Date: Thu, 28 Mar 2024 16:09:12 -0500 (CDT)
Message-ID: <214467525.3756.1711660152316@cornell1-cos-conf1.managed.contegix.com>
Subject: Exported From Confluence
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Numerical 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 genera=
te the ANSYS solution. The domain is a rectangle. This domain is discretize=
d into a number of small "elements". Recall that ANSYS solves the BVP and c=
alculates the displacements at the nodes. A finer mesh is used near the lef=
t and right ends where we expect greater stress concentration. We have chec=
ked that the solution presented to you is reasonably independent of t=
he mesh.
Units
Set the units for the results display by selecting Units > Metric (mm, kg, N, s, mV, mA) . The displacements will be reported in mm and=
the stresses in N/mm2 which is equivalent to MPa.
<=
/p>
D=
isplacement
To view the deformed structure, click on =
Solution > Displacement in the tree=
outline. The black rectangle shows the undeformed structure. The deformed =
structure is colored by the magnitude of the displacement. The displayed di=
splacement distribution is calculated by interpolating the nodal displaceme=
nts. Red areas have deformed more and blue areas less. You can see that the=
left end has not moved as specified in the problem statement. This means t=
his boundary condition has been applied correctly. The displacement increas=
es from left to right as we intuitively expect. There is also not much vari=
ation in the y-direction. So we can conclude that the model has been constr=
ained properly.
Note the extremely high deformation near the point load. This extremum i=
s unrealistic and should be ignored (there are no point loads in reality).<=
/p>
To view the Poisson effect (shrinking in the y direction), zoom into the=
top-rightright corner by drawing a rectangle around the region with the right mouse button.
You can do this multiple times to zoom in more. You do indeed see the sh=
rinking in the y-direction as expected but it is small for this model.
You can restore the front view of the entire model by right-clicking in =
the background and choosing Vi=
ew > Front .
=
Note that you can zoom in and out using the middle mouse wheel. You can =
translate the model by clicking on the Pan button and dragging the=
model with the left mouse button. There are also a bunch of zoom options n=
ext to the Pan button.
sigma_=
x
The stresses are derived from the nodal displacements using Hooke's law.=
In the following video, we look at the sigma_x distribution in the interio=
r and at the boundaries and compare the ANSYS values to the values expected=
from the analytical solution and traction boundary conditions.
Summary of the above video investigating sigma_x:
- Click on probe and hover over the bar. Using the probe may tell y=
ou the stress associated with a specific point on the bar.
- To view the less noticeable stress contours, click on the scale t=
o edit. In this video, the orange (2nd highest value) was changed to 250 an=
d the blue (2nd lowest value) was changed to 50. The contour map changed to=
display the subtle difference in sigma_x.
In the video, we saw that ANSYS's values for sigma_x matches with:
- The analytical solution in the interior (away from the left and right b=
oundaries)
- Traction boundary condition for sigma_x at the right boundary
Note that sigma_x at the location of the point load is infinite. So as the=
mesh is refined further, sigma_x at the point load will get larger and lar=
ger without bound.
sigma_=
y
Next, let's take a look at sigma_y. Click on Solution > sigma_y in the tree =
outline. Again, probe values in the middle as well as at the ends. Check th=
at:
- The value away from the boundaries is close to zero as expected from th=
e analytical solution. It is not exactly zero because of round-off errors.<=
/li>
- The value at the top and bottom boundaries are close to zero. This agre=
es with the boundary condition at these boundaries since the traction has t=
o be zero at these free boundaries. In other words, the normal component of=
the traction acting on these surfaces is sigma_y and that has to =
be zero since the traction on these free surfaces is zero.
- There is significant deviation from the analytical solution at both end=
s. The analytical solution breaks down at these ends because of the additio=
nal assumptions that we made. Note that there are areas where sigma_y is ne=
gative i.e. compressive.
=
tau_xy<=
/h3>
We expect tau_xy to be zero away from the ends. Near the ends, since sig=
ma_x and sigma_y are non-zero, we expect
Plot tau_xy, look at the range of values and use Probe to check actual v=
alues. Are the above statements valid?
Equivalent Stress (Von Mises):
The Equivalent or Von Mises stress is used to predict yielding of the ma=
terial. We can see that the analytical solution under-predicts the maximum =
equivalent stress. Thus, one would need to use a large factor of safety if =
using the analytical result while designing such a structure. One would use=
a factor of safety with the FEA result also but it does not have to be as =
large.
<=
/span>
Go to Step 3: Verification and Val=
idation
Go to all ANSYS L=
earning Modules
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