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Discrete modeling of nonlinear beams under uniform external load
Folorunsho, Sodiq Sunday ; Tomášek, Petr (oponent) ; Giorgio, Ivan (vedoucí práce)
The concept of Beam theory is extensively studied in the fields of computational and structural mechanics, with widespread applications in both industry and academia. However, the existing body of knowledge lacks the derivation of important deformation equations due to the overly constrained assumptions made by early researchers in this area. This research aims to overcome these limitations by investigating beam deformation through the study of the centerline beam deformation theory, thus relaxing the previously adopted assumptions. To achieve this goal, the energy functionals variational formulation was employed to derive a classical formulation that avoids the inherent assumptions of the Euler-Bernoulli and Timoshenko beam model equations. A discrete approach, known as Hencky-Type, was utilized to verify the inextensibility constraint of the nonlinear Euler-Bernoulli Beam. Furthermore, the linearized case was derived using variational methods applied to its nonlinear counterpart. The derived models were then applied to two types of beams: the cantilever or clamped-Free (CF) beam and the simply supported beam (SS). A comparison was made to evaluate the superiority of these models. The nonlinear model formulation was solved using the weak formulation math model of COMSOL Multiphysics software. This study aims to pave the way for more accurate model formulations and the development of novel numerical schemes that can effectively handle nonlinear models, which are often avoided due to their complexity. The findings from this work hold the potential to significantly advance the field and facilitate the exploration of various practical applications.
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