Week 5 Sphere pressing on a plate

OBJECTIVE

• To perform a Static-Structural analysis to simulate a sphere pressing on a plate using ANSYS workbench.
• Use Structural steel for both sphere and plate but the material of the plate must be Non Linear.
• Press the sphere onto plate 4mm downwards and retract it.
• Note the plastic deformation occurring the material & present the detailed report for it.

CASE SETUP

1. MATERIAL SELECTION

For the following simulation, Sphere is assigned with Structural steel while plate is assigned with Non-linear Structural steel.

Properties of Structural Steel

Properties of Structural Steel NL

2. GEOMETRY

Geometry consisting of a sphere and a plate is directly imported in the workbench from the available sources. However, because of symmetric nature of geometry only quarter portion of the assembly is considered & simulated.

Fig. Geometry

3. MESHING

Program controlled mesh is generated using default mesh size. However, finer mesh is applied by using separate body sizing in the region of contact i.e.( between sphere & plate).

Fig. Meshed Geometry Fig. Mesh Element Quality

4. SETUP

• SYMMETRIC REGION

As shown in the figure, by selecting the particular faces which have symmetricity along their perpendicular axis, symmetricity in the geometry is defined.

Fig. Symmetricity in Geometry

• CONTACT

Frictional contact with frictional coefficient 0f 0.74 is established between the sphere & plate interface.

Fig. Establishment of Frictional Contact

• BOUNDARY CONDITION

• Fixed support is applied to the base of the metal plate.
• While Displacement in incremental manner is applied to the sphere, such that it presses in the plate by descending 4mm downwards & then at the end retract to initial position.

Fig. Boundary Condition- Fixed Support

FIg. Boundary Condition - Displacement

5. ANALYSIS SETTINGS

To save the computational time & ease the convergence of solution, following changes have been made in the analysis setting:

• Solver type is change from iterative to direct type.
• Large Deflection option is enable to include the high distortion of geometry during the simulation.
• Simulation is made to occur in steps of 6 time steps. In addition, to further ease the convergence, auto-timing stepping is enabled.

RESULTS & DISCUSSION

1. Directional Deformation

Results are presented after Sphere is retracted back to orginal state.

Fig. Directional deformation along Y-Aixs ( for whole system)

Fig. Directional Deformation along Y-axis (for Plate only)

Fig. Showing Directional Deformation(along Y-axis) of Upper & lower Vertex of Spherical Body

Fig. Showing Directional Deformation(along Y-axis) of a top corner vertex of Plate

From the results of Directional Deformation along Y-axis, it is clearly observed that the spherical body descends downward by 4mm and during this, it pressed onto the plate thereby causing plastic (non-reversible) deformation in the plate. However, because of excessive resistance offered by the plate as a result of base support, sphere is only able to press the plate up to approx. 3.5mm. Out of which approx. 0.12 mm get recovered because of elastic behavior while 3.38 mm remains in it as a plastic deformation.

2. Equivalent Stress

Results are presented after Sphere is retracted back to orginal state.

Fig. Stress Distribution in the assembly

Fig. Stress Distribution in the plate

Results of Equivalent Stress, shows the development of high stress which are way beyond the Tensile & Compressive strength of Structural Steel. A maximum of 4331 MPa stress developed in the plate while stress of 8740 MPa is developed in the sphere when it tries to press the plate.

At the end of pressing, stress of magnitude 3550 MPa remains in the plate as a residual stress.

3. Equivalent Elastic Strain

Results are presented after Sphere is retracted back to orginal state.

Fig. Equivalent Elastic Strain development in the assemly

Fig. Equivalent Elastic Strain development in the plate

Similarly, as expected highest strain is developed in both plate & sphere when sphere descend to its maximum value.

Max. Equivalent Strain in Plate : 2.17E-2

4. Equivalent Plastic Strain

Fig. Plastic Strain in the Plate

From the results of Plastic strain, it is observed that the rate of plastic strain increases as the spherical body descend to max. provided displacement but after that it remains constant which is basically indicating that no further plastic strain is occuring in the plate.

Max. Plastic Strain developed in the plate : 1.9471

ANIMATION