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http://hdl.handle.net/10985/10441
Développement d’un nouvel élément fini prismatique « SHB6 » de type solide–coque : formulation et évaluation à travers des cas tests
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain
Cet article décrit le développement d’un nouvel élément fini prismatique SHB6 de type solide-coque, obtenu à partir d’une formulation purement tridimensionnelle. Cet élément possède six nœuds et cinq points d’intégration répartis selon la direction de l’épaisseur. L’objectif étant d’avoir des éléments à géométrie volumique capables de modéliser des structures minces, tout en prenant correctement en compte les différents phénomènes à travers l’épaisseur. Afin d’améliorer ses performances de calcul et d’éviter certains blocages, l’intégration réduite a été employée. On montre d’abord que cette sous-intégration ne génère pas de modes de hourglass. Ensuite, on met en évidence que l’élément SHB6, sans aucune modification ou projection de son opérateur gradient discrétisé, peut souffrir de certains verrouillages de type cisaillement transverse ou membrane.; This paper presents the development of a new solid-shell finite element “SHB6” derived from a purely three-dimensional formulation. It has six nodes as well as five integration points, all distributed along the “thickness” direction. The main goal of this research is to develop low-order solid elements that are able to model thin structures while correctly taking into account the various through-thickness phenomena. In order to improve its calculation performances and to prevent some locking phenomena, reduced integration was used. We demonstrate first that there are no hourglass modes generated by the reduced integration. On the other hand, we show that, without any modification or projection of its discrete gradient operator, the SHB6 element could suffer from some membrane and shear locking phenomena.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10985/104412007-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainCet article décrit le développement d’un nouvel élément fini prismatique SHB6 de type solide-coque, obtenu à partir d’une formulation purement tridimensionnelle. Cet élément possède six nœuds et cinq points d’intégration répartis selon la direction de l’épaisseur. L’objectif étant d’avoir des éléments à géométrie volumique capables de modéliser des structures minces, tout en prenant correctement en compte les différents phénomènes à travers l’épaisseur. Afin d’améliorer ses performances de calcul et d’éviter certains blocages, l’intégration réduite a été employée. On montre d’abord que cette sous-intégration ne génère pas de modes de hourglass. Ensuite, on met en évidence que l’élément SHB6, sans aucune modification ou projection de son opérateur gradient discrétisé, peut souffrir de certains verrouillages de type cisaillement transverse ou membrane.
This paper presents the development of a new solid-shell finite element “SHB6” derived from a purely three-dimensional formulation. It has six nodes as well as five integration points, all distributed along the “thickness” direction. The main goal of this research is to develop low-order solid elements that are able to model thin structures while correctly taking into account the various through-thickness phenomena. In order to improve its calculation performances and to prevent some locking phenomena, reduced integration was used. We demonstrate first that there are no hourglass modes generated by the reduced integration. On the other hand, we show that, without any modification or projection of its discrete gradient operator, the SHB6 element could suffer from some membrane and shear locking phenomena.A new locking-free formulation for the SHB8PS solid–shell element: non-linear benchmark problems
http://hdl.handle.net/10985/10454
A new locking-free formulation for the SHB8PS solid–shell element: non-linear benchmark problems
ABED-MERAIM, Farid; COMBESCURE, Alain
In this work, a new physically stabilized and locking-free formulation of the SHB8PS element is presented. This is a solid-shell element based on a purely 3D formulation. It has eight nodes as well as five integration points, all distributed along the “thickness” direction. Consequently, it can be used for the modeling of thin structures, while providing an accurate description of the various through-thickness phenomena. The reduced integration has been used in order to prevent some locking phenomena and to increase computational efficiency. The spurious zero-energy deformation modes due to the reduced integration are efficiently stabilized, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the Enhanced Assumed Strain (EAS) method.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10985/104542007-01-01T00:00:00ZABED-MERAIM, FaridCOMBESCURE, AlainIn this work, a new physically stabilized and locking-free formulation of the SHB8PS element is presented. This is a solid-shell element based on a purely 3D formulation. It has eight nodes as well as five integration points, all distributed along the “thickness” direction. Consequently, it can be used for the modeling of thin structures, while providing an accurate description of the various through-thickness phenomena. The reduced integration has been used in order to prevent some locking phenomena and to increase computational efficiency. The spurious zero-energy deformation modes due to the reduced integration are efficiently stabilized, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the Enhanced Assumed Strain (EAS) method.A new prismatic solid-shell element 'SHB6' : assumed-strain formulation and evaluation on benchmark problems
http://hdl.handle.net/10985/10256
A new prismatic solid-shell element 'SHB6' : assumed-strain formulation and evaluation on benchmark problems
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain
In this paper, the formulation of a new six-node solid–shell element denoted (SHB6) is proposed. This prismatic element is based on a purely three-dimensional approach, and hence has displacements as the only degrees of freedom. A reduced integration scheme is adopted consisting of one-point in-plane quadrature and an arbitrary number of integration points, with a minimum number of two, distributed along the ‘thickness’ direction. Moreover, in order to enhance its performance and to greatly reduce most locking effects, specific projections are introduced based on the assumed-strain method. The resulting derivation can then be used to model thin structural problems, while taking into account the various through-thickness phenomena. A careful analysis of potential stiffness matrix rank deficiencies reveals that no hourglass modes need to be controlled. However, without assumed-strain method, the element exhibits some shear and thickness-type locking, which is common in linear triangular elements associated with constant strain states. After the formulation of the element is detailed, its performance is assessed through a set of representative benchmark problems illustrating its capabilities in various situations. More specifically, this prismatic solid–shell element proves to be an essential complement to the SHB8PS hexahedral element in meshing arbitrarily complex geometries.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/102562009-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainIn this paper, the formulation of a new six-node solid–shell element denoted (SHB6) is proposed. This prismatic element is based on a purely three-dimensional approach, and hence has displacements as the only degrees of freedom. A reduced integration scheme is adopted consisting of one-point in-plane quadrature and an arbitrary number of integration points, with a minimum number of two, distributed along the ‘thickness’ direction. Moreover, in order to enhance its performance and to greatly reduce most locking effects, specific projections are introduced based on the assumed-strain method. The resulting derivation can then be used to model thin structural problems, while taking into account the various through-thickness phenomena. A careful analysis of potential stiffness matrix rank deficiencies reveals that no hourglass modes need to be controlled. However, without assumed-strain method, the element exhibits some shear and thickness-type locking, which is common in linear triangular elements associated with constant strain states. After the formulation of the element is detailed, its performance is assessed through a set of representative benchmark problems illustrating its capabilities in various situations. More specifically, this prismatic solid–shell element proves to be an essential complement to the SHB8PS hexahedral element in meshing arbitrarily complex geometries.Une nouvelle formulation solide–coque basée sur le concept "Assumed Strain" pour l'élément fini prismatique à six-noeuds "SHB6"
http://hdl.handle.net/10985/10022
Une nouvelle formulation solide–coque basée sur le concept "Assumed Strain" pour l'élément fini prismatique à six-noeuds "SHB6"
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain
Une nouvelle formulation de l'élément solide–coque SHB6 est décrite. Il s'agit d'un élément isoparamétrique prismatique à 6 noeuds, interpolation linéaire et intégration réduite dans le plan moyen. Les déplacements sont les seuls d.d.l. et les points d'intégration sont distribués à travers l'épaisseur. L'analyse de hourglass a révélé qu'il n'y a pas de modes à énergie nulle à stabiliser ; néanmoins, la méthode "assumed strain" est adoptée pour améliorer sa convergence. Les performances du nouvel élément, ainsi obtenu, sont évaluées à travers des cas tests standard.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/100222009-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainUne nouvelle formulation de l'élément solide–coque SHB6 est décrite. Il s'agit d'un élément isoparamétrique prismatique à 6 noeuds, interpolation linéaire et intégration réduite dans le plan moyen. Les déplacements sont les seuls d.d.l. et les points d'intégration sont distribués à travers l'épaisseur. L'analyse de hourglass a révélé qu'il n'y a pas de modes à énergie nulle à stabiliser ; néanmoins, la méthode "assumed strain" est adoptée pour améliorer sa convergence. Les performances du nouvel élément, ainsi obtenu, sont évaluées à travers des cas tests standard.Formulation d’éléments finis quadratiques de type solide-coque et leur évaluation sur des cas tests standards
http://hdl.handle.net/10985/10356
Formulation d’éléments finis quadratiques de type solide-coque et leur évaluation sur des cas tests standards
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain
Dans cet article, la formulation de deux éléments finis de type coque volumique sera présentée. Il s’agit d’un hexaèdre à vingt nœuds et d’un prisme à quinze nœuds obtenus à partir d’une approche purement tridimensionnelle. Ce concept solide-coque procure de nombreux avantages par rapport aux éléments finis traditionnels solides ou coques, puisqu’il consiste à combiner en une seule formulation certaines bonnes caractéristiques des coques avec quelques bonnes propriétés des solides. A noter que les éléments coques volumiques ainsi obtenus possèdent une direction privilégiée, le long de laquelle les points d’intégration sont disposés, et une intégration réduite dans le plan de l’élément est adoptée pour réduire un certain nombre de verrouillages et pour augmenter l’efficacité de calcul de ces éléments. Au travers de cas tests représentatifs, les performances de ces éléments sont montrées.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/103562013-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainDans cet article, la formulation de deux éléments finis de type coque volumique sera présentée. Il s’agit d’un hexaèdre à vingt nœuds et d’un prisme à quinze nœuds obtenus à partir d’une approche purement tridimensionnelle. Ce concept solide-coque procure de nombreux avantages par rapport aux éléments finis traditionnels solides ou coques, puisqu’il consiste à combiner en une seule formulation certaines bonnes caractéristiques des coques avec quelques bonnes propriétés des solides. A noter que les éléments coques volumiques ainsi obtenus possèdent une direction privilégiée, le long de laquelle les points d’intégration sont disposés, et une intégration réduite dans le plan de l’élément est adoptée pour réduire un certain nombre de verrouillages et pour augmenter l’efficacité de calcul de ces éléments. Au travers de cas tests représentatifs, les performances de ces éléments sont montrées.Assumed-strain solid-shell formulation for the six-node finite element SHB6: Evaluation on non-linear benchmark problems
http://hdl.handle.net/10985/10192
Assumed-strain solid-shell formulation for the six-node finite element SHB6: Evaluation on non-linear benchmark problems
ABED-MERAIM, Farid; TRINH, Vuong-Dieu; COMBESCURE, Alain
The current contribution proposes a six-node prismatic solid-shell denoted as (SHB6). The formulation is extended to geometric and material non-linearities, and focus will be placed on its validation on non-linear benchmark problems. The resulting derivation only involves displacement DOF, as it is based on a fully 3D approach. The motivation behind this is to allow a natural mesh connexion in problems where both structural and continuum elements need to be used. Another major interest is to complement meshes that use hexahedral finite element, especially when free mesh generation tools are employed. The assumed-strain method is combined with an in-plane one-point quadrature scheme in order to reduce both locking phenomena and computational cost. A careful analysis of possible stiffness matrix rank deficiencies shows that this reduced integration does not induce hourglass modes.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/101922012-01-01T00:00:00ZABED-MERAIM, FaridTRINH, Vuong-DieuCOMBESCURE, AlainThe current contribution proposes a six-node prismatic solid-shell denoted as (SHB6). The formulation is extended to geometric and material non-linearities, and focus will be placed on its validation on non-linear benchmark problems. The resulting derivation only involves displacement DOF, as it is based on a fully 3D approach. The motivation behind this is to allow a natural mesh connexion in problems where both structural and continuum elements need to be used. Another major interest is to complement meshes that use hexahedral finite element, especially when free mesh generation tools are employed. The assumed-strain method is combined with an in-plane one-point quadrature scheme in order to reduce both locking phenomena and computational cost. A careful analysis of possible stiffness matrix rank deficiencies shows that this reduced integration does not induce hourglass modes.New quadratic solid-shell elements and their evaluation on popular benchmark problems
http://hdl.handle.net/10985/10458
New quadratic solid-shell elements and their evaluation on popular benchmark problems
ABED-MERAIM, Farid; TRINH, Vuong-Dieu; COMBESCURE, Alain
In recent years, considerable effort has been devoted to the development of 3D finite elements able to model thin structures (Cho et al., 1998; Sze and Yao, 2000; Abed-Meraim and Combescure, 2002; Vu-Quoc and Tan, 2003; Chen and Wu, 2004). To this end, coupling solid and shell formulations proved to be an interesting strategy, providing continuum finite element models that can be efficiently used for structural applications. In the present work, two solid-shell elements are formulated (a 20-node and a 15-node element) based on a purely three-dimensional approach. The advantages of these elements are shown through the analysis of various structural problems. Note that their main advantage is to allow complex structural shapes to be simulated without classical problems of connecting zones meshed with different element types. These solid-shell elements have a special direction called the “thickness”, along which a set of integration points are located. Reduced integration is also used to prevent some locking phenomena and to increase computational efficiency. Focus will be placed here on linear benchmark problems, where it is shown that these solid-shell elements perform much better than their counterparts, conventional solid elements.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/104582012-01-01T00:00:00ZABED-MERAIM, FaridTRINH, Vuong-DieuCOMBESCURE, AlainIn recent years, considerable effort has been devoted to the development of 3D finite elements able to model thin structures (Cho et al., 1998; Sze and Yao, 2000; Abed-Meraim and Combescure, 2002; Vu-Quoc and Tan, 2003; Chen and Wu, 2004). To this end, coupling solid and shell formulations proved to be an interesting strategy, providing continuum finite element models that can be efficiently used for structural applications. In the present work, two solid-shell elements are formulated (a 20-node and a 15-node element) based on a purely three-dimensional approach. The advantages of these elements are shown through the analysis of various structural problems. Note that their main advantage is to allow complex structural shapes to be simulated without classical problems of connecting zones meshed with different element types. These solid-shell elements have a special direction called the “thickness”, along which a set of integration points are located. Reduced integration is also used to prevent some locking phenomena and to increase computational efficiency. Focus will be placed here on linear benchmark problems, where it is shown that these solid-shell elements perform much better than their counterparts, conventional solid elements.New prismatic solid-shell element : Assumed strain formulation and hourglass mode analysis
http://hdl.handle.net/10985/10198
New prismatic solid-shell element : Assumed strain formulation and hourglass mode analysis
ABED-MERAIM, Farid; COMBESCURE, Alain
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.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/101982011-01-01T00:00:00ZABED-MERAIM, FaridCOMBESCURE, AlainThe 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.Formulation of new quadratic solid-shell elements and their evaluation on popular benchmark problems
http://hdl.handle.net/10985/10459
Formulation of new quadratic solid-shell elements and their evaluation on popular benchmark problems
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain
Over the last decade, considerable progress has been made in the development of three-dimensional finite elements capable of modeling thin structures. The coupling between solid and shell formulations has proven to be an interesting way to provide continuum finite element models that can be efficiently used for structural applications. The current work proposes the formulation of two solid-shell elements based on a purely three-dimensional approach. These elements have numerous advantages for the analysis of various complex structural geometries that are common in many industrial applications. Their main advantage is to allow such complex structural shapes to be meshed without classical problems of connecting zones meshed with different element types (continuum and structural elements for instance). Another important benefit of solid-shell elements is the avoidance of tedious pure-shell element formulations needed for the complex treatment of large rotations. The two solid-shell elements developed are a 20-node and a 15-node element, respectively, with displacements as the only degrees of freedom. They also have a special direction called “the thickness”. Therefore, they can be used for the modeling of thin structures, while providing an accurate description of various through-thickness phenomena thanks to the use of a set of integration points in that direction. A reduced integration scheme has been introduced to prevent some locking phenomena and increase computational efficiency. To assess the effectiveness of the proposed solid-shell elements, a set of popular benchmark problems is investigated, involving linear as well as geometric nonlinear analyses. It is shown that these elements can support high aspect ratios, up to 500, and are especially efficient for elastoplastic bending behavior. The various numerical experiments in linear and nonlinear situations reveal that these solid-shell elements perform really better than standard solid elements having similar properties in terms of geometry, interpolation and degrees of freedom.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/104592010-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainOver the last decade, considerable progress has been made in the development of three-dimensional finite elements capable of modeling thin structures. The coupling between solid and shell formulations has proven to be an interesting way to provide continuum finite element models that can be efficiently used for structural applications. The current work proposes the formulation of two solid-shell elements based on a purely three-dimensional approach. These elements have numerous advantages for the analysis of various complex structural geometries that are common in many industrial applications. Their main advantage is to allow such complex structural shapes to be meshed without classical problems of connecting zones meshed with different element types (continuum and structural elements for instance). Another important benefit of solid-shell elements is the avoidance of tedious pure-shell element formulations needed for the complex treatment of large rotations. The two solid-shell elements developed are a 20-node and a 15-node element, respectively, with displacements as the only degrees of freedom. They also have a special direction called “the thickness”. Therefore, they can be used for the modeling of thin structures, while providing an accurate description of various through-thickness phenomena thanks to the use of a set of integration points in that direction. A reduced integration scheme has been introduced to prevent some locking phenomena and increase computational efficiency. To assess the effectiveness of the proposed solid-shell elements, a set of popular benchmark problems is investigated, involving linear as well as geometric nonlinear analyses. It is shown that these elements can support high aspect ratios, up to 500, and are especially efficient for elastoplastic bending behavior. The various numerical experiments in linear and nonlinear situations reveal that these solid-shell elements perform really better than standard solid elements having similar properties in terms of geometry, interpolation and degrees of freedom.New prismatic solid-shell element: Assumed strain formulation and evaluation on benchmark problems
http://hdl.handle.net/10985/10374
New prismatic solid-shell element: Assumed strain formulation and evaluation on benchmark problems
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain; TRINH, Vuong-Dieu
This paper presents the development of a six-node solid-shell finite element called (SHB6) and based on the assumed strain method adopted by Belytschko et al. [2]. It is integrated with a set of five Gauss points along a special direction, denoted “thickness”, and with only one point in the other in-plane directions. Its discrete gradient is modified in order to attenuate shear and membrane locking. A series of popular linear benchmark problems has been carried out with comparisons to geometrically similar, low-order three-dimensional elements.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/103742008-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainTRINH, Vuong-DieuThis paper presents the development of a six-node solid-shell finite element called (SHB6) and based on the assumed strain method adopted by Belytschko et al. [2]. It is integrated with a set of five Gauss points along a special direction, denoted “thickness”, and with only one point in the other in-plane directions. Its discrete gradient is modified in order to attenuate shear and membrane locking. A series of popular linear benchmark problems has been carried out with comparisons to geometrically similar, low-order three-dimensional elements.