Development of second-order three-node triangular element with drilling and strain degrees of freedom

In this study, a second-order three-node triangular element with drilling and strain degrees of freedom (DOF) (GNTri3-2nd) was developed. GNTri3-2nd was formulated by applying an approximation of the generalized finite element method and a second-order Taylor expansion. The boundary conditions of th...

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Main Authors: Koshi KIMURA, Yasuyuki KANDA
Format: Article
Language:English
Published: The Japan Society of Mechanical Engineers 2025-06-01
Series:Mechanical Engineering Journal
Subjects:
Online Access:https://www.jstage.jst.go.jp/article/mej/12/4/12_24-00486/_pdf/-char/en
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author Koshi KIMURA
Yasuyuki KANDA
author_facet Koshi KIMURA
Yasuyuki KANDA
author_sort Koshi KIMURA
collection DOAJ
description In this study, a second-order three-node triangular element with drilling and strain degrees of freedom (DOF) (GNTri3-2nd) was developed. GNTri3-2nd was formulated by applying an approximation of the generalized finite element method and a second-order Taylor expansion. The boundary conditions of the extra nodal DOF (drilling, normal strain, and curvature) without the zero-energy mode are discussed through eigenvalue analysis. The analysis accuracy of GNTri3-2nd was higher than that of the conventional six-node triangular element (FEM-Tri6) for the cantilever problem. Furthermore, in the case of plane-strain compression with a nearly incompressible material, the analysis performance of GNTri3-2nd was almost identical to that of FEM-Tri6 when a selective reduced integration was applied to the element stiffness matrix. Finally, we applied the GNTri3-2nd to the fundamental rigid-plastic finite element method. The analysis result of GNTri3-2nd is in good agreement with the slip line method and the conventional four-node quadrilateral element.
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publisher The Japan Society of Mechanical Engineers
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spelling doaj-art-eb79105753d845989da46e41d61aa8232025-08-20T01:59:35ZengThe Japan Society of Mechanical EngineersMechanical Engineering Journal2187-97452025-06-0112424-0048624-0048610.1299/mej.24-00486mejDevelopment of second-order three-node triangular element with drilling and strain degrees of freedomKoshi KIMURA0Yasuyuki KANDA1Engineering Material, Structural and Energy Engineering Course, Graduate School of University of the RyukyusMechanical Engineering Program, School of Engineering, Faculty of Engineering, University of the RyukyusIn this study, a second-order three-node triangular element with drilling and strain degrees of freedom (DOF) (GNTri3-2nd) was developed. GNTri3-2nd was formulated by applying an approximation of the generalized finite element method and a second-order Taylor expansion. The boundary conditions of the extra nodal DOF (drilling, normal strain, and curvature) without the zero-energy mode are discussed through eigenvalue analysis. The analysis accuracy of GNTri3-2nd was higher than that of the conventional six-node triangular element (FEM-Tri6) for the cantilever problem. Furthermore, in the case of plane-strain compression with a nearly incompressible material, the analysis performance of GNTri3-2nd was almost identical to that of FEM-Tri6 when a selective reduced integration was applied to the element stiffness matrix. Finally, we applied the GNTri3-2nd to the fundamental rigid-plastic finite element method. The analysis result of GNTri3-2nd is in good agreement with the slip line method and the conventional four-node quadrilateral element.https://www.jstage.jst.go.jp/article/mej/12/4/12_24-00486/_pdf/-char/enthree-node triangular elementgeneralized finite element methoddrilling and strain degrees of freedomnearly incompressible materialrigid plastic finite element method
spellingShingle Koshi KIMURA
Yasuyuki KANDA
Development of second-order three-node triangular element with drilling and strain degrees of freedom
Mechanical Engineering Journal
three-node triangular element
generalized finite element method
drilling and strain degrees of freedom
nearly incompressible material
rigid plastic finite element method
title Development of second-order three-node triangular element with drilling and strain degrees of freedom
title_full Development of second-order three-node triangular element with drilling and strain degrees of freedom
title_fullStr Development of second-order three-node triangular element with drilling and strain degrees of freedom
title_full_unstemmed Development of second-order three-node triangular element with drilling and strain degrees of freedom
title_short Development of second-order three-node triangular element with drilling and strain degrees of freedom
title_sort development of second order three node triangular element with drilling and strain degrees of freedom
topic three-node triangular element
generalized finite element method
drilling and strain degrees of freedom
nearly incompressible material
rigid plastic finite element method
url https://www.jstage.jst.go.jp/article/mej/12/4/12_24-00486/_pdf/-char/en
work_keys_str_mv AT koshikimura developmentofsecondorderthreenodetriangularelementwithdrillingandstraindegreesoffreedom
AT yasuyukikanda developmentofsecondorderthreenodetriangularelementwithdrillingandstraindegreesoffreedom