(a) State and prove the converse of...
Question

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

11th - 12th Class
Maths
Solution
160
4.0 (1 ratings)
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