Page 254 - Introduction to Continuum Mechanics

238 The Elastic Solid

5.7 Principle of Superposition

and

Adding the two equations, we get

It is clear from the linearity of Eqs. (5.5.8) and (5.5.9) that 7^ + lf^ is the stress field
2
1
corresponding to the displacement field u\ ' + u\ '. Thus, u\ ' + u} ^ is also a possible motion
under the body force field (B\ ' + B\ '). The corresponding stress fields are given by
Tfi' + llj' and the surface tractions needed to maintain the total motion are given by
t} ' + 4 \ This is the principle of superposition. One application of this principle is that in
a given problem, we shall often assume that the body force is absent having in mind that its
effect, if not negligible, can always be obtained separately and then superposed onto the
solution of vanishing body force.

5.8 Plane Irrotational Wave

In this section, and in the following three sections, we shall present some simple but
important elastodynamic problems using the model of linear isotropic elastic material.