The equations of equilibrium for large three-dimensional inextensible de- formations of rods are solved using an iterative shooting technique which essentially converts the original two-point boundary value problem into a sequence of initial value problems which converge to the desired solution. This method can be used efficiently and accurately on a personal computer. mainly due to the fact that the load and deformations can be applied in their entirety so that incremental methods are avoided.

The technique is applied to a variety of example problems in which linear clastic materials are considered. Where previous analytical, numerical or experimental results are available. the present technique is shown to compare favorably. The shooting technique employed is found to be well suited to finding multiple equilibrium solutions which are investigated for a cantilever beam under dead tip and uniform distributed loads.

This initial value 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 modeling complex rod structures as well as having practical numerical advantages. This is used to advantage in determining the force systems produced by a variety of orthodontic retraction appliances. Both planar and non-planar appliances and activations are considered.

The numerical procedure is then modified to include the analysis of nonlinear elastic materials. Constitutive relationships are employed which qualitatively model the behavior of shape memory alloys in planar situations. Qualitative agreement with the limited experimental results avail- able is demonstrated using the assumed constitutive behavior. This assumed shape memory behavior is then employed to investigate and compare the behavior of planar orthodontic retraction appliances to those made of linear elastic materials. The shape memory alloy appliances are shown to deliver relatively constant force systems which is a desirable characteristic in this application.