The Finite Element Method for the Analysis of Non-Linear and ...

The Beam Element in Large Displacements
Along the lines of the truss element formulation we need to express the
coordinates of a random point within the beam element. Using (r, s, t) as
the Cartesian coordinates at a point within an element with N nodal
points, this is written:
t x i =
N∑
N t k x k i + t 2
k=1
N∑
k=1
a k N k t V k
ti + s 2
N∑
k=1
b k N k t V k
si, i = 1, 2, 3
Vectors V s and V t define the orientation of the cross-section for the beam:
They are normal to the axis of the beam and to each other. The values a
and b define the size of the cross section of the beam.
The relative displacement components would be:
t u i = t x i − 0 x i
u i = t + ∆ t x i − t x i
are the incremental components
Institute of Structural Engineering Method of Finite Elements II 38