5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 123
© C.G. Daley
Proof:
As a linear system, superposition will hold. The structure will assume the same
final position regardless of the order of application of the forces. This means that
the same stored elastic energy will exist in either case. These are ‘conservative’
systems, meaning that all work done by the loads is converted to elastic potential
energy (and is ‘conserved’ to be recovered later). We will apply F to the structure in
two places, and compare the work done when we change the order in which we
apply the forces.
When F is applied at both 1 and 2, the total deflection at 1 and 2 will be;
∆ 1= ∆ 11 + ∆ 12
∆ 2= ∆ 21 + ∆ 22
If we imagine applying F at 1 first, and then at 2, the work done will be;