Tenzorski račun v mehaniki : delo diplomskega seminarja

Gradišek, Domen (author), Mejak, George (mentor)

Najprej bomo definirali tenzorje v vsej splošnosti in spoznali nekaj operacij z njimi.Nato bomo naše zanimanje zožili na poseben tip tenzorjev (tenzorje drugega reda)in opazovali njihove lastnosti. Potem se bomo osredotočili na eno vrsto funkcij in preslikav, ki slikajo iz prostora tenzorjev in jim pravimo izotropične funkcije oziroma preslikave. Na koncu pa bomo preko skalarnih, vektorskih in tenzorskih polj spoznali še integralske izreke kot posplošitev rezultatov iz vektorske analize.

• Language: Slovenian
• Keywords: Tenzor, endomorfizem, izotropičnost, gradient, divergenca, rotor
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-140305
• UDC: 512
• COBISS.SI-ID: 121250819
• Publication date in RUL: 14.09.2022

Secondary language

• Language: English
• Title: Tensor calculations in mechanics

Abstract

First, we will define tensors in all generality and define some operations with them. Then we will focus on special kinds of tensors, called tensors of second order, and observe their properties. Later we are going to study special functions mapping from tensor spaces, called isotropic functions. At the end, we will define scalar, vector and tensor fields, and prove some integral theorems.

• Keywords: Tensor, endomorphism, isotropic, gradient, divergence, curl