Open AccessExistence and continuous dependence of solutions for equilibrium configurations of cantilever beam
Author(s) -
Apassara Suechoei,
Parinya Sa Ngiamsunthorn,
Waraporn Chatanin,
Somchai Chucheepsakul,
Chainarong Athisakul,
Danuruj Songsanga,
Nutta Songsuwan
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022572
Subject(s) - cantilever , uniqueness , boundary value problem , adomian decomposition method , mathematics , beam (structure) , mathematical analysis , euler's formula , series (stratigraphy) , physics , partial differential equation , materials science , optics , composite material , paleontology , biology
This article explores the equilibrium configurations of a cantilever beam described by the minimizer of a generalized total energy functional. We reformulate the problem as a boundary value problem using the Euler-Lagrange condition and investigate the existence and uniqueness of minimizers. Furthermore, we discuss the dependence of solutions on the parameters of the boundary value problems. In addition, the Adomian decomposition method is derived for approximating the solution in terms of series. Finally, numerical results for the equilibrium configurations of cantilever beams are presented to support our theoretical analysis.