Finite Element Analysis of a Perforated Plate Using ANSYS (Report) Graphs

3.2. Graphs. Longitudinal stress at A/MPa R1, 4 nodes 160 140 120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 9 6 7 8 9 6 7 8 9 Mesh density Lonitudinal stress at A/ MPa R1, 8 nodes 139 138 137 136 135 134 133 132 131 130 129 0 1 2 3 4 5 Mesh density Longitudinal stress at C/MPa R2, 4 nodes 10 8 6 4 2 0 -2 0 -4 -6 -8 1 2 3 4 5 Mesh density R2, 8 nodes Longitudinal stress at C/MPa 0 -2 0 2 4 6 8 10 -4 -6 -8 -10 -12 -14 Mesh density R3, 4 nodes Displacement at C/mm 0.025 0.02 0.015 0.01 0.005 0 0 1 2 3 4 5 6 7 8 9 Mesh density Displacement at C/mm R3, 8 nodes 0.02285 0.0228 0.02275 0.0227 0.02265 0.0226 0.02255 0.0225 0.02245 0 2 4 6 Mesh density 8 10 R4, 4 nodes Average percentage errot (%) 120% 100% 80% 60% 40% 20% 0% 0 1 2 3 4 5 6 7 8 9 6 7 8 9 6 7 8 9 Mesh density R4, 8 nodes Average percentage error (%) 60% 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 Mesh density R5, 4 nodes Average percentage error (%) 45.00 40.00 35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 0 1 2 3 4 5 Mesh density Average percentage error (%) R5, 8 nodes 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 0 1 2 3 4 5 6 7 8 9 Mesh density R7, 4 nodes Longitudinal stress/MPa 160 140 120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 9 10 Nodes R7, 8 nodes 160 Longitudinal stress/MPa 140 120 100 80 60 40 20 0 0 2 4 6 8 10 Nodes 12 14 16 18 3.3. Fig 9. Example of a visual plot for longitudinal stress, corresponds with R1 and R2. Fig 10. Example of a visual plot for x directional displacement. Corresponds with R3 Corresponding diagrams and visual plots. Fig 11. Zoomed in section of the plate. Corresponds with R4. Fig 12. Zoomed in section of the plate. Corresponds with R5. Fig 13. Zoomed in section of the plate when elemental results are visually plotted with the finest mesh. Corresponds with R6. Fig 14. Zoomed in section of the plate with the finest mesh applied. Corresponds with R7. Fig 15. ANSYS generated graph showing relationship of stress between point A and B for R7/A1 Fig 16. ANSYS generated graph showing relationship of stress between point A and B for R7/A2 4. Discussion of results. 4.1. R1. Both graphs show a similar trend between the mesh densities of increasing and then converging to a value of approximately 140 MPa. The values for the 8 noded body begin considerably higher than the initial values for 4 noded body, the increase in stress is much greater for the 4 noded body compared to the 8 noded body, however they both begin to show steady state progression with a mesh density of 8 with both bodies producing stresses of approximately 140 MPa. From this I can say that the meshing will provide greater accuracy as it becomes finer, however from a base level the 8 noded body will produce more reasonable results even with a low mesh whereas the 4 noded body does not produce such results. It can also be said that point A is where the longitudinal stress is at its maximum. 4.2. R2. Once more, the graphs produce a similar result at the point of the finest mesh, with a result of approximately -5.8 MPa, however the data gets to this point of this converging result in two very different ways. For the 8 noded quad, there is an increase in stress between the coarsest mesh density and the finest mesh density, however with the 4 noded quad what occurs with the data is almost in the exact opposite to this. There is a decrease in longitudinal stress along the varying mesh textures. Similarly, to R1, both bodies yield a similar value with the finest mesh being applied however the initial values displayed by both bodies are almost equal and opposite in nature making it difficult to determine which body is the best one to use for the values. It can be said however that as long as the mesh is of a fine enough texture the progression of values and the errors associated with that does not necessarily matter. 4.3. R3. This test shows the slightest change in both bodies when changing the mesh density out of all the tests. The 8 noded quad reaches steady state readings of data very quickly by producing consistently similar results from mesh densities 2-8. Once more both bodies produce a similar value for the displacement at point C with the finest mesh applied with the x direction displacement being approximately 0.0022 mm at point C for both bodies. This test shows the quickest convergence in values from both bodies with the slight difference being that the value starts smaller and increases with the mesh density for the 4 noded body, and conversely decreases with the values of the 8 noded body. Yet again both bodies demonstrate the convergence of values with the increase in mesh density, even when applied to the quantity of displacement. 4.4. R4. When examining the average error produced by both bodies about a node around the hole in the plate that is connected to two different elements, the difference between the two is seemingly vast. The errors continually increase for the 4 noded body with experimental values going over 100% with the mesh density at its finest. This points to an inherent inconsistency in the distribution of the meshing throughout the 4 noded body and the uncertain placed going from element to element. For the 8 noded body however the trend shown by the graph is a consistent decrease in uncertainty with the increase in the mesh density, therefore meaning that consistency is more apparent within the 8 noded body when compared to the 4 noded body. Potential issues with any experimental data could be a factor in this summation and further inspection in a finer mesh would be required for the 4 noded body to see if this trend did continue. 4.5. R5. With this test, the node was selected as close to the central hole as possible that is surrounded by 4 different entities and the error found in longitudinal stress was calculated about the various nodes. For both bodies there was a noticeable decrease in average percentage error as a trend about the selected node(s). However, the 8 noded body’s error value decreased to a considerably lower value with the finest mesh density when compared to the 4 noded body. Both bodies again show convergence in values as the mesh density increases, but once again the 8 noded body produced an approximate final error value of 1% whereas the 4 noded body produces a 24% value for error. This shows slightly less inconsistency compared to R4 but the difference in error is still substantial even when taken as a total average and not from the absolute maximum and excluding the surrounding percentage errors about the node. 4.6. R6. The values for K remain constant over the two bodies when considering the empirical calculation, K remains to be 1.84 across both bodies as the empirical value for peak, and nominal stress will remain constant no matter the base setting of the component as the geometry of both remains the same. The percentage error between the two different generated values of K is also similar at 5 ad 6% the reason for this being that, as both bodies will be subjected to the finest mesh possible, they will both yield a very similar values for peak stress and therefore the generated value of K will not be vastly different between the two bodies subsequently meaning the error compared between empirical and generated values will not be hugely different from one another. However, the difference between empirical and generated results is noticeable. This illustrates that though the empirical calculation is a reasonably quick way to estimate the value of K, the generated value (especially when the body is subjected to the finest mesh) will be overall more accurate. 4.7. R7. As figure 14 shows, in correspondence to the R7 table, the directly upwards path between point A and point B runs through a line of symmetry, meaning each node on each entity will be complimentary to one another. The graphs may seemingly display a strange relationship however the reason for the large double back, on the x axis, is due to the simulations numbering of the nodes going vertically upwards from A to B. The trend uniformly in longitudinal stress is a decreasing one for both bodies and is better displayed in section 3.3 in figures 14 and 15. Showing more definitively that the greatest concentration in stress is at point A next to the hole, meaning the point of failure for the plate will most likely originate from said hole where the longitudinal stress is concentrated. 4.8. Overall evaluation of results. It can be said simply that all the graphs produced do show convergence towards a singular value as the mesh density becomes finer. Comparatively the 4 noded body produces a higher value of error consistently with its produced values showing inconsistency within the way the body is structured. More exploration into this would be interesting as aside from high error values, with a fine enough mesh the 4-node body produces very similar values to the 8 noded body. By comparison based of these tests on these bodies alone however, it can be said that the 8 noded body is more consistent and produces more reliable results with consistently lower values for error throughout the analysis. The point of failure for this plate will be about point A with the highest stress acting about this area therefore meaning if the load were to increase this would be the area most likely to cause the plate to fail structurally. 5. Conclusions. In conclusion, although when subject to the 7 tests, both bodies display convergence towards specific values as the mesh density increases. There is variance in initial values recorded with a coarse mesh and how the data tends towards a specific value however both bodies on the whole display data that converges be it via decrease or increase. However, the big comparable point between the two plates is that the 4 noded body consistently produces higher values for percentage error in its values of stress meaning greater inconsistency within the plate’s analysis and a higher uncertainty. Therefore, a base setting of an 8 noded quadrilateral should be taken as the more reliable way to carry out this type of finite element analysis. The plates data displayed convergence and then subsequently showed a far lower value of uncertainty throughout the data collected.