Problem Statement
Static Analysis of Plate (ANALYSIS OF A PLATE WITH A CIRCULAR HOLE BY Ansys)
Abstract:
Using the finite element method, the influence of the initial tension of a rectangular plate with a
cylindrical hole on the distribution of stresses and displacements around the hole, created by
additional loading, on a plate with a round hole subjected to uniform stress is studied. . It is believed
that the first stresses are created by forces acting on opposite ends that are equally stretched. The
cylindrical hole in the thick plate is also expected to extend between and run parallel to these ends.
The purpose of this study is to see how different meshes affect the results of a uniformly stressed
plate with a round hole.
Introduction:
In engineering, a plate structure with holes is commonly used. Making holes in the plate might be
done for a variety of reasons, including inserting bolts and other connections, as well as lowering
weight without impacting mechanical qualities. To study the plate subjected to max, we used the
finite element based simulation programme Ansys. There is a lot of tension and stress in our lives.
The plate's geometric characteristics and loads are listed below. A rectangular plate construction with
the left side fixed and the right side subjected to a 50N stress. In the centre of the plate is a round
hole.
The following presents a specific structure size, force size, and material parameters of structural steel
to better replicate the conditions and validate the validity of the data. The mesh parameter is then
defined, and the grids are generated. We set a rather thick mesh around the hole since the tension
surrounding it is relatively concentrated. The following are the mesh elements and nodes. There are a
total number of nodes and elements created.
Next, add two boundary conditions: one displacement limitation on the left surface and a 50N force
on the right surface. All of the analysis parameters are now configured. When you click the Solve
button, the results will appear shortly. Add total displacement and X normal stress result objects after
the computation. Evaluate the objects that have been created as a consequence of the process. The
contour that results is shown below.
Results:
Solidworks model
Boundary conditions
For mesh size 11.25
mm
For mesh size 9.45 mm
For mesh size 6.85 mm
For mesh size 4.90 mm
For mesh size 2.75 mm
STUD
Y
Mesh
1
Mesh
2
Mesh
3
Mesh
4
Mesh
5
MAX.
VON
MISES
STRESS(M
Pa)
1.681
ELEMENT
SIZE(mm)
# OF
NODES
# OF
ELEMENTS
# OF
DOF
MAX. STRAIN or
DISPLACEMENT(
mm)
11.25
1395
991
2
4.207E-04
9.45
1992
1037
2
4.212E-04
1.695
6.85
4391
2476
2
4.220E-04
1.719
4.9
10402
6190
2
4.224E-04
1.886
2.75
49491
32059
2
4.226E-04
1.899
This screen shoot for number of nodes and number of elements:
DOF vs Displacement
2,5
4,23E-04
4,23E-04
2
4,22E-04
1,5
4,22E-04
1
4,21E-04
4,21E-04
0,5
4,20E-04
0
4,20E-04
1
2
3
# OF DOF
4
5
MAX. STRAIN or DISPLACEMENT(mm)
max stress and strain(displacement) behalf of
DOF
4,23E-04
1,95
4,23E-04
1,9
4,22E-04
1,85
1,8
4,22E-04
1,75
4,21E-04
1,7
4,21E-04
1,65
4,20E-04
1,6
4,20E-04
1,55
2
2
2
MAX. STRAIN or DISPLACEMENT(mm)
2
2
MAX. VON MISES STRESS(MPa)
DOF VS Stress
2
2
1,681
1,695
1
2
# OF DOF
2
2
2
1,886
1,899
4
5
1,719
3
MAX. VON MISES STRESS(MPa)
Conclusion:
We can conclude that when the grid size decreases, the number of nodes and elements grows. As a
result, the accuracy of the results is improved.
As a result, we see that different meshes provide a wide variety of results. As you can see from the
table above, the meshing methodology has a big impact on FEA results. The symmetrical bar grid
(middle bar grid without puck) provides symmetrical response on graphs, but other grids do not
provide the same degree of symmetry. The influence of mesh quality factors on the results will also
be considered.
Reference:

Ulku Babuscu Yesil,“The effect of the initial stretching of the rectangular plate
with a cylindrical hole on the stress and displacement distributions around the
hole”, Yıldız Technical University, Faculty of Chemical and Metallurgical
Engineering, Department of Mathematical Engineering, Davutpa, sa Campus,
34210, Esenler, Istanbul-TURKEY Received 19.03.2010.

Warren C. Young And Richard G. Budynas, “Roark’s Formulas for Stress and
Strain”, McGraw-Hill, New York Chicago San Francisco Lisbon London, Madrid
Mexico City Milan New Delhi San Juan Seoul, Singapore Sydney Toronto.