Question
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I. Problem 1: Tangential, Radial & Longitudinal Stresses in a
Cylindrical Vessel
This problem was analyzed by using both 2D and 3D Analyses. The set-up and results for each analysis is given below.
A. 2D Analysis
The cylindrical vessel can be analyzed using 2D analysis. For this problem, sketch of the rectangular cross section was created with the given dimensions. This is shown in Fig 1.
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Figure 1: Rectangular cross section with its mesh
After 2D rectangular surface was generated, it was exported to Mechanical and its
2D behavior was set to ‘2D axisymmetric’. After mesh was generated, temperature boundary conditions were applied to the left and right edge of the rectangle. For this analysis type, the left edge of rectangle represents the inner side of the vessel whereas the right edge represents the outer side. The following thermal solutions were retrieved.
i. Temperature Distribution
Figure 2: Temp. Distribution along thickness of vessel
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ii. Temperature at x = 0.2788 in
A new coordinate system was set with its origin at (0.2788, 0). Using a temperature probe, with scoping method set to the new coordinate system called “Temp. Location”, the temperature at the specified distance was determined.
Figure 3: Value of Temp. At x = 0.2788 in
iii. Max. and Min. Tangential Stress In order to find thermal stresses developed within the vessel, the problem was treated as a coupled problem. Importing results from thermal analysis, a new static structural analysis was carried out. Frictionless supports were applied at the opposite ends of the rectangle to limit deformation in the z-direction. The generated result is shown below.
Figure 4 : Tangential Stress at inner layer (left edge) and outer layer (right edge)
FEA Results
(psi) Theoretical
(psi)
% Difference
419.93 420 0.016666667 -194.59 -194 0.304123711
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iv. Max. Radial Stress
Figure 5: Max Radial Stress
The max radial stress was determined to be 85.981 psi
FEA Results
(psi) Theoretical
(psi) % Difference
85.981 87 1.171264368
v. Max. and Min. Longitudinal Stresses
FEA Results
(psi) Max. 31380 Min. 30765
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B. 3D Analysis
The cylindrical vessel was analyzed using 3D analysis. For this problem, half of the cylindrical vessel was sketched and extruded by 5 in. This is shown in Fig 1.
Figure 7: 3D half vessel with mesh
Figure 6: Longitudinal Stresses
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After 3D half cylinder was generated, it was exported to Mechanical. After mesh was generated, temperature boundary conditions were applied to the inner and outer walls of the cylinder. The following thermal solutions were retrieved.
i. Temperature Distribution
Figure 8: Temp. Distribution along thickness of vessel
ii. Temperature at x = 0.2788 in
A new coordinate system was set with its origin at (0.2788, 0). Using a temperature probe, with scoping method set to the new coordinate system called “Temp. Probe”, the temperature at the specified distance was determined.
Figure 9: Value of Temp. At x = 0.2788 in
In order to find thermal stresses developed within the vessel, the problem
was treated as a coupled problem. Importing results from thermal analysis, a new static structural analysis was carried out. Symmetry condition was set at the two faces that are parallel to the plane of cut of the cylinder.
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Frictionless supports were applied at the two bottom faces of vessel as shown below:
Figure 10: Frictionless support faces
Displacement boundary condition was applied to the opposite faces in the longitudinal
direction to restrict deformation in the z- direction.
Figure 11: Displacement applied at face
The generated result is shown below.
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iii. Tangential Stress ( Inner Layer)
Figure 12 : Tangential Stress at inner layer
iv. Tangential Stress ( Outer Layer)
Figure 13: Tangential Stress at the Outer Wall
FEA
Results (psi)
Theoretical (psi)
% Difference
418.78 420 0.29047619 -194.54 -194 0.278350515
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v. Max. Radial Stress
Figure 14: Radial Stress
The max radial stress was determined to be 86.121 psi
FEA Results
(psi) Theoretical
(psi)
% Difference
86.121 87 1.010344
vi. Max. and Min. Longitudinal Stresses
Figure 15: Longitudinal Stress
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FEA Results
(psi) Max. 31380 Min. 30765
It can be observed that the results for longitudinal stress are exactly alike for both 2D and 2D analysis.
II. Problem 2: Development of Cortical/Trabecular Bones around Dental Implants
The dental implant was downloaded and the cortical/ trabecular layers were sketched and generated around the implant in the Design Modeler of ANSYS. The model of the bone is given in the picture below:
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Figure 16: Model
Figure 17: Trabecular Bone
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Figure 18: Cortical Bone
** The following volume percentage data is calculated from earlier results that were generated without convergence. The current solution with convergence is taking significant amount of time, therefore, I am presenting volume percentages of earlier results below instead. Trabecular Bone
No. of Elements Tot. Elements Vol. % Disuse 4 149838 0.0027 Adapted 118751 149838 79.2529 Mild Overload 30947 149838 20.6536 Pathological Overload 136
149838 0.0908
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Cortical Bone:
No. of Elements Tot. Elements Vol. % Disuse 1107 32319 3.43 Adapted 15432 32319 47.7 Mild Overload 14976 32319 46.3 Pathological Overload 804
32319 2.49