An 8-Nodes 3D Hexahedral Finite Element and an 1D 2-Nodes Structural Element for Timoshenko Beams, Both Based on Hermitian Intepolation, in Linear Range

Nelson Andrés López Machado, Juan Carlos Vielma Pérez, Leonardo Jose López Machado and Vanessa Viviana Montesinos Machado
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Nelson Andrés López Machado: Structural and Geotecnic Department, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile
Juan Carlos Vielma Pérez: Civil Engineering School, Pontificia Universidad Católica de Valparaíso, Valparaíso 2340000, Chile
Leonardo Jose López Machado: Structural and Geotecnic Department, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile
Vanessa Viviana Montesinos Machado: Structural Engineering Departament, Universidad Centroccidental Lisandro Alvarado, Barquisimeto 3001, Venezuela

Mathematics, 2022, vol. 10, issue 5, 1-23

Abstract: The following article presents the elaboration and results obtained from a 3D finite element, of the 8-node hexahedron type with 6 degrees of freedom (DOF) per node (48 DOF per element) based on third degree Hermitian polynomials, and of a 2-node structural element, with 6 DOF per node (12 DOF per element), based on third degree Hermitian polynomials and the theory of Timoshenko for beams. This article has two purposes; the first one is the formulation of a finite element capable of capturing bending effects, and the second one is to verify whether it is possible to obtain the deformation of the beam’s cross section of a structural member of the beam type, based on the deformations of its axis. The results obtained showed that the 8-node hexahedron FE was able to reproduce satisfactory results by simulating some cases of beams with different contour and load conditions, obtaining errors between 1% and 4% compared to the ANSYS software, educational version. Regarding the structural element of the beam type, it reproduced results that were not as precise as the FE Hexa 8, presenting errors of between 6% and 7% with regard to the axis but with error rounding between 10% and 20%.

Keywords: finite element; Hermitian polynomials; theory of Timoshenko; 8-node hexahedron (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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