Equivalent Nodal Forces

When deriving the formulation, IVW = EVW, simply we assumed that there is only nodal forces and that’s why EVW = . Now suppose that there are body forces and surface traction.

Let : body force per unit mass : prescribed boundary force or surface traction per unit area. (here I have used a bar over the traction vector to indicate that it is a prescribed one)

Then which can be written as However, or Therefore,

Equating EVW = IVW gives us where and

Example: If the beam is loaded as in the following figure,

then and the equivalent generalized nodal forces are: where