Ravnovesna stanja elastičnih plaščev prisekanih antistožcev in elastični tok Jordanovih krivulj na sferah

Robek, Aljaž (author), Brojan, Miha (mentor)

Preučena so osnovna ravnovesna stanja dveh struktur, elastičnih plaščev prisekanih antistožcev in elastičnih Jordanovih krivulj na sferi, v odvisnosti od kotnega presežka plaščev oziroma dolžine krivulj. Pri preučitvi plaščev so bili opravljeni eksperimenti, medtem ko smo za preučitev Jordanovih krivulj opravili numerične simulacije. Slednje smo na koncu primerjali z eksperimenti. Opazili smo ujemanje med eksperimenti in simulacijami v primeru prostih robnih pogojev. Na začetku imajo rešitve dvojno simetrijo, preko določene vrednosti kotnega presežka/dolžine pa obe vrsti struktur raje zavzameta konfiguracijo s poševno simetrijo.

• Language: Slovenian
• Keywords: diferencialna geometrija, sferične krivulje, eksplicitna Eulerjeva metoda, antistožci, Jordanove krivulje
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FS - Faculty of Mechanical Engineering
• Place of publishing: Ljubljana
• Publisher: [A. Robek]
• Year: 2022
• Number of pages: XXII, 57 str.
• PID: 20.500.12556/RUL-139340
• UDC: 514.7+004.942:519.876.5(043.2)
• COBISS.SI-ID: 119912707
• Publication date in RUL: 01.09.2022

ROBEK, Aljaž, 2022, Ravnovesna stanja elastičnih plaščev prisekanih antistožcev in elastični tok Jordanovih krivulj na sferah [online]. Master’s thesis. Ljubljana : A. Robek. [Accessed 26 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=139340

Secondary language

• Language: English
• Title: Equilibrium states of elastic lateral surfaces of truncated anticones and the elastic flow of Jordan curves on spheres

Abstract

We examine the basic equilibrium states of two types structures, elastic lateral surfaces of truncated anticones and elastic Jordan curves on a sphere, depending on the angular excess of the lateral surfaces and the length of the curves, respectively. Experiments were performed to study the lateral surfaces, while numerical simulations were performed to study the Jordan curves. The latter were finally compared with experiments. We observed a good agreement between experiments and simulations in the case of free boundary conditions. Initially, the solutions have two-fold symmetry, but beyond a certain angular excess/length value, both types of structures prefer to occupy a configuration with skew symmetry.

• Keywords: differential geometry, spherical curves, explicit Euler method, anticones, Jordan curves