COMSOL Multiphysics Labaratory Report

Mehmet Kelleci

30.03.2013

Question 1

Four distinct materials are used for calculations of stress concentration fac-tors. The four materials are aluminum 3013-H18, Tungsten, Silicon, StructuralSteel. To make healthy comparisons and stay consistent with the logic of con-trolled experiment, while calculating stress concentration factors for differentthicknesses, same thickness varieties are used for all four materials. Results areas follows.

Material Thickness[m] Applied Stress[N/m2] Stress Concentration FactorAluminum 3013-H18 0.005 10000 3.43Tungsten 0.005 10000 3.426Structural Steel 0.005 10000 3.4389Silicon 0.005 10000 3.422

Material Thickness[m] Applied Stress[N/m2] Stress Concentration FactorAluminum 3013-H18 0.05 10000 3.578Tungsten 0.05 10000 3.5223Structural Steel 0.05 10000 3.5478Silicon 0.05 10000 3.6658

Material Thickness[m] Applied Stress[N/m2] Stress Concentration FactorAluminum 3013-H18 0.1 10000 3.62Tungsten 0.1 10000 3.5631Structural Steel 0.1 10000 3.6203Silicon 0.1 10000 3.4963

Material Thickness[m] Applied Stress[N/m2] Stress Concentration FactorAluminum 3013-H18 0.15 10000 3.66Tungsten 0.15 10000 3.5989Structural Steel 0.15 10000 3.6692Silicon 0.15 10000 3.5088

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Material Thickness[m] Applied Stress[N/m2] Stress Concentration FactorAluminum 3013-H18 0.2 10000 3.5864Tungsten 0.2 10000 3.5375Structural Steel 0.2 10000 3.5864Silicon 0.2 10000 3.4731

The procedure applied during the obtain period of these datas is fix defineone edge of the given figure as fixed constraint. A boundary load applied to theopposite edge. Al the parameters are kept constant except thickness as men-tioned above. It is important to emphasize the importance of boundary load.As it can be seen on the table in COMSOL, the unit for the boundary loadis N/m2. Which means that, the software keeps the specimen under the samestress for all variations of thickness. Just like the logic is used in strain-straindiagrams, while calculating the stress concentration factor, it would be muchuseful to use stresses instead of using the magnitude of applied point load overnarrowest cross-sectional area. As it can be seen in the tables given above, forthe same values of stresses and different values of thicknesses for different typeof materials stress concentration factor is very very close to each other. Theconclusion can be made out of here is as follows. Stress concentration factor isnot a strong function of material property, it is highly dependent on the materialgeometry.

Increased Mesh Number:For material structural steel, a more extensive calculation is done by varyingthe mesh number. Calculations are started from extremely coarse and end atfiner. Extremely fine option cant be used because of computer memory issues.While these computations are done, the geometry of the specimen kept same.Because aim is to compare the accuracy of the results with changing number ofmesh. Thickness is taken t=0.1m.

Mesh Option Thickness[m] Applied Stress[N/m2] Stress Concentration Factor CPU TimeExtremely Coarse 0.1 10000 3.4918 4 sExtra Coarse 0.1 10000 3.8368 2 sCoarser 0.1 10000 3.6324 2 sCoarse 0.1 10000 3.6924 2 sNorma 0.1 10000 3.6203 3 sFine 0.1 10000 3.5327 3 sFiner 0.1 10000 3.5766 10 s

As the number of meshes are increased the required time for computation getslonger. The column stress concentration factor does not have any meaningfulmessage for the reader. Because there is not any correlation between the re-sulting values. They once gets bigger and gets smaller. The reason should beas follows. The simulation software COMSOL uses these meshes to solve thegoverning equations of stresses in the location of these meshes. As the numberof meshes are increased, the software is approaching to more accurate values,

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because of number of calculations are increased. Increased number of calcu-lations give more detailed information. For instance, while extremely coarseoption gives a rough value, extremely fine option gives a very accurate value.Of course, there is not a significant change between the datas according to themesh numbers, but this is not a detailed or complex geometry situation.

General Representation of Stress Tensor for Model Simulated:

=

x xy xzyx y yzxz yz z

.Numerically in Newtons:

=

3.6764 104 1.0484 104 2395.8

6997.4 7716.3 1.0484 1042395.8 1799.1 6997.4

.

Question 2

To get various type of datas, this time specimen is exerted to a stress 5000N .Geometry is same with the first question with t=0.1m.

b/a Thickness[m] Applied Stress[N/m2] Stress Concentration Factor2 0.1 5000 6.372.5 0.1 5000 7.43923.3 0.1 5000 9.47425 0.1 5000 13.67810 0.1 5000 41.82420 0.1 5000 32.1525 0.1 5000 48.5833 0.1 5000 33.67610000 0.1 5000 Does not executed.

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Question 3

The table given below shows the von-Mises stresses for different value ofmean radii. The values are taken from the scale in COMSOL.

Rmean von-Mises Stress[N/m2] Sigma/P

20.5 1660.9 16.60922.5 1539 15.3924.5 1425.6 14.25626.5 1398.3 13.98327.5 1361 13.6130.5 1290 12.9

The Plotting:

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In conclusion, through this lab work, four different materials are inspectedwith the help of COMSOL. Geometries were defined in the manual, and withholding the material and changing the geometry and conversely, the effects ofatomic structure and geometry of the object to stress concentration are in-spected. Methods of solid modeling is introduced. Usage of computer softwaressuch as drawing, computation and programming, simulation, typing programsare used as an integrated whole in this lab work. The most important infor-mation which is gained through these calculations is that stress concentrationfactor is a geometric peculiarity.

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