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EN222: Mechanics of Solids
Homework 6: Contact Mechanics
Due Thursday March 23, 2006
Division of Engineering
Brown University
1. The figure shows a rigid wedge with profile
()
f
xk
x
=
indenting an isotropic, linear elastic half
space with Young’s modulus
E
and Poisson ratio
ν
(a) Write down an integral equation for the contact
pressure distribution
(b) Solve the integral equation to find an expression for
the contact size
a
in terms of
k,
material properties,
and the applied load
P
, and find an expression for the
contact pressure distribution.
The following singular integral (which MAPLE has trouble with)
will be helpful
a
P
1
2
2
2
2
1
()1
11
21 l
o
g
1
1(
1 )
sign
x
dx
x
x
ξξ
ξ
−
⎛⎞
−
+−
⎜⎟
1
x
=
−−
−
<<
−
⎝⎠
∫
2. A sphere with radius
R
and Young’s modulus
E
and Poisson ratio
is pressed into the surface of
an elastic halfspace with identical elastic properties by an applied force
P
.
Using the procedure
outlined in class to model contact between two elastic cylinders, write down an integral equation for
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This note was uploaded on 01/10/2010 for the course EN 222 taught by Professor Huajiangao during the Spring '09 term at Brown.
 Spring '09
 HUAJIANGAO

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