CHAPTER 6 Discussion of Results
6.7 Overall Discussion of Results
As expected, the premium commercial packages readily solved all test cases. ANSYS and NX were able to generate results showing acceptable accuracy for every test case. For the most part, the no-cost/low cost FEA packages also dealt well with the generation and solution of the test cases.
For Test Case 1: Grid Point Load on an Articulated Truss, all packages besides SimScale were able to generate results. Looking at the X-direction displacement of what is labelled as Node C, none of the packages seemed to be able to generate accurate solutions. We see the largest deviation of 50.1 % from Mecway, a deviation of 49.15% from ANSYS and the smallest deviation of 9.35 % from Siemens NX. Bearing in mind that the target solutions are based on results verified computationally, it could be argued that this particular target solution may be inaccurate. The results for the remaining nodes form all the packages fell within an acceptable accuracy range.
Looking at Test Case 2: Thin Shell Wall in Pure Bending, it caused problems for Z88 and SimScale as 2-D meshes could not be created and suitable 3-D meshes could not be produced. The premium packages both produced essentially exact solutions which showed very little deviation as the mesh size was reduced. Looking at the target results in the test case data, it could be argued that round-off error is present as the test case data is presented with only two decimal points, whereas the packages tended to yield results with more than two decimal points. Code_Aster and Mecway produced displacement results with acceptable accuracy that showed little variation as the mesh size was reduced. We see the stress results from both packages remain within an acceptable accuracy throughout the mesh refinement process. However, the stress results do appear to fluctuate. An explanation for this is offered by (Kurowski, 2001). When a coarse mesh is used, larger elements in an FEM model tends to overlook the localized areas of high stresses. Using smaller elements reveals the higher stress concentrations at these areas. As element size is reduced, there may be no sign of convergence.
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In Test Case 3: Axisymmetric Pressure Vessel the inability for SimScale and Z88 to create a 2-D mesh was the reason for a 3-D model being used. The 3-D representation of the model could potentially affect the simulation results. Both packages were able to generate solutions of acceptable accuracy eventually. The remaining packages were able to analyse this test case in axisymmetric environments and generate acceptable solutions with some mesh refinement. It can be seen that all of the packages were able to generate solutions within a 0.5% deviation of the target solution within three mesh refinements.
For Test Case 4: Internal Pressure on Thick-Walled Spherical Container, all the packages besides Z88 were able to analyse the test case and yield the required stress and displacement outputs. The overall displacement results across all packages fell within acceptable accuracy and showed little deviation. For the circumferential and radial stress results, it appeared that the accuracy of the solutions was improved through mesh refinement and all packages were able to yield acceptable results with the smallest mesh size used. Noting that the stress value does not give a good indication of convergence, and taking into account that the displacement results showed apparent conversion for the mesh sizes used, it was deemed unnecessary to refine the mesh further.
All packages were able to analyse Test Case 5: Flat Bar with Stress Concentration and yield solutions. It is seen that the stress result generated by each package was heavily influence by the mesh size. Noting that the purpose of this test was to asses a packages capability when dealing with stress concentrations, we see that the results tended towards a more accurate solution as the mesh size was reduced. There was no evidence of a converged solution and no sign that one could be obtained considering once again that stress is not necessarily a good measure of solution convergence. It was decided that given all of the solutions yielded an acceptable accuracy solution, there was no need to further refine the mesh in pursuit of a more accurate solution.
All of the packages were able to analyse Test Case 6: Large deflection of a Z-Shaped Cantilever Beam under End Load. NX 10, Code_ Aster and Z88 did not used the prescribed incremental loading values but rather applied a linearly ramped load up to the full value over the increments. All this affected was the rate that the geometry deflected. Looking at the final deflection value from each package we see that the packages have generated solutions with high accuracy as the deviations range from 0.45 % to 0.21 %.
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For Test Case 7: Plastic Deformation of Tensile Test Specimen, all packages besides Z88 were able to generate desired solutions. The material data and stress-strain curve used was chosen as the median of a small sized data set. This could have affected the accuracy of the solution as it may not be the curve that best represents the actual material. The engineering stress and strain were converted to true stress and true strain using formulae that are only valid up to the UTS of a material. The target solution curve was chosen as it was the median of a small sized data set. The results yielded by the packages showed high correlation with the target response curve. The normalized root mean square deviation ranged from 2.24 % to 2.8% across the packages. It can be seen that in NX, Code_Aster and SimScale, the package solves for the stress output up to the UTS specified in the flow curve and then assumes a perfectly plastic material beyond that point. It would appear that ANSYS and Mecway (using the CalculiX solver) take into account geometrical effects and thus a dip in the stress value starts to appear beyond the point of the UTS.
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