Upogib slojevitega nosilca zaradi zaostalih napetosti

Štukelj, Ema (author), Brojan, Miha (mentor)

V zaključnem delu smo obravnavali upogib kompozitnega nosilca, ki je sestavljen iz več vzdolžnih plasti. Takšni nosilci se ponavadi uporabljajo za zmanjševanje mase ter prilagajanje želenih lastnosti materiala po debelini. V nalogi nas je zanimal preračun, ko ima nosilec dve plasti in več plasti. V prvem delu je izpeljana teorija upogiba tankih nosilcev, za katere velja Bernoullijeva predpostavka o ravnih prerezih. Izpeljali smo zvezo med napetostnim in deformacijskim stanjem za poljubno velike premike in zasuke pri čistem upogibu. Teorijo smo najprej preizkusili na nekaj računskih primerih, pri katerih smo upoštevali, da se ena plast v nosilcu segreje in zato raztegne. Za konec pa smo teorijo preverili še z eksperimentom, v katerem smo eno od plasti močno deformirali in jo pritrdili na nedeformirano plast. Po razbremenitvi se je takšen kompozitni nosilec deformiral v del krožnice. Primerjava med teoretičnimi izračuni in eksperimenti je pokazala dobro ujemanje med obema načinoma.

• Language: Slovenian
• Keywords: kompozitni nosilec, upogib, sistem enačb, robni pogoji, radij ukrivljenosti
• Work type: Final paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FS - Faculty of Mechanical Engineering
• Place of publishing: Ljubljana
• Publisher: [E. Štukelj]
• Year: 2020
• Number of pages: XIII, 25 f.
• PID: 20.500.12556/RUL-120016
• UDC: 539.413:624.016:519.6(043.2)
• COBISS.SI-ID: 32085251
• Publication date in RUL: 15.09.2020

ŠTUKELJ, Ema, 2020, Upogib slojevitega nosilca zaradi zaostalih napetosti [online]. Bachelor’s thesis. Ljubljana : E. Štukelj. [Accessed 11 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=120016

Secondary language

• Language: English
• Title: Bending of a layered beam due to residual stresses

Abstract

In the final thesis, we considered the bending of a composite beam consisting of several longitudinal layers. These kind of beams are typically used to reduce weight and adjust the desired properties of the material in thickness. We studied beams with two layers and several layers. In the first part, the theory of bending of thin beams is derived, to which Bernoulli's assumption of straight sections applies. We derived the relationship between the stress and strain state for arbitrarily large displacements and rotations in pure bending. At first we tested the theory on a few computational cases in which we considered that one layer in the support is heated up and therefore stretches. Then we tested the theory with an experiment in which one of the layers was highly deformed and attached to an undeformed layer. After release, this composite deformed into a circular arc. A comparison between theoretical calculations and experiments showed a good match between the two methods.

• Keywords: composite beam, bending, system of equations, boundary conditions, radius of curvature