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

 

Now, consider the pressure distribution of the form:

(7.1)

Where,

.

Hence the pressure distribution can be expressed as,

(7.2)

Similar to previous section, the displacement at the surface of the film, within the loaded region can be found out using equation, 4.49

(7.3a)

Here, is the positive root of the equation , i.e.

(7.3b)

Note the value of the following integral,

(7.4)

And since, , it easy to show that the integration of the second term over vanishes, so that, 4.67 yields,

(7.5)

which is independent of r, in other word, a pressure distribution of the type of equation 4.65 leads to uniform normal displacement of the loaded circle.

Furthermore the total pressure is obtained as,

(7.6)