The Analytical Model of the Initial Translational Displacements of the Tooth Root in the Linear Elastic Periodontal Ligament

Abstract

The mathematical modeling of the stress-strain state of the periodontal ligament for the translational displacement of the tooth root is carried out. The tooth root is absolutely rigid body and the periodontal ligament has a constant thickness. The solution for the displacements of the periodontal ligament is formulated in the plane stress state conditions. The boundary conditions correspond to the translational motion of the root in the force direction. The external surface of the periodontal ligament in the tooth alveolus is fixed. The expressions for the displacements of the periodontium points depending on the radial and circumferential coordinates are obtained. Comparative analysis of the magnitudes of concentrated forces for a fixed translational displacement of the tooth root on the basis of the proposed analytical model and the models in the form of an incompressible periodontal circular paraboloid and hyperboloid is carried out.

Keywords

• periodontal ligament
• translational displacement of the tooth root
• stress-strain state of the periodontium
• equilibrium of the tooth root in the periodontal ligament