20.500.12556/RUL-187159 Gaussova preobrazna deformacija tankih okroglih plošč in problem realizacije predpisane metrike Gauss morphnig of thin circular plates and the problem of prescribed metric realization Delo obravnava preobrazbo tanke krožne plošče, ki jo povzroči neenakomerno segrevanje. Zaradi prehodnega prevoda toplote se v plošči vzpostavijo temperaturni gradienti, ki povzročijo spontano ukrivljanje ter neenakomerno krčenje materiala. To spremembo lokalnih dolžinskih razmerij opišemo s predpisano neevklidsko metriko. Če takšne metrike ni mogoče v celoti realizirati, se v plošči razvijejo notranje napetosti, ki lahko povzročijo izgubo osne simetrije in nastanek gub. Razvit je model preprostega prototipičnega sistema, ki povezuje prehodni toplotni problem, geometrijo predpisane metrike, elastično ravnovesje in stabilnostno analizo. Na njegovi osnovi določimo kritične čase, število nastalih gub ter njihove amplitude. Z eksperimentom smo dobili rezultate, ki kvalitativno potrjujejo, da nastanek gub ni neposredna posledica geometrijske nezmožnosti realizacije predpisane metrike, temveč tlačnih membranskih napetosti, ki se pri tem razvijejo. Kritični način izgube stabilnosti ustreza dvema obodnima gubama in je energijsko najugodnejša ravnovesna veja. Ugotovljeno je bilo tudi, da plošča v obravnavanem režimu realizira le majhen delež predpisane ukrivljenosti, medtem ko večino metričnega neskladja prevzame v obliki membranskih napetosti. Čeprav je obravnavana geometrija preprosta, predstavlja osnovni sistem za raziskovanje preobraznih struktur z vsiljeno metriko. Delo zato prispeva k razumevanju povezave med geometrijo, napetostmi in stabilnostjo ter predstavlja osnovo za prihodnjo obravnavo inverznega problema načrtovanja preobraznih struktur. The work investigates morphing of a thin circular plate induced by non-uniform heating. Due to transient heat transfer, temperature gradients develop within the plate, causing spontaneous bending and non-uniform contraction of the material. This change in local length ratios is described by a prescribed non-Euclidean metric. If such a metric cannot be fully realized, internal stresses develop in the plate, which may lead to the loss of axisymmetry and the formation of wrinkles. A model of a simple prototypical system is developed, linking the transient thermal problem, the geometry of the prescribed metric, elastic equilibrium, and stability analysis. Based on this model, the critical times, the number of resulting wrinkles, and their amplitudes are determined. Qualitative experimental results confirm that the formation of wrinkles is not a direct consequence of the geometric non-realizability of the prescribed metric, but rather of the compressive membrane stresses that develop as a result. The critical mode of instability corresponds to two circumferential wrinkles and is the energetically most favorable equilibrium branch. It was also found that, in the regime considered, the plate realizes only a small fraction of the prescribed curvature, while most of the metric mismatch is accommodated in the form of membrane stresses. Although the geometry considered is simple, it represents a fundamental system for investigating morphing structures with an imposed metric. The work therefore contributes to the understanding of the relationship between geometry, stresses, and stability, and provides a basis for future investigations of the inverse design problem of morphing structures. preobrazne strukture neevklidska metrika Gaussova ukrivljenost termomehanski problem nestabilnost Donnell–Mushtari–Vlasova teorija lupin nelinearna mehanika morphing structures non-Euclidean metric Gaussian curvature thermomechanical problem instability Donnell–Mushtari–Vlasov shell theory nonlinear mechanics true false false [K. Shishkoski] Slovenski jezik Angleški jezik Diplomsko delo/naloga 2026-09-09 09:24:33 2026-09-09 09:24:36 2026-09-10 09:51:52 0000-00-00 00:00:00 2026 0 Ljubljana 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 2027-08-27 539.3:624.074.4(043.2) 289705 290608131 48919.pdf 48919.pdf 1 93A7CAA20D00EE399ABDF3068F1F8A38 07a1273b1751d08eda79dd3bac7cba49e0d0a5bd07ab0695ecfeec6c9eacd731 7cd80e24-ac1f-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=246612 Fakulteta za strojništvo 0 0 0