Mathematical Model for Analysis of Translational Displacements of Tooth Root

Analytical modeling of stress-strain state of a periodontal ligament in the case of the translational displacement of a tooth root was carried out. The tooth root was assumed as a rigid body. The boundary conditions corresponding to the translational displacement of the root and fixed external surface of the periodontal ligament in the dental alveolus were considered. The system of differential equations describing the periodontal ligament’s plane-strain state induced by the translational motion of the tooth were used as the governing equations. An analytical solution was found for the governing equations in the explicit form. Comparative analysis of the concentrated force generated by the prescribed translational motion of the tooth root was performed using the obtained analytical solution and the model of an incompressible periodontal ligament in the form of a circular paraboloid and hyperboloid. The mathematical model developed in this paper can be used to analyze stresses and strains in the periodontal tissue during orthodontic movement