Author: Carlos Lázaro
Kratos version: 8.1
Source files: Beam Non-Linear Cantilever 3D Bathe
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
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 |
[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.