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Article
Comparative Analysis of the Deflections of Two Beams Using the Finite Difference Method
Author(s)
Mariana Coelho Portilho Bernardi1, Adilandri Mércio Lobeiro2, Rogério Zolin Bertechini1 and Tamara Liz Schwab Ribeiro3
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DOI:10.17265/2159-5275/2020.03.002
Affiliation(s)
1. Academic Department of Civil Engineering, Universidade Tecnológica Federal do Paraná, Campo Mourão 87301-899, Brazil
2. Academic Department of Mathematics, Universidade Tecnológica Federal do Paraná, Campo Mourão 87301-899, Brazil
3. Academic Department of Informatics, Universidade Tecnológica Federal do Paraná, Ponta Grossa 84017-220, Brazil
ABSTRACT
In this paper, a comparative analysis of two beams’ deflections, one
supported-embedded beam and a bi-supported beam, is presented. For such
comparison, first the respective second-order linear Ordinary Differential
Equations (ODEs) were obtained. Along with the boundary conditions, there are
two Boundary Value Problems (BVPs), making it possible to perform their
numerical and analytical solutions. For numerical solutions, a Matlab algorithm
was implemented based on the Finite Difference Method (FDM). The analytical
solutions were also obtained for comparison with the numerical ones and with
the validation method. In the end we analyzed the shapes of the elastic lines
of the two beams caused by the loads coming from the weight of each one.
KEYWORDS
FDM, BVP, ODE, beams, deflection.
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