Numerička aproksimacija modela poroelastične ljuske

master's thesis

• Author: Matko Ljulj
• Mentor: Josip Tambača (mentor)
• Committee member: Josip Tambača (predsjednik povjerenstva)
• Committee member: Zvonimir Tutek (član povjerenstva)
• Committee member: Mladen Jurak (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu uveli smo model poroelastične ljuske Naghdijevog tipa, koji je najsličniji modelu elastične ljuske opisanom u [9, 8]. Za razliku od modela poroelastične ljuske opisanom u [5] model opisan u radu uz fleksijske dopušta i membranske efekte. Glavni rezultat u radu su dokaz egzistencije i jedinstvenosti sustava. Dokaz jedinstvenosti rješenja temelji se na metodi energija, dok se egzistencija temelji na iterativnom postupku sličnom numeričkoj metodi opisanoj u [4]. Na kraju smo i pokazali neke numeričke aproksimacije rješenja modela u dva slučaja zanimljiva u primjeni, poput filtera u automobilima. Metoda dokaza egzistencije rješenja i numerička metoda kojom smo dobili rezultate u zadnjem poglavlju nisu ista metoda. Stoga je cilj daljnje istraživanje usmjeriti ka implementaciji prve numeričke metode i formalnom opravdanju druge.

Abstract (english)

In this thesis we introduced the poroelastic shell model of Naghdi’s type, which is the most similar to the elastic shell model described in [9, 8]. While the poroelastic shell model described in [5] captures only bending effects, the model introduced in this thesis captures membrane effects, as well. The main result in this thesis is the proof of existence and uniqueness of the system of equations. The proof of uniqueness is based on the energy method, while the proof of existence is based on iterative procedure similar to the numerical method described in [4]. At the end, we showed numerical approximation of solutions of the model in two cases interesting in application, such as car filters. The method which we used in the proof of existence of solutions and numerical method which we used to obtain numerical results are not the same method. Thus, our goal is to extend our research to implementation of the first method and justification of the second one.

• Keywords: model poroelastične ljuske Naghdijevog tipa; dokaz egzistencije sustava; dokaz jedinstvenosti sustava; numeričke aproksimacije rješenja
• Keywords (english): poroelastic shell model of Naghdi’s type; proof of existence of the system of equations; proof of uniqueness of the system of equations; numerical approximation of solutions of the model
• Language: croatian
• URN:NBN: urn:nbn:hr:217:080677
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-28 14:06:29