1. New prismatic solid-shell element: assumed strain formulation and hourglass mode analysis
- Author
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Farid Abed-Meraim, Alain Combescure, MeNu, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Mécanique Multiéchelle pour les solides (MIMESIS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), HESAM Université (HESAM)-HESAM Université (HESAM)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, Laboratoire de physique et mécanique des matériaux (LPMM), and Université Paul Verlaine - Metz (UPVM)-Institut National Polytechnique de Lorraine (INPL)-Ecole Nationale d'Ingénieurs de Metz (ENIM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Institut National Polytechnique de Lorraine (INPL)-Ecole Nationale d'Ingénieurs de Metz (ENIM)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3)
- Subjects
assumed-strain solid-shell SHB6 ,Displacement gradient ,[SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph] ,02 engineering and technology ,[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph] ,01 natural sciences ,[SPI.MAT]Engineering Sciences [physics]/Materials ,law.invention ,[PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph] ,0203 mechanical engineering ,law ,Variational principle ,[SPI.MECA.MEMA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph] ,SHB8PS ,Mécanique: Mécanique des matériaux [Sciences de l'ingénieur] ,Mécanique: Mécanique des structures [Sciences de l'ingénieur] ,Assumed-strain solid-shell SHB6 ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Stiffness matrix ,Mécanique [Sciences de l'ingénieur] ,Six-node prism ,Mécanique: Mécanique des solides [Sciences de l'ingénieur] ,Mathematical analysis ,Génie des procédés [Sciences de l'ingénieur] ,Structural engineering ,[SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph] ,hourglass ,Finite element method ,[SPI.MECA.GEME]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph] ,010101 applied mathematics ,020303 mechanical engineering & transports ,Mechanics of Materials ,Matériaux [Sciences de l'ingénieur] ,Shear and thickness locking ,[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph] ,Solid shell ,shear and thickness locking ,Mécanique: Vibrations [Sciences de l'ingénieur] ,Mécanique: Génie mécanique [Sciences de l'ingénieur] ,[SPI.GPROC]Engineering Sciences [physics]/Chemical and Process Engineering ,0101 mathematics ,six-node prism ,[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph] ,Civil and Structural Engineering ,business.industry ,Mechanical Engineering ,Mécanique: Matériaux et structures en mécanique [Sciences de l'ingénieur] ,[SPI.MECA.VIBR]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph] ,Building and Construction ,[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph] ,Stress field ,Nonlinear system ,[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph] ,[PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph] ,Hourglass ,business - Abstract
The formulation of a six-node solid-shell called SHB6, which is a linear, isoparametric element, is discussed. An eigenvalue analysis of the element stiffness matrix is first carried out. Several modifications are introduced into the formulation of the SHB6 element following the assumed strain method adopted by Belytschko and Bindeman. SHB6's coordinates and displacements are related to the nodal coordinates and displacements through the linear shape functions. Applying the simplified form of the Hu-Washizu nonlinear mixed variational principle, in which the assumed stress field is chosen to be orthogonal to the difference between the symmetric part of the displacement gradient and the assumed strain field, the formula is obtained. The newly developed SHB6 element was implemented into the finite element codes INCA and ASTER. It represents some improvement since it converges well and performs much better than the PRI6 six-node three-dimensional element in all of the benchmark problems tested.; International audience; The formulation of a six-node solid-shell called SHB6, which is a linear, isoparametric element, is discussed. An eigenvalue analysis of the element stiffness matrix is first carried out. Several modifications are introduced into the formulation of the SHB6 element following the assumed strain method adopted by Belytschko and Bindeman. SHB6's coordinates and displacements are related to the nodal coordinates and displacements through the linear shape functions. Applying the simplified form of the Hu-Washizu nonlinear mixed variational principle, in which the assumed stress field is chosen to be orthogonal to the difference between the symmetric part of the displacement gradient and the assumed strain field, the formula is obtained. The newly developed SHB6 element was implemented into the finite element codes INCA and ASTER. It represents some improvement since it converges well and performs much better than the PRI6 six-node three-dimensional element in all of the benchmark problems tested.
- Published
- 2011