Metoda elastičnih multipolov za napoved napetostno-deformacijskega stanja v ravninskih elastičnih strukturah z vključki

Mlinarič, Tilen (author), Brojan, Miha (mentor)

Metoda elastičnih multipolov (MEM) nudi hitro in enostavno napoved napetostno-deformacijskih vzorcev v ravninskih elastičnih mehansko obremenjenih strukturah z okroglimi vključki. Proučili smo teoretične osnove reševanja mehanskih problemov po MEM in predstavili geometrijski pomen različnih vrst elastičnih nabojev. Rešili smo primere ene in več izvrtin v neskončni plošči pri različnih postavitvah. Problem smo rešili s pomočjo optimizacijskih algoritmov in reševanja sistema enačb. Naredili smo tudi konvergenčno analizo. Analizirali smo vpliv reda upoštevanih multipolov in števila aproksimacijskih členov na točnost rezultatov. Rezultate smo primerjali z numeričnimi izračuni po metodi končnih elementov.

• Language: Slovenian
• Keywords: metoda elastičnih multipolov, elastični naboji, Airyjeva napetostna funkcija, Michellova rešitev, optimizacijski algoritem, ravninsko napetostno stanje, ravninsko deformacijsko stanje
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FS - Faculty of Mechanical Engineering
• Place of publishing: Ljubljana
• Publisher: [T. Mlinarič]
• Year: 2021
• Number of pages: XXIV, 64 str.
• PID: 20.500.12556/RUL-133412
• UDC: 539.31:620.178.3:519.6(043.2)
• COBISS.SI-ID: 86684163
• Publication date in RUL: 26.11.2021

Secondary language

• Language: English
• Title: Elastic multipole method for prediction of stress-strain state in planar elastic structures with inclusions

Abstract

The elastic multipole method (MEM) offers a quick and easy way of predicting stress-strain patterns in planar elastic mechanically loaded structures with round inclusions. We studied the theoretical foundations of solving mechanical problems according to MEM and presented the geometric significance of different types of elastic charges. We solved examples of one and more holes in an infinite plate at different layouts. We solved the problem with the help of optimization algorithms and solving a system of equations. We also did a convergence analysis. We analysed the influence of the order of the considered multipoles and the number of approximation terms on the accuracy of the results. The results were compared with numerical calculations using the finite element method.

• Keywords: elastic multipole method, elastic charges, Airy stress function, Michell's solution, optimization algorithm, plane stress state, plane strain state