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Finite Element Coursework
1. Instructions
You are requested to work through this problem using the ABAQUS finite element software. ABAQUS is available on the computer cluster, as well as on the PCs located in the computer rooms belonging to the Faculty of Engineering. Alternatively, you can obtain a free copy of ABAQUS student edition from the 3DS Academy web site at the following URL:
http://academy.3ds.com/software/simulia/abaqus-student-edition/
Downloading ABAQUS from the link above requires registering with your Imperial credentials. The ABAQUS student version is node limited, but perfectly adequate forthe tasks set in this coursework.
A brief report (instructions in Sec. 4 of this handout) must be submitted via Blackboard. This report will be worth a maximum of 10% of your overall mark for this course.
Submission deadline on Monday Week 19
2. Problem Description
This example is taken from a series of benchmarks developed by NAFEMS, an International organisation whose purpose is promoting good practise in the use of numerical analysis. Benchmarks are test cases which are well defined and for which the solution is known. They can therefore be used to assess the accuracy of finite element formulations. The benchmark chosen for this coursework consists in the stress analysis of an elliptical membrane and it defined in the specification sheet shown below. The benchmark defines the problem (geometry, loading, boundary conditions, material properties and mesh) and the target value for the tangential stress at a certain geometrical point/node (point D).
3. Tasks
The benchmark from NAFEMS introduced in the previous section is intended for both quadrilateral and triangular elements. In this coursework, we are only interested in the quadrilateral elements.
You are required to set up five finite element models using:
1) the geometry described in the NAFEMS benchmark;
2) the material properties given in the NAFEMS benchmark;
3) the constraints and loads prescribed in the NAFEMS benchmark;
4) quadrilateral elements only (not triangular);
3.a First Model
The first model should use a coarse mesh (corresponding to the mesh with rectangular elements shown on the left of the NAFEMS specification sheet) with reduced integration. For this model, use a total of 6 4-noded bilinear plate elements available in ABAQUS.
3.b Second Model
The second model should use a coarse mesh (corresponding to the mesh with rectangular elements shown on the left of the NAFEMS specification sheet) with full integration. For this model, use a total of 6 4-noded bilinear plate elements available in ABAQUS.
3.c Third Model
The third model should use a refined mesh (corresponding to the mesh with rectangular elements shown on the right of the NAFEMS specification sheet) with
reduced integration. For this model, use a total of 24 4-noded bilinear plate elements available in ABAQUS.
3.d Fourth Model
The fourth model should use a refined mesh (corresponding to the mesh with rectangular elements shown on the right of the NAFEMS specification sheet) with full integration. For this model, use a total of 24 4-noded bilinear plate elements available in ABAQUS.
3.e Fifth Model
The fifth model should use a further refined mesh with full integration. For this model, use a total of 96 4-noded bilinear plate elements available in ABAQUS. The mesh should be obtained by halving the mesh seeds used for refined models 2.c and 2.d
4. Reporting (up to 5 pages)
4.1 Comment on the level of accuracy of the geometric representation obtained by using 4-node quadrilateral elements and refining the mesh (150 words maximum).[10 marks]
4.2 Discuss how the load is introduced in the model and how its representation is influenced by the element topology and mesh refinement (150 words maximum).[10 marks]
4.3 Discuss how stress results are obtained for 4-noded quadrilateral elements within the context of FE analysis, with particular emphasis on the difference between reduced and full integration (200 words maximum).[20 marks]
4.4 Summarize your results in a table where you report the tangential edge stress (yy) at point D for the five models described above and the associated percentage error with respect to the value provided in the NAFEMS benchmark.[20 marks]
4.5 Plot in a separated figure the deformed shape of each of the five models withoverlaid contours/fringes showing the distribution of the yy stress component.[20 marks]
4.6 Comment on whether any of the aforementioned models exhibits spuriousdeformation modes, e.g. mechanisms and/or hourglassing (150 words maximum).[20 marks]
You may use equations from FE theory to support your answers where appropriate.