Non-Linear cantilever beam (Bathe & Bolourchi)

Author: Carlos Lázaro

Kratos version: 8.1

Source files: Beam Non-Linear Cantilever 3D Bathe

Problem definition

This is a classical test for coupled 3D bending, torsion and traction of a curved cantilever subjected to a transverse load. The cantilever has circular shape of radius 100 and spans 45 deg. The cross section is square (1 x 1). The transverse end load F increases up to a magnitude of 600. The load has fixed direction throughout the whole process.

Bathe & Bolourchi cantilever: static system

According to [1], E = 1.0 E+07, ν = 0 and A = 1.0
Iy = Iz = 0.0833333
The value of It is not given in the original article. The best approximation to the results of the article is achieved taking It = I0 = 0.1666667

Results

The 8-element discretization follows the original example in reference [1]. The load is applied in 60 steps with a load-control strategy. The following figure shows the (non-scaled) final configuration corresponding to the load of magnitude 600.

Bathe & Bolourchi cantilever: Non-scaled deformed shape for the total load (8 elements, tip load F = 600 applied in 60 steps)

The equilibrium paths corresponding to the tip displacements are plotted following the style of [1]:

Bathe & Bolourchi cantilever: Equilibrium paths for each component of the tip displacement in non-dimensional coordinates

The comparison between the computed displacements of the tip and those given in [1] is:

	Computed	Reference [1]
u	-13.4890	-13.4
v	-23.5318	-23.5
w	53.4998	53.4

References

[1] K.-J. Bathe, S. Bolourchi. Large displacement analysis of three-dimensional beam structures. International Journal for Numerical Methods in Engineering, 1979, vol. 14, pp. 961-986.