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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 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.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 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.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.A new assumed strain solid-shell formulation "SHB6" for the six-node prismatic finite element
http://hdl.handle.net/10985/10193
A new assumed strain solid-shell formulation "SHB6" for the six-node prismatic finite element
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain
This paper presents the development of a new prismatic solid-shell finite element, denoted SHB6, obtained using a purely three-dimensional approach. This element has six nodes with displacements as the only degrees of freedom, and only requires two integration points distributed along a preferential direction, designated as the "thickness". Although geometrically three-dimensional, this element can be conveniently used to model thin structures while taking into account the various phenomena occurring across the thickness. A reduced integration scheme and specific projections of the strains are introduced, based on the assumed-strain method, in order to improve performance and to eliminate most locking effects. It is first shown that the adopted in-plane reduced integration does not generate "hourglass" modes, but the resulting SHB6 element exhibits some shear and thickness-type locking. This is common in linear triangular elements, in which the strain is constant. The paper details the formulation of this element and illustrates its capabilities through a set of various benchmark problems commonly used in the literature. In particular, it is shown that this new element plays a useful role as a complement to the SHB8PS hexahedral element, which enables one to mesh arbitrary geometries. Examples using both SHB6 and SHB8PS elements demonstrate the advantage of mixing these two solid-shell elements.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/101932011-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainThis paper presents the development of a new prismatic solid-shell finite element, denoted SHB6, obtained using a purely three-dimensional approach. This element has six nodes with displacements as the only degrees of freedom, and only requires two integration points distributed along a preferential direction, designated as the "thickness". Although geometrically three-dimensional, this element can be conveniently used to model thin structures while taking into account the various phenomena occurring across the thickness. A reduced integration scheme and specific projections of the strains are introduced, based on the assumed-strain method, in order to improve performance and to eliminate most locking effects. It is first shown that the adopted in-plane reduced integration does not generate "hourglass" modes, but the resulting SHB6 element exhibits some shear and thickness-type locking. This is common in linear triangular elements, in which the strain is constant. The paper details the formulation of this element and illustrates its capabilities through a set of various benchmark problems commonly used in the literature. In particular, it is shown that this new element plays a useful role as a complement to the SHB8PS hexahedral element, which enables one to mesh arbitrary geometries. Examples using both SHB6 and SHB8PS elements demonstrate the advantage of mixing these two solid-shell elements.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.Éléments finis de type coques volumiques pour la simulation des structures minces
http://hdl.handle.net/10985/10357
Éléments finis de type coques volumiques pour la simulation des structures minces
TRINH, Vuong-Dieu; ABED-MERAIM, Farid; COMBESCURE, Alain
Ce travail concerne le développement d’une nouvelle famille d’éléments finis (EF) de type coques volumiques quadratiques. Deux éléments seront présentés, un hexaèdre à vingt nœuds et un prisme à quinze nœuds, qui sont formulés à partir d’une approche purement tridimensionnelle. La performance de ces éléments sera montrée à travers l’analyse de problèmes structuraux variés.; This work is concerned with the development of a new family of solid–shell finite elements. Two elements will be presented, a twenty-node hexahedron and a fifteen-node prism, which are formulated based on a purely three-dimensional approach. The performance of these solid–shell elements will be shown through the analysis of various structural problems.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/103572013-01-01T00:00:00ZTRINH, Vuong-DieuABED-MERAIM, FaridCOMBESCURE, AlainCe travail concerne le développement d’une nouvelle famille d’éléments finis (EF) de type coques volumiques quadratiques. Deux éléments seront présentés, un hexaèdre à vingt nœuds et un prisme à quinze nœuds, qui sont formulés à partir d’une approche purement tridimensionnelle. La performance de ces éléments sera montrée à travers l’analyse de problèmes structuraux variés.
This work is concerned with the development of a new family of solid–shell finite elements. Two elements will be presented, a twenty-node hexahedron and a fifteen-node prism, which are formulated based on a purely three-dimensional approach. The performance of these solid–shell elements will be shown through the analysis of various structural problems.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.Les simulations numériques de la mise en forme sont-elles fiables ?
http://hdl.handle.net/10985/10475
Les simulations numériques de la mise en forme sont-elles fiables ?
COMBESCURE, Alain; BRUNET, Michel; MAUREL, Bertrand; NEFUSSI, Germaine; ABED-MERAIM, Farid
Cette présentation porte un regard critique quant aux capacités des simulations actuelles (utilisant les logiciels de calcul par éléments finis disponibles) à prédire de manière fiable les phénomènes observés lors de la mise en forme des matériaux métalliques et dans les procédés de fabrication associés.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/104752008-01-01T00:00:00ZCOMBESCURE, AlainBRUNET, MichelMAUREL, BertrandNEFUSSI, GermaineABED-MERAIM, FaridCette présentation porte un regard critique quant aux capacités des simulations actuelles (utilisant les logiciels de calcul par éléments finis disponibles) à prédire de manière fiable les phénomènes observés lors de la mise en forme des matériaux métalliques et dans les procédés de fabrication associés.