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http://hdl.handle.net/10985/10458
New quadratic solid-shell elements and their evaluation on popular benchmark problems
TRINH, Vuong-Dieu; COMBESCURE, Alain; ABED-MERAIM, Farid
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/10985/104582012-01-01T00:00:00ZTRINH, Vuong-DieuCOMBESCURE, AlainABED-MERAIM, Farid 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.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
TRINH, Vuong-Dieu; COMBESCURE, Alain; ABED-MERAIM, Farid
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/10985/101922012-01-01T00:00:00ZTRINH, Vuong-DieuCOMBESCURE, AlainABED-MERAIM, Farid 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.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; COMBESCURE, Alain; ABED-MERAIM, Farid
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-DieuCOMBESCURE, AlainABED-MERAIM, Farid 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.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; COMBESCURE, Alain; ABED-MERAIM, Farid
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-DieuCOMBESCURE, AlainABED-MERAIM, Farid 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.Assumed-strain solid–shell formulation for the six-node finite element SHB6: evaluation on nonlinear benchmark problems
http://hdl.handle.net/10985/10358
Assumed-strain solid–shell formulation for the six-node finite element SHB6: evaluation on nonlinear benchmark problems
TRINH, Vuong-Dieu; COMBESCURE, Alain; ABED-MERAIM, Farid
Because accuracy and efficiency are the main features expected within the finite element (FE) method, the current contribution proposes a six-node prismatic solid–shell, denoted (SHB6). The formulation is extended here to geometric and material nonlinearities, and focus will be placed on its validation on nonlinear benchmark problems. This type of FE is specifically designed for the modeling of thin structures, by combining several useful shell features with some well-known solid element advantages. Therefore, the resulting derivation only involves displacement degrees of freedom as it is based on a fully 3D approach. Some of the motivation behind this formulation is to allow a natural mesh connection in problems where both structural (shell/plate) and continuum (solid) elements need to be simultaneously used. Another major interest of this prismatic solid–shell is to complement meshes that use hexahedral solid–shell FE, especially when free mesh generation tools are employed. To achieve an efficient formulation, the assumed-strain method is combined with an in-plane one-point quadrature scheme. These techniques are intended to reduce both locking phenomena and computational cost. A careful analysis of possible stiffness matrix rank deficiencies demonstrates that this reduced integration procedure does not induce hourglass modes and thus no stabilization is required.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/103582011-01-01T00:00:00ZTRINH, Vuong-DieuCOMBESCURE, AlainABED-MERAIM, Farid Because accuracy and efficiency are the main features expected within the finite element (FE) method, the current contribution proposes a six-node prismatic solid–shell, denoted (SHB6). The formulation is extended here to geometric and material nonlinearities, and focus will be placed on its validation on nonlinear benchmark problems. This type of FE is specifically designed for the modeling of thin structures, by combining several useful shell features with some well-known solid element advantages. Therefore, the resulting derivation only involves displacement degrees of freedom as it is based on a fully 3D approach. Some of the motivation behind this formulation is to allow a natural mesh connection in problems where both structural (shell/plate) and continuum (solid) elements need to be simultaneously used. Another major interest of this prismatic solid–shell is to complement meshes that use hexahedral solid–shell FE, especially when free mesh generation tools are employed. To achieve an efficient formulation, the assumed-strain method is combined with an in-plane one-point quadrature scheme. These techniques are intended to reduce both locking phenomena and computational cost. A careful analysis of possible stiffness matrix rank deficiencies demonstrates that this reduced integration procedure does not induce hourglass modes and thus no stabilization is required.Développement d’un nouvel élément fini prismatique « SHB6 » de type solide–coque : formulation et évaluation à travers des cas tests
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; COMBESCURE, Alain; ABED-MERAIM, Farid
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-DieuCOMBESCURE, AlainABED-MERAIM, Farid 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.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; COMBESCURE, Alain; TRINH, Vuong-Dieu; ABED-MERAIM, Farid
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-DieuCOMBESCURE, AlainTRINH, Vuong-DieuABED-MERAIM, Farid 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.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; COMBESCURE, Alain; ABED-MERAIM, Farid
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-DieuCOMBESCURE, AlainABED-MERAIM, Farid 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.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; COMBESCURE, Alain; ABED-MERAIM, Farid
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-DieuCOMBESCURE, AlainABED-MERAIM, Farid 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.New quadratic solid-shell elements and their evaluation on linear benchmark problems
http://hdl.handle.net/10985/10228
New quadratic solid-shell elements and their evaluation on linear benchmark problems
TRINH, Vuong-Dieu; COMBESCURE, Alain; ABED-MERAIM, Farid
This paper is concerned with the development of a new family of solid- shell finite elements. This concept of solid-shell elements is shown to have a number of attractive computational properties as compared to conventional three-dimensional elements. More specifically, two new solid-shell elements are formulated in this work (a fifteen-node and a twenty-node element) on the basis of a purely three-dimensional approach. The performance of these elements is shown through the analysis of various structural problems. Note that one of their main advantages 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 denoted as 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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102282013-01-01T00:00:00ZTRINH, Vuong-DieuCOMBESCURE, AlainABED-MERAIM, Farid This paper is concerned with the development of a new family of solid- shell finite elements. This concept of solid-shell elements is shown to have a number of attractive computational properties as compared to conventional three-dimensional elements. More specifically, two new solid-shell elements are formulated in this work (a fifteen-node and a twenty-node element) on the basis of a purely three-dimensional approach. The performance of these elements is shown through the analysis of various structural problems. Note that one of their main advantages 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 denoted as 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.