Module 2 : Solid bodies in contact with and without interactions
  Lecture 7 : Pressure Apllied to a circular region (contd...)
 

 

We can consider also following pressure distribution:

(7.11)

From which the total force is obtained as

(7.12)

Again putting following expression for t

We have, the following expression for pressure distribution,

(7.13)

Then the displacement at the surface of the film, within the loaded region can be found out using equation, 4.49

(7.14)

Where

 as before.

in which integration of and over 0 to vanishes, then the displacement of the surface within the loaded region.

 

(7.15)

We can find also the tangential displacement at B, which must be radial.

(7.16)

Integration with respect to s is as before, so the final result is obtained as,

 

(7.17)

Assignment: Find out the normal and radial displacements when the point B lies outside the loaded circle.