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Results:
Before we explore the ANSYS results, let's take a peek at the mesh.
Mesh:
Click on Mesh (above Solution) in the tree outline.This shows the mesh used to generate the ANSYS solution. The domain is a rectangle. This domain is discretized into a number of small "elements". For each element, ANSYS approximates how the structure responds to the forces acting on the element. A finer mesh is used in areas of greater stress concentration. We have checked that the solution presented to you is reasonably independent of the mesh.
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. If we were to pick a section near the middle of the bar, our analytical result would be nearly accurate. The solution, however, no longer applies when considering the stresses at the wall, and the stresses near the point load. Obviously, the stresses in the x-direction maximizes at the point load.
Sigma_y:
The analytical method assumed a long bar, therefore by definition, the stresses in the y direction are assumed to be zero. Since this bar does have width, the stresses in the y direction are symmetrical about the middle axis. Note that there are areas where sigma_y is negative. This is a consequence of deformation along the x-axis. Since no extra material is being added, stretching the bar in the x direction would cause a contraction of the bar in the y-direction, and therefore compressive stresses in the y direction.
Tau_xy:
Von Mises:
Von Mises stress is used to predict yielding of the material. We can consider the maximum and minimum von mises stress as the critical design points. For example, in this case, we would want to design our beam with reference to the area around the point load to prevent reaching limit load of the material anywhere on the bar.
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.