SHB8PS solid-shell

Top PDF SHB8PS solid-shell:

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

4. Discussion and conclusions A new formulation of the solid-shell element SHB8PS has been performed and implemented into the implicit, nonlinear finite element code Stanlax-INCA. This new version has been evaluated, based on a variety of a large number of popular benchmark problems frequently used in the literature. Let us recall that this solid- shell element is based on a purely three-dimensional formulation (eight-node hexahedron and only three translational degrees of freedom per node). A reduced integration is used to improve the computational efficiency and an effective stabilization is built for hourglass mode control. Five integration points are used along a particular chosen direction designated as the “thickness”, allowing for accurate modeling of bending-dominated structural problems using only a single element through the thickness. Moreover, the projection adopted in this new version of the element much better eliminates the various numerical locking phenomena. Indeed, the excellent efficiency and convergence properties of the element have been clearly demonstrated through numerous tests. All these tests show that there is no residual locking (membrane, shear). In particular, the improvement is significant in the pinched hemispherical shell problem, where the amount of locking observed in the former version has been eliminated. The validation of this element through nonlinear applications, including elastic-plastic buckling problems and large displacement and rotation simulations, is currently performed. Also, a new explicit version of this element will be implemented into an explicit dynamic code for impact and crash analyses.
En savoir plus

38 En savoir plus

Locking-free formulation for the stabilized enhanced strain solid-shell element (SHB8PS): geometrically non-linear applications

Locking-free formulation for the stabilized enhanced strain solid-shell element (SHB8PS): geometrically non-linear applications

farid.abed-meraim@metz.ensam.fr Abstract In this work, a new locking-free and physically stabilized formulation of the SHB8PS solid-shell element is presented. The resulting finite element consists of a continuum mechanics shell element based on a purely three- dimensional approach. This eight-node hexahedron is integrated with a set of five Gauss points, all distributed along the “thickness” direction. Consequently, it can be used for the modeling of thin structures, while providing an accurate description of various through-thickness phenomena. The reduced integration has been used in order to prevent some locking phenomena and to increase its 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.
En savoir plus

6 En savoir plus

Improved formulation for the stabilized enhanced strain solid-shell element (SHB8PS): geometric linear and nonlinear applications

Improved formulation for the stabilized enhanced strain solid-shell element (SHB8PS): geometric linear and nonlinear applications

Abstract In this study, the formulation of the SHB8PS solid-shell element is reviewed in order to eliminate some persistent membrane and shear locking phenomena. The resulting physically stabilized and locking-free finite element consists in a continuum mechanics shell element based on a purely three-dimensional formulation. In fact, this is a hexahedral element with eight nodes as well as five integration points, all distributed along the “thickness” direction. Consequently, it can be used for the modelling 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.
En savoir plus

11 En savoir plus

A new locking-free formulation for the SHB8PS solid–shell element: non-linear benchmark problems

A new locking-free formulation for the SHB8PS solid–shell element: non-linear benchmark problems

Summary. 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.
En savoir plus

6 En savoir plus

Elastic-plastic analyses using the solid-shell finite element SHB8PS and evaluation on sheet forming applications

Elastic-plastic analyses using the solid-shell finite element SHB8PS and evaluation on sheet forming applications

Figure 7: Deformed shape of the sheet in the unconstrained bending problem 4 CONCLUSIONS An extended version of the solid--shell finite element SHB8PS has been implemented into the implicit finite element code Abaqus/Standard via the UEL subroutine. The formulation of this element employs a combination of the reduced integration scheme with the assumed strain method and a specific projection to eliminate locking phenomena. The resulting hourglass modes are controlled using a physical self-adapting stabilization procedure. This version of the SHB8PS element can deal with problems involving anisotropic elastic-plastic behavior at large deformations and double-sided contact between sheet and tools, which are typical in sheet metal forming applications.
En savoir plus

13 En savoir plus

Evaluation of a new solid-shell finite element on the simulation of sheet metal forming processes

Evaluation of a new solid-shell finite element on the simulation of sheet metal forming processes

Figure 6. Comparison of the predicted results, using SHB8PS and C3D8 FE, and measured cup height profiles. 4. CONCLUSIONS In this work, the performance of the SHB8PS solidshell element has been successfully evaluated in the con- text of sheet metal forming applications involving various sources of non-linearities (geometric, material, contact …) as well as anisotropic plastic behavior at large strain. To this end, this element technology has been implemented into the implicit finite element code Abaqus via the UEL subroutine. Its formulation has been only briefly summa- rized in this paper; its main features consist of the physical stabilization of the hourglass patterns caused by the re- duced integration, and the assumed strain method aiming at alleviating locking phenomena. Cylindrical cup drawing simulations have been performed for AA2090-T3 Alumi- num alloy sheet. At equivalent mesh density, yet with much fewer integration points than the Abaqus C3D8 solid element, the earing profiles obtained with the SHB8PS element are in better agreement with experiments. For the thickness strain distributions, the results are in good
En savoir plus

5 En savoir plus

Modeling of viscoelastic sandwich beams using solid-shell finite elements

Modeling of viscoelastic sandwich beams using solid-shell finite elements

In order to emphasize the benefits of the proposed modeling approach, some numerical applications are presented in Section 5 for validation purposes. 5. Numerical tests and discussions To assess the ability of the present SHB8PS solidshell element to model vibrations of multi-layer structures, various beam structures in different material and geometric configurations of sandwich contrast are first investigated. The results are compared to those given by some state-of-the-art finite elements available in the commercial software package Abaqus/Standard. The three-dimensional elements selected from Abaqus for comparison consist of the linear solid element C3D8 (eight nodes, full integration) and the quadratic solid element C3D20R (twenty nodes, reduced integration). The latter is supposed to be a reference in this study, which will also be confirmed later, because of its well-recognized performance in this type of problems.
En savoir plus

26 En savoir plus

On the implementation of the continuum shell finite element SHB8PS and application to sheet forming simulation

On the implementation of the continuum shell finite element SHB8PS and application to sheet forming simulation

the thickness, e.g. for metal forming problems. The hourglass modes caused by this reduced integration are efficiently controlled by a physical stabilization technique based on the assumed strain method [8]. In the current contribution, the formulation of the SHB8PS solidshell finite element is extended to anisotropic elastic–plastic behavior models with combined isotropic-kinematic hardening at large deformations. The resulting element is then implemented into the commercial implicit finite element code Abaqus/Standard via the UEL subroutine. Its good performance is demonstrated through non-linear benchmark problems involving large strains, plasticity and contact. Particular attention is given to springback prediction for a NUMISHEET benchmark problem.
En savoir plus

7 En savoir plus

Modeling of viscoelastic sandwich beams using solid-shell finite elements

Modeling of viscoelastic sandwich beams using solid-shell finite elements

In order to emphasize the benefits of the proposed modeling approach, some numerical applications are presented in Section 5 for validation purposes. 5. Numerical tests and discussions To assess the ability of the present SHB8PS solidshell element to model vibrations of multi-layer structures, various beam structures in different material and geometric configurations of sandwich contrast are first investigated. The results are compared to those given by some state-of-the-art finite elements available in the commercial software package Abaqus/Standard. The three-dimensional elements selected from Abaqus for comparison consist of the linear solid element C3D8 (eight nodes, full integration) and the quadratic solid element C3D20R (twenty nodes, reduced integration). The latter is supposed to be a reference in this study, which will also be confirmed later, because of its well-recognized performance in this type of problems.
En savoir plus

27 En savoir plus

Vibration modeling of sandwich structures using solid-shell finite elements

Vibration modeling of sandwich structures using solid-shell finite elements

These models have shown their limitations and an alternative approach could be the use of three-dimensional finite element assemblies, but this generally leads to a large number of degrees of freedom. Another approach proposed in this work can be the use of a solid-shell element based on a fully three-dimensional formulation. Such a solid-shell element has been developed in order to correctly take into account the through-thickness phenomena, while maintaining the CPU time at reasonable levels [ 1 , 11 , 12 ]. This is a linear isoparametric hexahedral element having only nodal displacements as degrees of freedom and provided with a set of integration points distributed along the thickness direction. To avoid locking phenomena, the fully three-dimensional elastic constitutive matrix was also modified in order to approach shell-like behavior. To eliminate the zero-energy hourglass modes due to the reduced integration, an effective stabilization technique was used following the “Assumed Strain” method of Belytschko and Bindeman [ 13 ]. Several benchmark tests were analyzed to show the effectiveness of this solid-shell element in linear and non-linear problems. Recently, Salahouelhadj et al. [ 14 ] successfully simulated sheet metal forming processes using the SHB8PS solid-shell element coupled with an anisotropic large strain elastic-plastic model.
En savoir plus

9 En savoir plus

Assumed-strain solid-shell formulation for the six-node finite element SHB6: Evaluation on non-linear benchmark problems

Assumed-strain solid-shell formulation for the six-node finite element SHB6: Evaluation on non-linear benchmark problems

4. Discussion and conclusions A new solidshell element SHB6 bar has been developed and implemented into the finite element code ASTER. The key idea of this development is the adequate combination of a reduced integration rule with the well-known assumed-strain method. An interesting feature of this approach is the convenient fully three- dimensional framework on which this solidshell element is based (six-node prism with only three translational degrees of freedom per node). Also it has been shown that no zero-energy modes arise from the adopted reduced integration scheme, and thus no stabilization procedure is required. As revealed by the benchmark problems, the SHB6 bar element brings significant improvements compared to the standard three-dimensional six-node prismatic element denoted PRI6. The projection using the assumed-strain technique makes the quality of the element even better under combined bending and shearing. This type of element blends naturally with the eight-node hexahedral solidshell element SHB8PS, thus enabling one to analyze any structural geometry quite easily, which is the main motivation behind the development of the present SHB6 bar element. Recall that meshing arbitrarily complex geometries is not permitted using only hexahedral elements. Due to the better performance of quadrangular-based elements, it is advisable to mesh with SHB8PS solidshell elements, wherever possible, and to keep the SHB6 element for the only purpose of completing the meshes.
En savoir plus

27 En savoir plus

Limit-point buckling analyses using solid, shell and solid–shell elements

Limit-point buckling analyses using solid, shell and solid–shell elements

The remainder of the paper is structured as follows. The formulation of the SHB8PS solidshell element is briefly described in Section 2, together with some general comments on limit-point buckling and the modified Riks method. In Section 3, a representative set comprising six limit-point buckling benchmark tests is thoroughly investigated to compare the respective performance of the SHB8PS element and Abaqus linear solid, shell and solidshell elements. In Section 4, these solutions are shown to be sensitive to the particular location of boundary conditions along the thickness (on the upper edge, lower edge or mid-line, respectively). It is shown, in particular, that elements with three-
En savoir plus

37 En savoir plus

Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation

Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation

the date of receipt and acceptance should be inserted later Abstract This paper proposes an extension of the SHB8PS solidshell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the "thickness" direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elastic–plastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications – both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems.
En savoir plus

26 En savoir plus

New prismatic solid-shell element : Assumed strain formulation and hourglass mode analysis

New prismatic solid-shell element : Assumed strain formulation and hourglass mode analysis

This newly developed SHB6 element was implemented into the finite element codes INCA and ASTER. It represents some improvement since it converges well and it performs much better than the PRI6 six-node three- dimensional element in all of the benchmark problems tested. Furthermore, it shows very good performances in problems using mixed meshes composed of SHB6 and SHB8PS elements. Thus, we can couple the SHB6 with other finite elements to mesh complex geometries, which could be obtained by free mesh generation tools.

5 En savoir plus

New prismatic solid-shell element: Assumed strain formulation and evaluation on benchmark problems

New prismatic solid-shell element: Assumed strain formulation and evaluation on benchmark problems

[1] Abed-Meraim F and Combescure A. SHB8PS a new adaptive, assumed-strain continuum mechanics shell element for impact analysis. Computers & Structures 2002; 80:791-803. [2] Belytschko T and Bindeman LP. Assumed strain stabilization of the eight node hexahedral element. Computer Methods in Applied Mechanics and Engineering 1993; 105:225-260.

6 En savoir plus

A new prismatic solid-shell element 'SHB6' : assumed-strain formulation and evaluation on benchmark problems

A new prismatic solid-shell element 'SHB6' : assumed-strain formulation and evaluation on benchmark problems

Because reduced integration schemes are known to introduce spurious mechanisms associated with zero energy, an adequate hourglass control is generally needed. An effec- tive treatment for kinematic modes was proposed by Belytschko and Bindeman [1], with a physical stabilization procedure to correct the rank deficiency of eight-node hexahedral elements. As the SHB6 is also under-integrated, a detailed eigenvalue analysis of the ele- ment stiffness matrix is carried out. We demonstrate that the kernel of this stiffness matrix only reduces to rigid body movements and hence, in contrast to the eight-node solidshell element (SHB8PS), the SHB6 element does not require stabilization. Nevertheless, we pro- pose modifications, based on the well-known assumed-strain method [1], for the discrete gradient operator of the element in order to improve its convergence rate.
En savoir plus

16 En savoir plus

Quadratic solid‒shell elements for nonlinear structural analysis and sheet metal forming simulation

Quadratic solid‒shell elements for nonlinear structural analysis and sheet metal forming simulation

3 of zero-energy (hourglass) modes, which are induced by the reduced-integration rule (see, e.g., Abed-Meraim and Combescure [12], Schwarze et al. [18]). In this paper, two quadratic solidshell elements are proposed for the 3D nonlinear analysis of thin structures. These formulations are extended to include geometric and material nonlinearities, following the earlier works on the family of SHB elements. The first solidshell element in this family was developed by Abed-Meraim and Combescure [6], and consists of an eight-node hexahedral element denoted SHB8PS. Its formulation was subsequently improved by Abed- Meraim and Combescure [12], especially in terms of locking reduction, while the hourglass modes were efficiently controlled by implementing a new stabilization procedure. The performance of the SHB8PS element was demonstrated through a representative set of selective benchmark tests as well as sheet metal forming processes involving large strains, anisotropic plasticity, and contact (see Abed-Meraim and Combescure [12], Salahouelhadj et al. [19]). Then, a six-node prismatic solidshell element denoted SHB6 was developed by Trinh et al. [20], as a complement to the SHB8PS element for the modeling of complex geometries whose meshing requires the combination of hexahedral and prismatic elements. Although the performance of the SHB6 is good in the whole, its convergence rate remains slower than that of the SHB8PS, and requires finer meshes to obtain accurate solutions. More recently, the quadratic counterparts of the above hexahedral and prismatic solidshell elements were developed by Abed-Meraim et al. [21], in order to improve the overall performance and convergence rate. These quadratic versions consist of a twenty-node hexahedral element, denoted SHB20, and a fifteen-node prismatic element, denoted SHB15. Likewise, their formulation is based on a fully three-dimensional approach with an in-plane reduced-integration rule. The performance of these elements has been evaluated by Abed-Meraim et al. [21] within the framework of small strain and elastic benchmark problems. In the present work, however, the formulation of the quadratic SHB15 and SHB20 elements is extended to the framework of large displacements and rotations. Moreover, the resulting formulations are coupled with large-strain anisotropic elasto-plastic constitutive equations, which allows modeling complex and challenging structural problems, such as sheet metal forming processes.
En savoir plus

54 En savoir plus

Assumed-strain solid–shell formulation for the six-node finite element SHB6: evaluation on nonlinear benchmark problems

Assumed-strain solid–shell formulation for the six-node finite element SHB6: evaluation on nonlinear benchmark problems

Because reduced integration schemes are known to introduce spurious mechanisms associated with zero energy, an adequate hourglass control is generally needed. An effective treatment for kinematic modes was proposed by Belytschko and Bindeman [1], with a physical stabilization procedure to correct the rank deficiency of eight-node hexahedral elements. As the SHB6 is also under-integrated, a detailed eigenvalue analysis of the element stiffness matrix has been carried out. We demonstrate that the kernel of this stiffness matrix only reduces to rigid body modes and hence, in contrast to the eight-node solidshell element (SHB8PS) [4, 16], the SHB6 element does
En savoir plus

10 En savoir plus

A new assumed strain solid-shell formulation "SHB6" for the six-node prismatic finite element

A new assumed strain solid-shell formulation "SHB6" for the six-node prismatic finite element

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract This paper presents the development of a new prismatic solidshell 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 im- prove 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 solidshell elements.
En savoir plus

21 En savoir plus

New quadratic solid-shell elements and their evaluation on linear benchmark problems

New quadratic solid-shell elements and their evaluation on linear benchmark problems

aims to combine in a single formulation the well-recognized 3D element advantages with several useful shell features. The evaluation of this element on a variety of bench- mark problems confirmed its good performance in terms of accuracy and convergence properties, while using only a single element layer along the thickness. However, with the advent of free mesh generation tools that do not only generate hexahedrons and in order to automatically mesh arbitrarily complex geometries, the development of prismatic solidshell elements has been made necessary. To this end, a six-node pris- matic solidshell designated as SHB6 has been proposed [ 32 ]. Although playing a useful role as a complement to the SHB8PS, the SHB6 element exhibits some shear and thickness-type locking, which is common in linear triangular elements where the strain is constant. The latter limitation represents one of the main motivations behind the current development of alternative complementary solidshell elements. These proposed elements have quadratic interpolation with both versions, hexahedral and prismatic.
En savoir plus

24 En savoir plus

Show all 1229 documents...