Use of Fea Siemens Nx 7.5 - Part 5 - Mathematics Essay Example

Section 2 Stress Concentration Analysis Problem Targets: * Describe the steps involved in creating the preliminary FE model and why it is necessary. * Show the development of the final FE model including vague step-by-step instructions. * Describe the application of the final FE model and how it can be beneficial in its purpose. Brief (Provided In Assessment 1) A uniform Steel flat bar (material Modulus of Elasticity 200 GN/m2, Poisson’s Ratio 0. 3) of width W 400 mm and a length of 4000 mm is restrained as appropriate at one end and under an axial tensile load of 500 KN applied to the other end face.

It has been initially designed with a thickness of 50 mm. This gives a hand calculated stress value of 25 MN/m2, which is 1/8 of the material’s Yield Stress, of 200 MN/m2, giving a factor of safety of eight, which is deemed to too conservative. The flat bar now requires stepped down in size from W to h, forming a shoulder with fillet, at the middle of the bar along its length. For a given radius of fillet, determine the (new) minimum thickness of t capable of withstanding the same tensile force with the factor of safety of four using finite element analysis.

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Assume Von Mises failure criterion applies, i. e. the maximum Von Mises (un-averaged) stress should not exceed 50 MN/m2. Your final thickness must be an integer millimetre value to use standard size material. Brief Assessment The problem is that with a wall thickness of 50 mm the maximum stress at the radius point will be too high and is in too much risk of distorting or failing. The factor of eight is too high and needs to be reduced to a factor of four. Brief Proposal There are two main changeable features in this arrangement, which include the radius and the general thickness.

It is assumed that changing the thickness will have a more direct effect on the results and in this scenario that is the only factor which will change. However realistically both these factors would be changed to optimize for design/material/costing. To bring the factor of safety down to four the thickness will be altered to the point where the maximum stress in the model is 50 MN/m? which is twice what it was previously hence ? of the yield stress of steel (200MN/m? ). The thickness of the material is calculated analytically and then simulated and verified in a FEA (Finite Element Analysis) model.

This could be done entirely through FEA i. e. trial and error; however the result would need to be proven, therefore it is logical to do this step before proceeding to the final FE model. Development Of The Preliminary Model The first stage of creating an FEA solution in this case is realising what is wrong with is initially. Therefore the original model with a thickness of 50 mm is drafted. Some of the details for the original design are not listed (such as the radius) therefore the results will likely differ to the ones calculated previously.

This makes the exercise less useful, but the general profile and set up of the model can be determined in this step and are easily altered later on. The model is based on the following figures: P| w| h| r| t| L| 500 kN| 400 mm| 200 mm| 6. 5 mm| 50 mm| 4000 mm| Figure [ 1 ] General Profile- Stays The Same Throughout Figure 1 shows the profile of what will be extruded to create the model from the above dimensions. This profile stays the same throughout. Figure [ 2 ] Mesh Detail After starting an advanced simulation; the next step is to right-click the model in (simulation navigator) and select start new FEM and simulation.

Following this a double-click on the fem file will open up the mesh options. A 3D mesh is then applied to the part which after selecting auto-fit will size the mesh to roughly 80 mm. Then using mesh control a finer mesh can be applied to the point of interest, which is the radius. These meshes need an assigned material; this is done using the collector and the material steel should be applied with a Young’s Modulus of 200 GN/m? and Poisson’s ratio of 0. 3. Figure [ 3 ] Simulation Preparation Figure 3 shows the model pinned and a force pulling on the thinner h section.

This is done by double-clicking the simulation panel and applying a fixed translation constraint and adding a force in the shown direction. This part is now ready for solving. Figure [ 4 ] Von Mises Display – T=50 mm The Von Mises display shows clearly the main factors for its weakness: the radius and the thickness. The maximum stress is very high in comparison to its materials yield stress and this is the factor which needs to be reduced. Calculating Desired Thickness The thickness could easily be calculated through trial and error and a fairly accurate result could be found in a few minutes.

However the mesh type can either take a long time to simulate or not give accurate enough results. This is the key reason why analytical calculations are to be configured at this point. The FEM model is great for finding results fast, but in the end a good engineer would cover their tracks by ensuring their results are feasible. Calculations Figure [ 5 ] – Found at: http://www. mae. ncsu. edu/eischen/courses/mae316/docs/Appendix_C. pdf Figure [ 6 ] – Found at: http://www. aaronklapheck. com/Downloads/Engr112_Handouts/ENGR112%20Solutions/02-07ChapGere%5b1%5d.

pdf The information in figure 5 is used to calculate the k value, which is used to calculate max stress and avg stress using the information which is already known. The thickness is found by adopting the method used in figure 6 and simply reversing the order in which the steps are taken. ?max=k ? ?avg ?avg=PA ? ? max=k? ( PA ) k=1. 1(6. 5200)-. 321=3. 304 ?avg=50? 1063. 304=15,133,171. 91 N/m2 A=P? avg=500,00015,133,171. 91=0. 03304? ?T=0. 03304h=0. 1652 m Therefore for the desired safety factor the thickness would need to be 165.

2 mm, however it is requested that only an integer can be selected which means the desired thickness is rounded down to 165 mm. Solved Simulation Figure [ 7 ] Von Mises Display – T=165 mm After changing the thickness to 165 mm the simulation was within 0. 5 M/Nm? of 50 M/Nm?. The next step is to adjust the mesh making it finer as to show a more accurate result. The result shown in figure 7 has come up with a maximum stress of 49. 88 M/Nm? and the simulation takes just over a minute to run. If the mesh is made any finer the simulation time take longer, so the assumption is made that after further analysis the accuracy would increase.

Conclusion Using FEA to run analysis on this part is useful in many ways. First of all it gives a perspective view of the problem which a free body diagram cannot even compare. Where a change in dimension would eat up time in hand calculations, a model can be changed in a matter of seconds and optimized for the best results. This is beneficial as rather than calculating first and making changes second; it is just a case of optimization and then checking manually afterwards. A final great feature with FEA is the way you can demonstrate complicated features with a simple colour coded drawing or animation.

This means that you can show and quite easily explain; something complicated to a person who knows absolutely nothing about the subject. References Figure 5 Stress Concentration Factors-2013. (Online) http://www. mae. ncsu. edu/eischen/courses/mae316/docs/Appendix_C. pdf Figure 6 Stress Concentration-Aaron Klapheck. -2011-2013. (Online) http://www. aaronklapheck. com/Downloads/Engr112_Handouts/ENGR112%20Solutions/02-07ChapGere%5b1%5d. pdf Calculation Hibbeler, R. C. (2011). 4. 9 Residual Stress. In: Disanno, S Mechanics of Materials. Boston: Pearson Prentice Hall. p164-168.

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