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Analiza konstrukcij z metodo končnih elementov je zelo razširjena v inženirski praksi. Ta metoda je relativno enostavna za uporabo, njena glavna prednost pa je možnost enostavne nadgradnje, zlasti za linearne deformacije. V primeru, ko konstrukcija vsebuje vitke elemente pa je potrebna dodatna pazljivost, saj se lahko izkaže, da sistem nima več enolične rešitve. To velja predvsem pri problemih izgube stabilnosti. V magistrskem delu smo izdelali algoritem za analizo takšnih problemov. Pri tem smo uporabili korotacijske končne elemente ter metodo ločne poti. Z izdelanim algoritmom smo se lotili reševanja Eulerjevih primerov uklona v nadkritičnem območju, rešitve pa primerjali z rezultati komercialnega programa za računanje s končnimi elementi Abaqus. Pokazali smo še, da je izdelan algoritem sposoben reševanja limitnih primerov, kot je preskok sistema, okvirna konstrukcija ter Sternov mehanizem, ki je sestavljen iz togega in fleksibilnega elementa. Finite element analysis of structures is widely used in engineering practice. This method is relatively easy to use, and its main advantage is the possibility of easy upgrades, especially for linear deformations. However, in the case where the construction contains slender elements, additional care is required, as it may turn out that the system no longer has a unique solution. This is especially the case for problems where the system loses its stability. In the master thesis we make a computer code for the analysis of such problems. The corotation finite elements and the arc length method were used. With the algorithm, we analysed Euler's buckling cases, deflections in the supercritical range and compared the solutions with the results obtained from a commercial program for computing with finite elements Abaqus. We also showed that the computer code can tackle limit buckling cases, such as snap through, frame constructions and Stern's mechanism, which consists of a rigid and flexible element. |
