20.500.12556/RUL-171372 Numerična analiza termomehanskih napetosti na CT modelu človeškega zoba ter primerjava z analitičnim modelom Numerical analysis of thermomechanical stresses on a CT model of a human tooth and comparison with analytical model Eden od vzrokov za nastanek razpok v človeških zobeh so napetosti, ki so posledica hitrih temperaturnih sprememb. Za boljše razumevanje pojava je v zaključni nalogi predstavljena numerična analiza s končnimi elementi CT modela človeškega zoba in primerjava rezultatov z analitičnim modelom s poenostavljeno geometrijo. Oba modela upoštevata slojevitost zoba z vključevanjem vseh treh tkiv: sklenine, zobovine in pulpe. Za model v simulaciji izhajamo iz CT slik človeškega zoba, iz katerih je preko segmentacije različnih tkiv z odprtokodnimi programskimi paketi izdelan 3D model. Model je po dodatni obdelavi vstavljen v numerično simulacijo v programskem paketu ANSYS. Obremenitev predstavlja stacionaren in nestacionaren temperaturni profil, ki nastane kot posledica nenadnih temperaturnih sprememb. V analitičnem modelu se kompleksno geometrijo človeškega zoba poenostavi s troplastnim cilindrom. V programskem okolju Wolfram Mathematica se preko reševanja Fourier-jeve diferencialne enačbe prevoda toplote izračuna časovno in prostorsko odvisen temperaturni profil. Z uporabo Hooke-ovega zakona in ravnovesnih enačb mehanike se ob predpostavki posplošenega ravninsko deformacijskega stanja izračuna pripadajoče napetosti in deformacije. Rezultat obeh se nato primerja glede na dobljeno temperaturno funkcijo in napetostno-deformacijsko stanje. One of the causes of cracks in human teeth is stress resulting from rapid temperature changes. For a better understanding of the phenomenon, this master thesis presents a numerical analysis with finite elements of a CT model of a human tooth and a comparison of the results with an analytical model with a simplified geometry. Both models follow the layering of the tooth by including all three tissues: enamel, dentine and pulp. For the model in the simulation, we start from a CT image of a human tooth, from which a 3D model is created through the segmentation of various tissues using open source software packages. After additional processing, the model is inserted into the numerical simulation in the ANSYS software package. The load represents the stationary and non-stationary temperature profile that occurs as a result of sudden temperature changes. In the analytical model, the complex geometry of the human tooth is simplified with a three-layered cylinder. In the Wolfram Mathematica software environment, the time- and space-dependent temperature profile is calculated by solving the Fourier differential equation of heat transfer. Using Hooke's law, the equilibrium equations of mechanics and assuming a generalized plane strain state, the associated stresses and strains are calculated. Both models are then compared according to the obtained temperature function and stress-strain state. termomehanika nestacionaren prevod človeški zobje CT slike numerični modeli analitični modeli termomechanics transient conduction human teeth CT images numerical models analitical models true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-08-23 08:32:43 2025-08-23 08:32:45 2025-08-31 03:51:17 0000-00-00 00:00:00 2025 0 0 XX, 56 str. 2025 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6:539.3:616.314(043.2) 274667 246957059 42946.pdf 42946.pdf 1 9F8D7F5398DC40EBF34DF7434D61F978 baf48339a2d3a8303fe5f747262f292d83b8bf4d3cbfb7226053d563d641e838 ddc25799-7fea-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=214659 Fakulteta za strojništvo 0 0 0