Formulacija končnih elementov na osnovi teorije velikih pomikov

Jevnikar, Miha (author), Halilovič, Miroslav (mentor)

V magistrskem delu smo predstavili različne metode za obravnavo nelinearnih problemov v mehaniki. Na podlagi celotne Lagrangeove formulacije smo izpeljali nelinearni 1D končni element za obravnavo paličnih struktur in nelinearni 3D končni element, ki smo ga uporabili za analizo rotacije kocke in upogiba nosilca. Iz rezultatov numeričnih analiz smo ugotovili, da je uporaba 3D nelinearnih končnih elementov nujna v primeru velikih pomikov in velikih rotacij strukture. Ugotovili smo še, da je uporaba inkrementalnega reševanja nujno potrebna v nelinearnih primerih.

• Language: Slovenian
• Keywords: majhne deformacije, metoda končnih elementov, nelinearna analiza, veliki pomiki, velike rotacije
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FS - Faculty of Mechanical Engineering
• Place of publishing: Ljubljana
• Publisher: [M. Jevnikar]
• Year: 2021
• Number of pages: XXII, 86 str.
• PID: 20.500.12556/RUL-125645
• UDC: 531.01:519.61:517.9(043.2)
• COBISS.SI-ID: 58912515
• Publication date in RUL: 30.03.2021

Secondary language

• Language: English
• Title: A finite element formulation based on finite strain theory

Abstract

In the master's thesis, we presented varous methods for solving nonlinear problems in mechanics. Based on the Total Lagrangian formulation, we derived a nonlinear 1D finite element for solving truss structures and a nonlinear 3D finite element that was used to analyse the rotation of the cube and bending of the beam. From the results of numerical analysis, we found that it is necessary to use 3D nonlinear finite elements in the case of large displacements and large rotations. We also found that the use of incremental formulation is essential in nonlinear cases.

• Keywords: small strain, finite element method, nonlinear analysis, large displacement, large rotation