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Stress and deformation analyses of the bridge near the Jedov mill
Hort, Michal ; Kovář, Jaroslav (referee) ; Fuis, Vladimír (advisor)
Bridges serve to many people every day, so it is necessary to be concerned about theirsafety. Analysis of bridge superstructures are used to increase their safety - and this is also the mainsubject of this thesis. Specifically, it is the analysis of the pedestrian bridge located near Jedov Mill on the Oslava river. For the stress and strain calculations, the method of joints is used, and that iscompared with the finite element method. During the comparison of the methods which hadbeen used, it was found, that the method of joints is suitable for identifying critical points, but cannot accurately determine stress values. While the finite element method can both, identify critical locations and determine the exact stress values. These calculations determinedthe critical locations on the footbridge, which are in the outmost members of the structure. By enlarge their cross-section would increase the safety of the structure. Among the critical trusses do not belong trusses damaged by the footbridge crash. The safety factor of the pedestrian bridge to the elasticity limit state, which is k = 1.74, provides a sufficient reserve for the further use of the footbridge, even if the cross-sections of the above mentioned members are not increased.
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Hellinger-Reissner Variational Principle Based Quadrilateral Finite Element
Středulová, Monika ; Eliáš, Jan
The Finite Element Method is without a doubt one of the most prominent tools in solving the equations governing mechanics of solids. It is an approximative method and, as such, its performance largely depends on the definition of the finite element used in a computation. The simplest elements, based on one primary field, tend to suffer from “locking”, that is excessive stiffness when an element is subjected to bending or the material is nearing the limit of incompressibility. One of the alternatives is the use of an element based on multiple primary fields. The present article aims to describe one such element (based on mixed-field Hellinger-Reissner variational principle) and analyze its robustness in comparison to other methods which were used in the past to mitigate locking. The analysis will be done in the framework of linear elastostatics.
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Peridynamic and nonlocal models in continuum mechanics
Pelech, Petr ; Kružík, Martin (advisor) ; Zeman, Jan (referee)
In this work we study peridynamics, a non-local model in continuum me- chanics introduced by Silling (2000). The non-locality is reflected in the fact that points at finite distance exert a force upon each other. If, however, these points are more distant than a characteristic length called horizon, it is customary to assume that they do not interact. We compare peridynamics with elasticity, especially in the limit of small horizon. We restrict ourselves, concerning this vanishing non-locality, to variational formulation of time- independent processes. We compute a Γ-limit for homogeneous and isotropic solid in linear peridynamics. In some cases this Γ-limit coincides with linear elasticity and the Poisson ratio is equal to 1 4. We conclude by clarifying why in some situation the computed Γ-limit can differ from the linear elasticity. 1
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