TY - JOUR

T1 - 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

AU - Machado, Nelson Andrés López

AU - Pérez, Juan Carlos Vielma

AU - Machado, Leonardo Jose López

AU - Machado, Vanessa Viviana Montesinos

N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/3/1

Y1 - 2022/3/1

N2 - 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%.

AB - 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%.

KW - 8-node hexahedron

KW - Finite element

KW - Hermitian polynomials

KW - Theory of Timoshenko

UR - http://www.scopus.com/inward/record.url?scp=85126311469&partnerID=8YFLogxK

U2 - 10.3390/math10050836

DO - 10.3390/math10050836

M3 - Article

AN - SCOPUS:85126311469

SN - 2227-7390

VL - 10

JO - Mathematics

JF - Mathematics

IS - 5

M1 - 836

ER -