Problems for Chapter 5
Analytical Techniques and Solutions for
Linear Elastic Solids
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
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
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
that the hole only influences the stress field in a region close to the hole.