5. Nonlinear 1 DOF system

This simple rod snap problem consists of two rods. The FE model is show below. The rod dimensions are B=H=10 and the sections are circular with a radius of 0.5641896, i.e. a cross section area of 1.0. The material is linear isotropic with a modulus of elasticity E=1.e6. The rods are restrained at nodes 1 and 3, node 2 being free to move in the x- and y-direction, and the node 2 is initially deformed to 1 at time 0 and released. The example has been described by Argyris et.al[30], where the analytical formulation of the equation of motion of the two rod system can be found.

Non-linear one-dof problem: FE model and dimensions.

Figure 79. Non-linear one-dof problem: FE model and dimensions.


The figure below plots the FE solution (node 2, dof 2) vs the analytical one:

Non-linear one-dof problem: Displacement response as function of time. Red dots: B2000++, every fifth point plotted. Black line: analytical solution.

Figure 80. Non-linear one-dof problem: Displacement response as function of time. Red dots: B2000++, every fifth point plotted. Black line: analytical solution.




[30] Non-linear oscillations using the finite element technique; J.H. Argyris, P.C. Dunne, T. Angelopoulos; ISD Report 36, Stuttgart, (1972).