INTRODUCTION
FEM methods allows us to do simulations to compute FEA models that helps us in optimization of the
models and products. In this assignment, the model of a cantilever beam shown below was modeled
on CAD and the effect of the loading shown simulated on a FEM software.
PROBLEM.
It is required to produce the model shown below and analyse it using a FEM software such as Ansys.
Figure 1. Model required to be made.
The FEA analysis was done on Ansys R3 2019. Inside the mechanical Workbench, a static structural
study was opened. The figure below shows the analysis study done. In Ansys, the analysis is divided
by steps. There is engineering data, geometry, model, set up solution, and results. The order in which
they appear should always be the order in which the study should be executed. One should set the
engineering data first before importing or drawing a geometry like so on. It is also the sequence which
the Ansys solver uses to solve the analysis.
Figure 2. Ansys’ static structural window.
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ENGINEERING DATA
The material was configured inside the engineering data. The material required for this task was steel.
By default, the material in ANSYS structural is structural steel. There was no need to change the
material but the material data was checked whether it had the same properties as those of the
required material, which was the same.
Figure 3. Material property configuration in engineering data
GEOMETRY
The geometry shown below was created inside the Ansys SpaceClaim. The geometry in this case is a
bit complex thus it would be better if the modelling was done on a 3D modeler. For this case I chose
the modeler which comes with Ansys.
Figure 4. Sketch on SpaceClaim.
The 3d model was create by selecting the appropriate geometrical section and then extruding using
the pull command to the appropriate length. Then the extrusions were combined selectively to form
certain solids. The solids were renamed components 1 to 6. These were the stiffeners. At the back of
the stiffer, a solid was pulled to thickness of 0.25 in. this represented the thin sheet of metal. A plane
was created passing through the middle of the thin sheet. All the components 1 to 6 were reflected
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to the other side of the thin sheet using the mirror command. This way the geometry required was
created.
Figure 5. 3D object made on Ansys.
The part was saved and the analysis tree updated.
MODEL
Having created the geometry, the model was edited by activating the model command in the
structural analysis tree.
Geometry.
The model was generated. The figure below shows the components of the geometry.
Figure 6.geometry inside the Model.
Materials
The materials were configured to the components. By default the material set in the engineering data
section above is automatically assigned to the components. However, it is a good practice to cross
check whether the correct material has been detected and assigned to the components. Also in case
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the model is an assembly, with different material, then it would be appropriate to assign the materials
to the components.
Mesh
An automatic mesh was applied for the model geometry. In ansys, one can select an automatic mesh,
a tetrahefra mesh, multisweep and hexagonal mesh. The automatic mesh seelcts the meshing method
that is best suited for the model automatically.
Figure 7. Mesh scoping method selection.
Also, an element size was applied on the mesh. The element sizing helps to reduce or increase the size
of the element on various geometries. For this task an element size of 0.05 inches (15.24 mm) was
selected and applied to all the solid components. This would be the size of the largest element size.
The behavior of the mesh was set to soft as shown below.
Figure 8.Mesh body sizing method.
The mesh was generated. The figure below shows the mesh generated.
Figure 9. Generated mesh.
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Boundary condition
The boundary condition describes the forces, moments, torques, pressures, thermal loads and other
loading which is applied to the model. For this study, a force of 20000 lbs was applied to the edges of
the vertical stiffener. The two forces are labelled A and B on the diagram below. Also the left end was
fixed so that the model forms a cantilever. This is shown by label C on the diagram below.
Figure 10. Boundary conditions (loads and fixed geometries).
RESULTS AND DISCUSSION
At result, one inserts the properties that he want to study. Results types such as stresses, strains,
fatigue, strain energy, probe tools, volume and contact tool. The figure below shows the window for
inserting results in to the study for simulation.
Figure 11. Inserting result types into the solution.
The results were inserted. We wanted to investigate the Von Mises stresses on the model. Therefore,
equivalent stress was inserted. Also, the residual deformation and the equivalent strain were inserted.
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Figure 12. Solution types inserted.
Deformation
The maximum deformation was 3.2282 mm at the free end. The minimum residual deformation was
zero on the constrained faces.
Figure 13. Residual deformation on the model.
The contours shows that the residual deformation of a cantilever beam increases with increase in the
distance x from the fixed end. The downward forces causes the beam to bend downwards as shown
on the figure above.
Von Mises stresses.
The maximum Von Mises stresses was 43.839 kpsi around the hole in the thin sheet. The minimum
Von Mises stress was 40.392 psi at the vertical stiffener at the extreme end.
Figure 14Von Mises stresses on the model.
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The distribution of stresses shows that the Von Mises stresses increase as you move towards the
restrained faces. Normally, if the model did not have the 10 in hole on the thin sheet, then the Von
Mises stresses would have occurred at the restrained faces. The stresses ranges from 40 psi to 48 kpsi,
all positive values. This means that the model is under compression.
Equivalent Strains
The maximum equivalent strain was 0.0015113 inch per inch at the edge of the circular hole.
Figure 15. Equivalent strains on the model.
Strain Energy
In order to determine which area had the most strain energy, a strain energy was inserted. The
maximum strain was 0.00025854 BTU at around the holes. The minimum strain energy was 1.549e-09
BTU at the furthest vertical stiffener from the constrained end.
Figure 16. Stain energy distribution on the model.
Areas with the high strain energy showed the regions where a mesh refinement should be done. The
regions with the yellow and red colors should be refined either by minimizing the element size around
them or by applying a contact mesh on the edges of the hole.
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Further studies shows that the model under the current loading will fail. Results of factor of safety
showed very small factor of safety in Von Mises stresses around the hole. The minimum factor of
safety in Von Mises stress is 0.8271 which is higher than 1 meaning that the model will fail.
Figure 17. Factor of safety in Von Mises stress.
From the figure above, we can see that only a small portion around the circular have a factor of safety
which is below 1. The rest of the regions have the factor of safety between 3 and 15. Optimization
should be carried out on the sheet either by changing the diameter of the holes or by increasing the
thickness of the sheet metal or by optimizing the topology around the hole. As it is currently, the beam
assembly will fail and will fail only because of a localized stresses in small regions around the hole. If
the hole would be used to support objects such as to hang items then the stresses would even be
higher.
REFERENCES
Panchal, Nitesh & Mohanty, Akash. (2016). “A Paper Review on Finite Element Analysis with Fatigue
Characteristics of Composite Multi-Leaf”. International Journal of Advance Research in Engineering,
Science & Technology. 3. 226-233. Retrieved from;
https://www.researchgate.net/publication/310486893_A_Paper_Review_on_Finite_Element_Analy
sis_with_Fatigue_Characteristics_of_Composite_Multi-Leaf . Retrieved on 11/12/2019.
