Week 5 Sphere pressing on a plate

Objective: To analyse the simulation of a sphere pressing a plate and its relevant parameters like stress, deformations and strains  were observed. 

(For the ease of simulation the 1/4th of the geometry is considered, and then it is further multiplied  using symmetry option for the whole geometry).

1. Geometry :

                                                

2. Material data:

  

3. Symmetry:

As mentioned earlier, for the ease of working, 1/4th of geometry is considered and the symmetry option is applied.

                                                    

The side A is with respect to Z axis and side B is with respect to x Axis.

4. Simulation Set up and Settings:

i. Connection:

Frictional connection is made with the sphere and the plate. The frictional coefficient of 0.74 for steel is taken from roymech tribology tables.

                                                             

ii. Mesh:

Default mesh element size is considered. The sphere is a hexagonal element and the plate is of tetragonal element.

                                                          

iii. Structural Inputs:

a. Analysis setting:

The pressing process was done in 4 steps. Large deflection is turned on, and the solver type is made to direct.

                                                             

b. Fixed support:

For proper fixation of the geometry, the bottom base of the geometry is fixed.

                                                       

c. Displacement:

With the 4 steps, the sphere is made to deform the plate and is retracted back to its original state. The sphere is pressed onto the plate for 4 mm in y direction.

 

5. Solution:

a. Directional Deformation (Y axis):

                                                     

b. Equivalent stress:

                                                     

c. Equivalent strain on Plate:

                                                    

d. Equivalent strain on sphere:

                                                    

6. Result:

(Max values are considered)	Directional Deformation (mm)	Equivalent stress (MPa)	Equivalent strain on Plate (mm)	Equivalent strain on sphere (mm)
Sphere pressing Result	-3.379	3330.3	0.0167	9.6e-6

7. Conclusion

• The plasticity of the Non-linear structural steel on the plate is observed. The directional deformation in Y axis is about -3.379 mm, which is significantly higher.
• The sphere has negligible deformation, as the equivalent strain on the sphere is 9.6e-6 mm.
• Symmetry Option is utilized for the efficient calculation of the Analysis.  

8. Animation