Module 1 : Brief Introduction
  Lecture 2: Stress
 

Moment of external forces:

Let's write the resultant moment about the OX axis of the body forces and the surface stresses acting on a surface S containing the volume V:

(2.13)

Using the relations for and from 2.7, we have,

Now, using of Green's Transformation, we obtain,

Gauss's Transformation

Text Box: Gauss's Transformation: Proof of the Green's transformation can be found in Kreyszig

Proof of the Green's transformation can be found in Kreyszig

(2.14)

In order that the last integral(s) is(are) zero in any arbitrary region , we should have,

(2.15)

Which implies that

the stress tensor is symmetric.