The generalised displacement at any point on the cross section of the beam may be expressed in terms of nodal degrees of freedom () as

(40.4)

the differential operator matrix  is

The elastic strain and the active strain components at any point in the beam may be written as

(40.5)

(40.6)

where,  and

The derivation of the governing equations of motion is standard: the governing equations, in terms of , are

(40.7)

Where, the global matrices , ,  and   are assembled from the corresponding element matrices , , , defined as, and generalised applied force . Closed form expressions of , , , and are evaluated using MATHEMATICA and used for efficient computation.