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Gubanje tanke krožne plošče na elastičnem substratu
ID Robek, Aljaž (Author), ID Brojan, Miha (Mentor) More about this mentor... This link opens in a new window

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Abstract
Gubanje je pojav, ki je prisoten pri problemih stabilnosti. Čeprav nezaželen na makro skali, lahko zanj najdemo potencialno uporabo na mikro skali. Več modelov je bilo že razvitih za opis gubanja, vendar primanjkuje takih, ki bi podali enostave analitično rešljive zveze za določitev osnovnih značilnosti sistemov, kjer se gubanje lahko pojavi. Take zveze so možne le za primere z enostavno geometrijo in napetostno porazdelitvijo. Eno takšno konfiguracijo analiziramo v zaključni nalogi. Obravnavamo gubanje filma krožne oblike na substratu, ki je enakomerno obremenjen po robu. Razvit je matematičen model gubanja plošče, ki temelji na von Kármánovi teoriji znatnih premikov, s katerim nato preučimo mehansko stabilnost plošče na elastični podlagi. Izpeljana je splošna diferencialna enačba gubanja, iz katere je nato določena pogojna enačba stabilnosti plošče, ki jo uporabimo za izpeljavo izraza za določitev kritične napetosti. Napovedi in rezultate teorije nato primerjamo s simulacijami v programu Abaqus. Izvedemo več simulacij, pri katerih spreminjamo debelino plošče in njen elastični modul. Ugotovimo, da se rezultati med teoretično idealnim modelom in simulacijami nekoliko razlikujejo.

Language:Slovenian
Keywords:gubanje, filmi, substrati, krožne plošče, Winklerjeva podlaga
Work type:Final paper
Typology:2.11 - Undergraduate Thesis
Organization:FS - Faculty of Mechanical Engineering
Place of publishing:Ljubljana
Publisher:[A. Robek]
Year:2019
Number of pages:XII, 28 f.
PID:20.500.12556/RUL-110014 This link opens in a new window
UDC:519.876.5:621.981(043.2)
COBISS.SI-ID:16946715 This link opens in a new window
Publication date in RUL:11.09.2019
Views:993
Downloads:204
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Secondary language

Language:English
Title:Wrinkling of a thin circular plate on an elastic substrate
Abstract:
Wrinkling is a phenomenon associated with problems of stability. Although being an unwelcome occurence on macroscale examples, potential use can be found on the microscale. Quite a few models describing wrinkling have been developed, yet few give simple, analitically solvable expressions for determining the properties of wrinkling. Such relations are possible for configurations with simple geometries and stress distributions. One such example is analysed in this work. We investigate wrinkling of a circular film on a substrate, evenly loaded at the edge. A mathematical model for wrinkling of thin circular plates, which is based on von Kármán plate theory, is derived as a tool for predicting its mechanical properties. The general differential equation is derived, from wich the stability equation and the expression for the critical stress follow. The model's predictions and results are then compared with simulations that were done in Abaqus. We run a few simulations where we vary the thickness of the plate and its Young's modulus. Some differences are found between the results obtained from the model and the simulations.

Keywords:wrinkling, films, substrates, circular plates, Winkler foundation

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