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Problems
for Chapter 5
Analytical
Techniques and Solutions for Linear Elastic Solids
5.1. General
Principles
5.1.1.
A spherical
shell is simultaneously subjected to internal pressure, and is heated
internally to raise its temperature at  to a temperature ,
while at its surface is traction free, and
temperature is . Use the principle of superposition,
together with the solutions given in Chapter 4.1, to determine the stress
field in the sphere.
5.1.2.
The stress
field around a cylindrical hole in an infinite solid, which is subjected to
uniaxial tension far from the hole, is given by
Using the principle of superposition, calculate the
stresses near a hole in a solid which is subjected to shear stress at infinity.
5.1.3.
The stress
field due to a concentrated line load, with force per unit out-of-plane
distance P acting on the surface of
a large flat elastic solid are given by
The stress field due to a
uniform pressure distribution acting on a strip with width 2a is
where and
Show that, for the stresses due to the uniform pressure
become equal to the stresses induced by the line force (you can do this
graphically, or analytically).
5.1.4.
The stress
field in an infinite solid that contains a spherical cavity with radius a at the origin, and is subjected to a
uniform uniaxial stress far from the sphere is given by
Show
that the hole only influences the stress field in a region close to the hole.
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