Page 205 - Introduction to Continuum Mechanics
P. 205
190 Stress
Solution. Substituting the given stress distribution in the first term on the left-hand side of
Eq. (4.7.3b), we obtain
Therefore,
or,
4.8 Equations of Motion in Cylindrical and Spherical Coordinates
In Chapter 2, we presented the components of divT in cylindrical and in spherical coor-
dinates. Using those formulas, we have the following equations of motion: [See also
Prob. 4.34]
Cylindrical coordinates
We note that for symmetric stress tensor, T^-TQ r=Q.
Example 4.8.1
The stress field for the Kelvin's problem (an infinite elastic space loaded by a concentrated
load at the origin) is given by the following stress components in cylindrical coordinates
where
