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Srpski arhiv za celokupno lekarstvo 2010 Volume 138, Issue 1-2, Pages: 19-25
https://doi.org/10.2298/SARH1002019P
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Three dimensional mathematical model of tooth for finite element analysis

Puškar Tatjana (Klinika za stomatologiju Vojvodine, Medicinski fakultet, Novi Sad)
Vasiljević Darko ORCID iD icon (Laboratorija za optoelektroniku i lasere, Institut za fiziku, Zemun)
Marković Dubravka (Klinika za stomatologiju Vojvodine, Medicinski fakultet, Novi Sad)
Jevremović Danimir (Klinika za stomatološku protetiku, Stomatološki fakultet, Beograd)
Pantelić Dejan (Laboratorija za optoelektroniku i lasere, Institut za fiziku, Zemun)
Savić-Šević Svetlana (Laboratorija za optoelektroniku i lasere, Institut za fiziku, Zemun)
Murić Branka (Laboratorija za optoelektroniku i lasere, Institut za fiziku, Zemun)

Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Keywords: abutment, finite element analysis, biomechanics, stress, deformation

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