An assumed strain approach avoiding artificial thickness straining for a non‐linear 4‐node shell element

Betsch, Peter; Stein, Erwin

doi:10.1002/cnm.1640111104

Cited by 184 publications

(107 citation statements)

References 14 publications

(11 reference statements)

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“…The problem has been considered in Refs. (Kim et al 2008;Sze et al 2004Sze et al , 2002aSze et al , 2002bBuechter and Ramm 1992;Sansour and Kollmann 2000;Park et al 1995;Saleeb et al 1990;Simo et al 1990aSimo et al , 1990bLee et al 1984;Basar et al 1992;Sansour and Bufler 1992;Betsch and Stein 1995;Hauptmann and Schweizerhof 1998;Providas and Kattis 1999;Hong et al 2001 andKim et al 2003), among others. In one hand, we consider the case of isotropic material.…”

Section: Hemispherical Fgm Shell With 18° Holementioning

confidence: 99%

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

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In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is investigated using Abaqus software. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the FG shells in large displacements and rotations. The material properties are introduced according to the integration points in Abaqus via the UMAT subroutine. The predictions of static response of several non-trivial structure problems are compared to some reference solutions in order to verify the accuracy and the effectiveness of the new developed nonlinear solution procedures. All the results indicate very good performance in comparison with references. Lee et al. 2009). Typically, FG shell structures were presented using: (i) Kirchhoff-Love theory, Chi and Chung (2006), where the shear strains are assumed zero, which is not acceptable for FG shell; (ii) the First-order Shear Deformation Theory (FSDT) (Praveen and Reddy 1998;Thai and Kim 2015), which gives a correct overall assessment. Notice that the shear correction factors should be incorporated to adjust the transverse shear stiffness; (iii) the High-order Shear Deformation Theory (HSDT) (Neves et al. 2012;Wali et al. 2014Wali et al. , 2015Frikha et al. 2016) in which the equations of motion are more complicated to obtain than those of the FSDT; among other theories. KeywordsIt is certainly plausible that linear finite element (FE) models cannot be able to accurately predict the structural response presenting large elastic deformations and finite rotations. Indeed, according to Yu et al. (2015), several practical problems of FG structures require a geometrically non-linear formulation, such as the post-buckling behavior of structures used in aeronautical, aerospace as well as in mechanical and civil engineering. In such cases, it becomes crucial to develop efficient and accurate nonlinear FE models.It is well known that analytical solutions of shell problems are very limited. Hence, most of reference solutions are previously reported numerical solutions. Particularly, for FE geometric nonlinear analysis of FG shells, several research papers are surveyed (Praveen and Reddy 1998;Reddy 2000;Kattimani and Ray 2015;Duc et al. 2017; Reddy 2007a, 2007b;Alinia and Ghannadpour 2009;Phung-Van et al. 2014;Kim et al. 2008;Hajlaoui et al. 2017;Frikha and Dammak 2017;Asemi et al. 2014 andAnsari et al. 2016). In these references, a number of theoretical formulation and finite element models based on von Karman, Kirchhoff-Love, FSDT and HSDT theories were proposed to study the geometrically non-linear behavior of FGMs Structures.Hosseini Kordkheili and Naghdabadi (2007) derived a FE formulation for the geometrically nonlinear thermoelastic analysis of FGM plates and shells using the updated Lagrangian approach. Later, Zhao and Liew (2009) conducted a geometrically non-linear analysis of FGM shells under mechanical and thermal loading using the element-free kp-Ritz method. The formulation was based on the modified version of Sander's non-li...

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Section: Hemispherical Fgm Shell With 18° Holementioning

confidence: 99%

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

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“…• To improve the behavior of the low order hexahedral element some assumed natural strain interpolations, see [33], [34], are employed in the finite element formulation. Furthermore it is noted that a part of the independently assumed strains are interpolated in the same manner as proposed by Simo and Rifai [35].…”

Section: Introductionmentioning

confidence: 99%

A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

Klinkel

Wagner

2005

Int. J. Numer. Meth. Engng

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This paper is concerned with a geometrically nonlinear solid shell element to analyze piezoelectric structures. The finite element formulation is based on a variational principle of the Hu-Washizu type and includes six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has 8 nodes with 4 nodal degrees of freedoms, 3 displacements and the electric potential. A bilinear distribution through the thickness of the independent electric field is assumed to fulfill the electric charge conservation law in bending dominated situations exactly. The presented finite shell element is able to model arbitrary curved shell structures and incorporates a 3D-material law. A geometrically nonlinear theory allows large deformations and includes stability problems. Linear and nonlinear numerical examples demonstrate the ability of the proposed model to analyze piezoelectric devices.

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“…This effect is particularly severe when coarse meshes and strong curvatures of the shell geometry exist. This locking phenomenon can be avoided by applying the ANS method on the element's transverse normal strain ε 33 , as proposed by Betsch and Stein [39].…”

Section: Curvature Lockingmentioning

confidence: 99%

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

Bettaieb

Sena

Sousa

et al. 2015

Finite Elements in Analysis and Design

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In the present paper, a detailed description of the formulation of the new SSH3D solid-shell element is presented. This formulation is compared with the previously proposed RESS solid-shell element [1,2]. Both elements were recently implemented within the LAGAMINE in-house research finite element code. These solid-shell elements possess eight nodes with only displacement nodal degrees of freedom (DOF). In order to overcome various locking pathologies, the SSH3D formulation employs the well known Enhanced Assumed Strain (EAS) concept originally introduced by Simo and Rifai [3] and based on the Hu-Veubeke-Washizu variational principle combined with the Assumed Natural Strain (ANS) technique based on the work of Dvorkin and Bathe [4]. For the RESS solid-shell element, on the other hand, only the EAS technique is used with a Reduced Integration (RI) Scheme. A particular characteristic of these elements is their special integration schemes, with an arbitrary number of integration points along the thickness direction, dedicated to analyze problems involving non-linear through-thickness distribution (i.e. metal forming applications) without requiring many element layers. The formulation of the SSH3D element is also particular, with regard to the solid-shell elements proposed in the literature, in the sense that it is characterized by an in-plane full integration and a large variety in terms of (i) enhancing parameters, (ii) the ANS version choice and (iii) the number of integration points through the thickness direction. The choice for these three parameters should be adapted to each problem so as to obtain accurate results and to keep the calculation time low. Numerous numerical examples are performed to investigate the performance of these elements. These examples illustrate the reliability and the efficiency of the proposed formulations in various cases including linear and non-linear problems. SSH3D element is more robust thanks to the various options proposed and its full in-plane integration scheme, while RESS element in more efficient from a computational point of view.

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An assumed strain approach avoiding artificial thickness straining for a non‐linear 4‐node shell element

Cited by 184 publications

References 14 publications

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

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