. Report structure, clarity and good use of English, figures and tables.
Below is some previous lecturer's advice on writing your report that are still relevant to this coursework.
- Content: scope and correctness of the material presented. As I have reiterated in the lectures, once you have your report properly structured, it is time for a reader to start reading the content. He or she may have already scrolled through the headings, illustrations and so on. These include presentation of your problem and explanation of it to the reader. Keep in mind that when marking I do not know anything about your problem, because it is unique and chosen by you. The only way I can learn about your problem is by reading about it in your report. In order to understand the problem, I expect good mixture of text, illustrations, etc. If you are using technical drawings these have to satisfy the standards you have mastered in previous years. The most common problem is an incomplete explanation hard to follow with bad illustrations, wrong equations, incomplete dimensions, etc.
2. Problems solved:
- Do not copy a problem from a friend - no need to elaborate
- Present a problem in such a way that one can reproduce your results. Now we are coming to
modelling issues where I ask you to "Present a problem in such a way that one can reproduce your results". As I have many times explained to you in the class, this is an important aspect of any simulation - completeness, correctness and reproducibility. You have performed the simulation, but in order for a third person to have any confidence in it, all has to be fitted within your report to enable somebody else to take Abaqus or other package and solve your problem again thus comparing the results with your results. This step requires skill especially given the fact that the report is limited to 7 pages. To attain the highest marks these issues must be address and few pieces of coursework provided evidence in support of these criteria at the highest level.
3. Results analyzed, i.e. post-processing and interpretation of results. Many of you have just presented Abaqus screen dumps in your reports. Most of these do not even have a caption and have never been explained in the text or cross-referenced. Some of you have simply put these into some sort of appendix making the report very long - I have given you a seven page limit for a good reason so that you have to be creative with the content, layout, structure of your report, in order to satisfy the key criterion of completeness, correctness and reproducibility within the given page limit. Again this requires skill and some of you have done this well and have been given comfortable A. Others have not done as well and have been given maybe B or in cases of work which is more limited against these criteria, mostly C.
4. Do not come with similar report as your friend. In this report you also demonstrate that you have mastered Abaqus during Laboratory teaching. We do not examine Abaqus in the exam paper. So when I see that you have solved a unique problem of your own, I can have some confidence that you have not grabbed results from somebody else and can focus on your individual Abaqus skills.
5. Do not get a report from last year or somebody else. See 4.
6. Your coursework is an integral part of the exam and any offence will produce consequences. As I said, we examine here your hands on skills using the industry leading simulation software. Knowledge of this package can make or break your CV and it is not unheard off that one would take the simulation report for the interview with prospective employers.
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