The results from the graph show that the 8 node depicted an increasing rate for both the mesh density ant the stress at A. The increase was not proportional as the more the mesh density the more the mesh density became flatter. The 4 node on the other hand started at a lower point (stress at A) than the 8 node.

Still it experienced the increasing but at a decreasing characteristic. There was the possibility of the stress and mesh density converging for both the 4 and 8 node though they do not. Generally, there was a positive relationship between the stress and the mesh density whereby both nods exhibited the same characteristics (increase in stress led to a more proportionate increase in the mesh density)

From experiment 2: From the graph, it can be seen that 4 node graph starts at a high point and starts to decrease meaning that longitudinal stress at C reduces with increase in the mesh density though not proportionally. This will continue up to a certain point when it stops decreasing and remains constant with increase in mesh density (on the negative side of the longitudinal stress). 8 node on the other hand starts at a lower point in fact negatively then increases meaning that increase in longitudinal stress a C was followed by an increase in the mesh density though less proportionately.

This continues for a while until it reaches a point where increase in mesh density had not effect on the longitudinal stress at C. It still maintained the negative side. Both the 8 and 4 node crosses each other at a point where they both increase and decrease at a decreasing rate, respectively. This showed the exact point.

From experiment 3: The 4 node tends to increase at a decreasing rate. When mesh density increases, the longitudinal deflection increases less proportionately. On the other hand, the 8 node increase rapidly and reaches a point where it remains constant. The mesh density continues to increase while the longitudinal increases with the increase in the mesh density but reaches a point where it remains constant.

From experiment 4: The 8 node, the percentage error was decreasing with the increase in the mesh density. The decrease is less proportionally as it tends to approach the x axis. On the other hand, the 4 node mesh density increases with a corresponding increase in the percentage error. This increase in the percentage error increases at a decreasing rate until it reaches a point where increase in mesh density led to the decrease of the percentage error. Initially, it has been shown that both the 8 and the 4 nodes appeared to diverged from some common point though it was not the same point. This showed that initially, both the percentage error and the mesh density exhibited almost the same value.

From experiment 5: For the 4 node, there was a negative slope exhibited where by increase in mesh density was followed by a proportionate decrease in the percentage error. On the other hand, the 8 node also showed the decreasing level but at a decreasing rate. Increase in mesh density was accompanied by a decrease in the percentage error though less proportionately. Percentage error appeared to approach the X axis with the increase in the mesh density.

From experiment 6: The calculation was trying to compare the concentration factor for the finest finite element mesh. The ANSYS value was compared with the theoretical value both calculated in the results.. The result showed that there was a difference with a small margin of 0.005, thus proving the fact that the analysis was very exact.

From experiment 7: This experiment showed the same shape graph depicting an inverse solution for the stress against the nodes 4 and 8. They showed a decreasing graph the first phase showing steep gradient as it reduces when stress reduces with the increase in the node. Both the 8 and the 4 node showed almost the same results with small differences in their values though had the same shape of the graph.

Reference

Giuseppe, P. 2007. “The finite-element method, part I:R.L. courant: Historical corner”

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