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Results:

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Again, it must be stressed that the mesh, geometry, boundary conditions and solver steps have been skipped in this exercise. You are instead given the solutions to the aforementioned problem simulated by ANSYS workbench. You are encouraged to explore these results and understand the different underlying assumptions of the analytical 1D Boundary Value Problem compared to the ANSYS 2D Boundary Value Problem. As you will see, the analytical approach can successfully account for the stresses in the middle of the bar, but fails to accurately model stresses at the point load and end effects.

Mesh:



The figure above depicts the mesh used to generate the results you see below. The domain is rectangle. Please note that although this problem has been solved using discrete elements, it is not uniformly discretized. A finer mesh is used in areas of predicted greater stress concentration. We want to be able to accurately simulate the end effects of the bar.

Displacement:



Please note that the displacement throughout the bar is not uniform. There is no displacement at the end attached to the wall and the displacement increases until the maximum at the point load as we move along the bar.

Sigma_x:



Note here that the stress in x direction is not constant as assumed in the analytical method. The point load at the end of the bar means the stress will be greater on the top and bottom of the bar. There are also higher stresses in the area close to the wall.

Sigma_y:



The analytical method assumed a long bar, therefore by definition, the stresses in the y direction are assumed to be zero. From the simulation, it is clear to see this is obviously not the case.

Tau_xy:



Von Mises:


 

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