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Stress analysis of a cantilever beam using FDMby rajaditya
Tags: cantilever beam, finite difference, stress analysis, stress beams, stress calculation 
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Jun2513, 06:49 PM

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I am a CSE researcher with a not so in depth background of physics. As a part of my research in object modelling, I am trying to computationally figure out the stress for various objects by using Finite Difference Method (not FEM which is the defacto standard for stress analysis). The reason for this has to do with the other part of my research.
Anyhow I have written and solved the 3D elastostatic Lame equations and calculated the Von Mises stress. This is the problem I am facing : When I am doing this for a 2D beam, the stress is calculated correctly. The Stress gradually decreases from the hinge point to the other parts. But in 3D the calculations are not correct as I am seeing the maximum Von Mises stress only in the middle portion of the beam instead of at the starting. I am only considering the weight of the grid cell at each grid point for the external force. (in the Z direction). The displacements at the hinge points are all 0. My question is : What changes in the stress computation of a cantilever beam between a 2D and a 3D formulation. Or am I ignoring some reactive forces which are of importance in 3D that is likely causing the maximum mises stress to shift to the center of the beam. (Of course it is entirely possible that my code is wrong but in that case it should have given haywire results for 2D case also). If my question is not clear, I can supply as many details as required. Any inputs will be greatly appreciated. 


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