Abstract
The purpose of this research was to verify a proposed closed-form solution which solved for the reaction forces on a patient’s teeth during orthodontic treatment using finite element analysis.
The results were verified by constructing a progressive series of models in Abaqus and comparing the calculated displacements to their closed form solutions. The final orthodontic model featured a Nickel Titanium archwire subjected to the fourteen reaction forces obtained from the proposed closed form solution. Elastic and plastic behavior was considered through use of a bi-linear model. The displacements obtained from the FEA model were compared to the actual displacements measured between the start and end positions of the patients teeth.
The error between the analytical and numerical solution in the elastic regime was miniscule. The graphs of displacement obtained from the closed form and FEA solutions overlapped each other. The error between the analytical and numerical solution in the plastic regime was found to be approximately 25%.
The results of this research is the validation of the closed form solution using a modified form of Castigliano’s Theorem, as well as the establishment and visual representation of the relationship between applied force and orthodontic displacement.