Week 5 Sphere pressing on a plate
Sphere pressing on a plate
OBJECTIVE: The objective of this challenge is to perform a static structural analysis and to simulate a sphere pressing on a plate by using Structural steel for both sphere and plate but the material of the plate must be Non Linear. And to Press the sphere onto plate 4mm downwards and retract it, as well as we have to capture the plastic peformation of plate.
SOFTWARE USED: ANSYS Workbench 2021 R1 and ANSYS Mechanical for Analysis.
INTRODUCTION:
A sphere is a geometrical object in three-dimensional space that is the surface of a ball. Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space. A plate is a geometrical object, which is having some thickness and it is treated as solid. In this challenge we have both sphere and plate, we have to know the deformation of the plate, so the plate is assigned with non linear structural steel, while the sphere is assigned with general strutural steel material.
Fig.1: Sphere on a Plate
PROCEDURE:
1. Open the ANSYS Workbench software. Under the Analysis system select the Static structural and wait for few seconds to pop up the window, which contains Engineering data, Geometry, Model, setup, Solution and Results.
2. Rename the static structural as Sphere plate Plasticity.
3. Under geometry import the Sphere pressing on a plate model.
4. Update the model by right click and edit the Model for Preprocessing.
5. Wait for few seconds and ANSYS Mechanical will open as shown below. As the given model is two planes of symmetric region, we has used only quater part of whole geometry. So that the simulation time will be reduced as well cost will be reduced. Under geometry rename it as sphere and flat plate.
Fig.2: Quater part of whole geometry of Sphere on a Plate
6. Assign the material to the model, as in our case we have general structural steel and non-linear structural steel, we have concentrated on deformation of plate so assign the structural steel material to the sphere and non-linear structural steel to the plate.
FIG 3: Material properties of a structural steel
FIG 4: Material properties of a non-linear structural steel
7. Frictional contact between the Sphere and the plate is Defined with a frictional coefficient of 0.74 based on the standard table. So delete the default contact and create a new manual contact region and select th face as shown below.
Fig.5: Frictional contact between the Sphere and the plate
8. Insert a fixed joints for the plate in order to act stable . So click on Static structural, go to insert and select Fixed support. select the face as shown in below.
Fig.6: Fixed Support
We have to dispalce the sphere onto plat by 4mm, so click on Static structural, go to insert and select Displacement. select the face as shown in below. Give the values for the displacement of sphere as shown in the below table as well as in order to know wether the plate is deformed plastically add to more step with o value, so that the sphere will come to its oriinal position.
Fig.7: Displacement
9. In ANSYS automatic mesh will be performed with Default mesh size and change the mesh size as 1mm for the plate and 2mm for the sphere (i.e Ansys student version will have a limted number of elements and nodes.)
As it is a solid we have to use element type as tetrahedrans.So click on mesh and select the insert option. Under insert option select the method and slect the gemetry as well as under the method, select the tetrahedrons.
FIG 8: Selecting Bodies for 3D Meshing
FIG 9: 3D Meshing
10. As we had choosen quater part of the whole model we have make symmetic for the respected faces. So from the tool bar insert symmetry, choose the faces as shown below and select the axis normal to respect face.
Fig.10: Selecting Faces for symmetry
11. Analysis settings Change no. of steps as 4, large deflection on, solver type as direct.
Fig.11: Analysis settings
12. Now request for the outputs such as equivalent stress, equivalent elastic strain, total deformation and plastic strain.
13. SOLVE the solution and we can see the simulation run under soluion information.
FIG 12: Solver output
Fig.13: Force Convergence
RESULT:
Simulation results for Sphere pressing on a plate is as shown in below.
Fig.14: Equivalent stress on plate
Fig.15: Equivalent elastic strain on plate
Fig.16: Equivalent stress on Sphere
Fig.17: Equivalent elastic strain on Sphere
Fig.18: Directional Deformation Y-axis
Fig.19: Equivalent stress
Fig.20: Equivalent elastic strain
Fig.21: Equivalent Plastic Strain
TABULAR RESULT:
| Sl no. |
Equivalent stress on plate (MPa) |
Equivalent elastic strain on plate |
Equivalent stress on Sphere (MPa) |
Equivalent elastic strain on Sphere |
Directional Deformation Y-axis (mm) |
Equivalent stress (MPa) |
Equivalent elastic strain | Equivalent Plastic Strain |
| 1 |
Max: 3796.6 Min: 2.5989 |
Max: 0.019451 Min: 2.1893e-5 |
Max: 8042.4 Min: 0.010447 |
Max: 0.040213 Min: 5.7397e-8 |
Max: 0.33005 Min: -4 |
Max: 8042.4 Min: 0.010447 |
Max: 0.040213 Min: 5.7397e-8 |
Max: 1.7003 Min: 0 |
CONCLUSION:
From the above table we conclude that the Max Equivalent stress on plate is 3796.6MPa. and Max Equivalent elastic strain on plate is 0.019451. The directional deformation in Y-axis is 0.33005mm. Equivalent Plastic Strain is 1.7003mm. Grid Dependency test is performed and the results with current mesh size is better than the default mesh. Further reducing the element size will gives results closer to the current value and the time for simulation will takes more, when compared with the current value.
The plastic deformation is captured by retracting the sphere to its initial positon, if the plate returns to its intial position after removing the sphere, then we can say that the material does not undergo plastic deformation. But in our case the material remains in deform state after removing the sphere (i.e desnot come to its initial position), so we can conclude that the plate remains in plastic state after the sphere is removed.
LINK: https://drive.google.com/drive/folders/1YJZ2qnffwEQb7I64-mvkk3Vf-2NG54M1?usp=sharing