Question

The principle of virtual work has nothing to do with linear elasticity, but it is convenient to start thinking about energy methods by reviewing a principle that you've probably seen before.
Let ( { }_{sigma_{q}} ) be a state of stress satisfying
( -t )
Furthermore, let ( _{4} ) be a displacement field on and define
( 6_{0}-frac{1}{2}left(4 x_{4}+4 x_{4}right) )
Then
( 8+frac{1}{2}+44 )
This is known as the Virtual Work equation.
Proof: It has been suggested that every result in solid mechanics is obtained by applying the divergence theorem. So, observe that
Hence

# (a) State and prove the converse of the principle of virtual work for a system of forces.

Solution