Nelinearne metode redukcije modelov v dinamiki podstruktur

Pogačar, Miha (author), Čepon, Gregor (mentor), Boltežar, Miha (comentor)

Dinamska analiza kompleksnih struktur je računsko zahtevna, zato se poslužujemo delitve strukture na več podstruktur. Vsako izmed podstruktur analiziramo ločeno in z metodami redukcije zmanjšamo število njenih prostostnih stopenj, nato pa podstrukture sklopimo v celoto, kar omogoča hitrejšo analizo. V prvem delu magistrske naloge je predstavljena geometrijsko linearna formulacija končnega elementa ter Craig–Bamptonova in Rubinova metoda redukcije modelov. V drugem delu magistrske naloge je formulacija končnega elementa razširjena z nelinearno zvezo med pomiki in deformacijami, kar predstavlja geometrijsko nelinearnost. Zaradi nelinearnosti sistema je potrebna tudi nadgradnja redukcijske metode. Dinamski odziv smo izračunali z uporabo analitičnih enačb, analizo celotne strukture z metodo končnih elementov in uporabo redukcijskih metod. V izbranem frekvenčnem območju smo pokazali dobro ujemanje.

• Language: Slovenian
• Keywords: dinamika geometrijska nelinearnost metoda končnih elementov podstrukturiranje redukcija modelov
• Work type: Master's thesis
• Typology: 2.09 - Master's Thesis
• Organization: FS - Faculty of Mechanical Engineering
• Publisher: [M. Pogačar]
• Year: 2018
• PID: 20.500.12556/RUL-102520
• UDC: 519.6:531/533(043.2)
• COBISS.SI-ID: 16391451
• Publication date in RUL: 01.09.2018

POGAČAR, Miha, 2018, Nelinearne metode redukcije modelov  v dinamiki podstruktur [online]. Master’s thesis. M. Pogačar. [Accessed 22 March 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=102520

Secondary language

• Language: English
• Title: Nonlinear Model Reduction in Dynamic Substructuring

Abstract

Dynamic analysis of complex structures can be very demanding, therefore such structures are being divided into several substructures. Each of the substructures is analysed separately and the number of degrees of freedom is reduced using model order reduction methods. Then the initial structure is obtained by assembly of the reduced substructures, providing faster analysis. In the first part of the dissertation geometrically linear formulation of the finite element and Craig–Bampton model reduction method is presented. In the second part of the dissertation the finite element formulation is upgraded using nonlinear displacement – deformation relations. Due to the geometrical nonlinearity of the system also reduction methods have to be upgraded. The comparison of the beam dynamic responses, obtained by analytical equations, finite element analysis of the complete structure and use of model reduction method indicates good correspondence within the selected frequency interval.

• Keywords: dynamics geometrical nonlinearity finite element method substructuring model reduction