A segmental approach for large three-dimensional rod deformations

The equations of equilibrium for inextensible large three-dimensional deformations of rods are solved using an iterative shooting technique which essentially converts the original boundary value problem to a sequence of initial value problems that converge to the desired solution. This approach is combined with a method for considering the rod using a number of segments. The use of segments in this fashion is found to be useful for modelling complex rod structures, as well as having practical numerical advantages. The technique is applied to a variety of example problems. Where previous analytical or numerical results are available, the present approach is shown to compare favourably. The shooting technique employed is also found to be well suited to finding multiple equilibrium solutions. This method can be used efficiently and accurately on a personal computer, mainly due to the fact that the load can be applied in its entirety so that load increments are not required. In addition, there is no need for large computer memory to store the detailed information for all the segments simultaneously, as the solution of one segment is simply used as the input to the next