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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| Language: | English |
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The Japan Society of Mechanical Engineers
2025-06-01
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| Series: | Mechanical Engineering Journal |
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| 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. |
| format | Article |
| id | doaj-art-eb79105753d845989da46e41d61aa823 |
| institution | OA Journals |
| issn | 2187-9745 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Mechanical Engineering Journal |
| 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 |