FOLORUNSHO, S. Discrete modeling of nonlinear beams under uniform external load [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2023.

Posudek vedoucího

Giorgio, Ivan

The Thesis describes a research study focused on the concept of beam theory in computational and structural mechanics. Beam theory is a fundamental topic that has wide-ranging applications in both industry and academia. However, the existing knowledge in this field has limitations due to the assumptions made by early researchers, which have restricted the derivation of important deformation equations. Typically, it is treated only the linearized case. On the contrary, the most interesting case of nonlinear behavior is often relegated to a very narrow context of postbuckling analysis. The primary objective of this research is to overcome these limitations by investigating beam deformation using the centerline beam deformation theory and relaxing the previously adopted assumptions to delve deeper into the nonlinear cases. To achieve this, the variational formulation using energy functionals to derive a classical formulation that avoids the simplified assumptions made usually for the Euler-Bernoulli and Timoshenko beam model has been adopted. The variational methods are applied also to derive the linearized cases to re-obtain the classical equation for the sake of comparison. To validate the inextensibility constraint of the nonlinear Euler-Bernoulli beam, a discrete approach called Hencky-Type has been utilized. In the thesis, then, nonlinear beams with two types of boundary conditions are analyzed: the cantilever or clamped-free beam and the simply supported beam. A comparison has been made to evaluate the validity of these models. To solve the nonlinear model formulation, the weak formulation tool of the commercial software COMSOL Multiphysics has been used. The overall aim of this study is 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 research hold the potential to significantly advance the field of beam theory and facilitate the exploration of various practical applications. This is an interesting thesis dealing with a significant subject, so the reviewer approves it. The reviewer finds no fault whatsoever with the mathematical formulation, the analysis, the discussion, the numerical analysis, and the conclusions.

Posudek oponenta

Tomášek, Petr

The thesis deals with mathematical modelling of beams. Several approaches are introduced (Euler-Bernoulli, Timoshenko, their linear and non-linear version, Hencky-type discrete model). Numerical solutions obtained by Euler-Bernoulli and Timoshenko approaches  are compared  in section 5. The computations were done in COMSOL Multiphysics software.  There is quite a lot of language and style mistakes in the text, e.g., subject and predicate mismatches; punctuation; p. 30: "Theroem" p. 40: "Using the following definition,"; p. 45: "Using the definition that:"; p. 45: "the the".   I find much better to be equations (2.1) and (2.2) formulated in vector form, not using a cases environment. "Integration by parts" is more convenient than "integration by part" used in the thesis. In considerations on page 25 a usage of symbols A, a, Q for bilinear forms is confusing, especially in Theorem 1.2 and its proof. Young's modulus is denoted by three symbols: E, Y, Yb. Finally, the numerical simulation is considered only for one setting of parameters of the task (Table 5.2). It would significantly improve the thesis to add analysis of numerical results for more input data and investigation of the response of numerical solution on a value changes of particular input parameters.  I recommend the diploma thesis to a defense with an overall classification: satisfactory/D.

eVSKP id 150107