# OS-E: 0105 Nonlinear Analysis of Cantilever Beams with Follower Forces

Three cantilever beams are analyzed.

The objective is to evaluate the response of the beams under (i) linear static analysis (small displacements) and (ii) geometric nonlinear analysis (large displacements) with and without the application of follower forces as shown in Figure 1. Considering the example is a static problem, the NLSTAT solver is used.

## Model Files

Refer to Access the Model Files to download the required model file(s).

The model file used in this example includes:

follow_force_nlstat.fem

## Model Description

As described in Table 1 three beams are all identical with a length of 100mm, width of 10mm and thickness of 1mm. Small displacement (linear static) analysis is performed on beam 1. Large displacement analysis is performed on beams 2, and 3.
Table 1. Analysis and Load Type
Beam 1 Static analysis is performed Applied Regular Force load
Beam 2 Nonlinear Static Analysis Applied Regular Force load
Beam 3 Nonlinear Static Analysis Applied Follower Force load

Follower forces imply that the direction of the load is assumed to rotate with the rotation at the node (where the load is applied). The purpose of this example is to compare the deformation characteristics of several cantilever beams – with and without the application of follower forces in a geometrically nonlinear analysis (NLSTAT) and that in a geometrically linear static analysis.

The linear material properties are:
Young's Modulus
2.1E5 MPa
Poisson's Ratio
0.3
Initial Density
7.9E-9 Mg/mm3

## Results

The displacement contour on the beams is shown in Figure 2. As expected, beam 1 for which static analysis has been performed, shows the largest deformation. Beam 2 (for which loading has been defined in a fixed coordinate system). Beam 3 for which large displacement analysis has been performed with follower forces, shows higher deformations than beams 2, and the end where load is applied bulges out into a spherical shape.

Figure 2 also shows the differences in deformation characteristics with and without the application of follower forces for geometrically linear and geometrically nonlinear analyses.

Whether follower force should be applied or not depends on the application. For situations where the applied force rotates with the rotation of the load application point, follower forces should be defined for correct representation of the physical situation. In all other situations where the direction of the force remains constant, follower forces do not need to be considered.