Discrete modeling of nonlinear beams under uniform external load
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Date
Authors
Folorunsho, Sodiq Sunday
ORCID
Advisor
Referee
Mark
B
Journal Title
Journal ISSN
Volume Title
Publisher
Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstract
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.
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.
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.
Description
Keywords
Euler-Bernoulli, Timoshenko, Hencky-Type, Centerline Beam Theory, Variational, Weak, Classical Formulation, Energy Functional, Cantilever Beam, Simply Supported Beam, COMSOL Multiphysics, Euler-Bernoulli, Timoshenko, Hencky-Type, Centerline Beam Theory, Variational, Weak, Classical Formulation, Energy Functional, Cantilever Beam, Simply Supported Beam, COMSOL Multiphysics
Citation
FOLORUNSHO, S. Discrete modeling of nonlinear beams under uniform external load [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2023.
Document type
Document version
Date of access to the full text
Language of document
en
Study field
bez specializace
Comittee
doc. Ing. Luděk Nechvátal, Ph.D. (předseda)
prof. RNDr. Josef Šlapal, CSc. (místopředseda)
doc. RNDr. Jiří Tomáš, Dr. (člen)
doc. Ing. Jiří Šremr, Ph.D. (člen)
prof. RNDr. Miloslav Druckmüller, CSc. (člen)
prof. Bruno Rubino (člen)
prof. Giuli Massimiliano (člen)
prof. Lattanzio Corrado (člen)
Date of acceptance
2023-06-14
Defence
The student introduced his diploma thesis to the committee members and explained the fundamentals of his topic called Discrete modeling of nonlinear beams under uniform external load.
The supervisor's review was read.
The opponent Petr Tomasek read his review.
The student answered the opponent's questions well.
Sremr had the additional questions:
page 29 of the presentation - about linear vs. nonlinear solution
page 12 - about isolated force on the beam
The student answered the committee's questions well.
Result of defence
práce byla úspěšně obhájena
Document licence
Standardní licenční smlouva - přístup k plnému textu bez omezení