Deformacije objekta metodom konačnih elemenata

master's thesis

• Title (english): Object deformation based on the finite element method
• Author: Josip Sito
• Mentor: Željka Mihajlović (mentor)
• Committee member: Željka Mihajlović (predsjednik povjerenstva)
• Committee member: Vlado Glavinić (član povjerenstva)
• Committee member: Dejan Škvorc (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2019-09-13, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu izložene su metode za deformiranjem objekata, a posebice su proučene metode koje se temelje na konačnim elementima. Proučene su metode koje se koriste za diskretizaciju objekta na konačne elemente pri čemu je istaknuta Delaunayeva triangulacija i Varijacijska triangulacija. Objašnjen je fizički model deformabilnog objekta, a od metoda za izračun deformacija opisan je sustav masa i opruga i metoda konačnih elemenata. Proučene su različite metode vremenske integracije. Implementirana je 2D simulacija deformacije u stvarnom vremenu u Unity grafičkom alatu i C\# programskom jeziku. U aplikaciji je deformacija ostvarena pomoću metoda konačnih elemenata koji su generirani preko Delaunayeve triangulacije i Varijacijske metode, a za vremensku integraciju je korišten semi-implicitni Euler. Također, implementirana je jednostavna detekcija kolizije. Prikazani su rezultati simulacije za određene vrijednosti parametara te je objašnjeno na koji način neki parametri utječu na stabilnost.

Abstract (english)

This paper present methods for object deformation, especially methods based on finite elements. Methods used to discretize the object to finite elements were studied, highlighting Delaunay's triangulation and Variation triangulation.
The physical model for a deformable object is explained, and from the methods for calculating the deformation, the mass and spring system and the finite element method is presented. Different methods for time integration have been studied. A 2D real-time deformation simulation was implemented in Unity and C\# programming language. In the application, deformation was accomplished by the finite element method that was generated through Delaunay triangulation and variational method. Semi-implicit Euler was used for time integration. Also, a simple collision detection has been implemented. The simulation results for certain parameters values are shown and it is explained how some parameters affect stability.

• Keywords: računalna grafika; deformacija; Unity; elastičnost; plastičnost; Delaunayeva triangulacija; Hookeov zakon; semi-implicitni Euler; simulacija
• Keywords (english): computer graphics; deformation; Unity; elasticity; plasticity; Delaunay triangulation; Hooke's law; semi-implicit Euler; simulation
• Language: croatian
• URN:NBN: urn:nbn:hr:168:070142
• Study programme: Title: Computing; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2020-01-07 22:01:58