Page 29 - Introduction to Continuum Mechanics

14 Tensors

Example 2B2.1

Obtain the matrix for the tensor T which transforms the base vectors as follows:
Te x = 4CJ+C2
Te 2 = 2e!+3e 3
Te 3 = --e 1+3e2+e3
Solution. By Eq. (2B2.1a) it is clear that:
4 2 -1~
[T]= 1 0 3
[0 3 1

Example 2B2.2

Let T transform every vector into its mirror image with respect to a fixed plane. If ej is
normal to the reflection plane (e 2 and 63 are parallel to this plane), find a matrix of T.

Solution. Since the normal to the reflection plane is transformed into its negative and vectors
parallel to the plane are not altered:

Tej = - Cl

Te 2 = e 2
Te 3 = e 3
Thus,