Bosiakov S.M., Candidate of Physical-Mathematical Sciences, Associate Professor, Associate Professor of the Department "Theoretical and Applied Mechanics", Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

Mikhasev G.I., Doctor of Physical-Mathematical Sciences, Professor, Head of the Department of Bio and Nano Mechanics, Belarusian State University, Minsk, Republic of Belarus

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.

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