RESEARCH ARTICLE


Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load



Alberto Borboni*, 1, Diego De Santis1, Luigi Solazzi1, Jorge Hugo Villafañe2, Rodolfo Faglia1
1 Università degli Studi di Brescia – Mechanical and Industrial Engineering Department, Via Branze, 38 – 25123 Brescia, Italy
2 IRCCS don Gnocchi, Largo Paolo VI - Rovato (BS), Italy


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© Borboni et al.; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/legalcode), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this author at the Università degli Studi di Brescia - Mechanical and Industrial Engineering Department, Via Branze, 38 – 25123 Brescia, Italy; Tel: +390303715401; E-mail: alberto.borboni@ing.unibs.it


Abstract

The aim of this paper is to calculate the horizontal and vertical displacements of a cantilever beam in large deflections. The proposed structure is composed with Ludwick material exhibiting a different behavior to tensile and compressive actions. The geometry of the cross-section is constant and rectangular, while the external action is a vertical constant load applied at the free end. The problem is nonlinear due to the constitutive model and to the large deflections. The associated computational problem is related to the solution of a set of equation in conjunction with an ODE. An approximated approach is proposed here based on the application Newton-Raphson approach on a custom mesh and in cascade with an Eulerian method for the differential equation.

Keywords: Cantilever beam, constant load, large deflections, large deformations, ludwick material, non-linear material.