An eight‐node hybrid‐stress solid‐shell element for geometric non‐linear analysis of elastic shells

Sze, K. Y.; Chan, W. K.; Pian, T. H. H.

doi:10.1002/nme.535

Cited by 143 publications

(169 citation statements)

References 29 publications

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“…Using symmetry, only one eighth needs to be modeled with 20x40, S4 elements. This test is non-trivial which was considered in Arciniega and Reddy (2007a), Sze et al (2004Sze et al ( , 2002aSze et al ( , 2002b, Brank et al (1995), Sansour et al (2000), Gruttmann et al (1989);Peng and Crisfield (1992) and Park et al (1995). The initial and meshing configuration are shown in Fig. 14.…”

Section: Case Of Pulled Cylindermentioning

confidence: 99%

“…The present problems have been considered in Refs. (Sze et al 2004(Sze et al , 2002a(Sze et al , 2002bBrank et al 1995;Klinkel et al 1999 andFontes et al 2003).…”

Section: Pinched Cylinder Fgm Shellmentioning

confidence: 99%

“…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%

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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: Case Of Pulled Cylindermentioning

confidence: 99%

“…The present problems have been considered in Refs. (Sze et al 2004(Sze et al , 2002a(Sze et al , 2002bBrank et al 1995;Klinkel et al 1999 andFontes et al 2003).…”

Section: Pinched Cylinder Fgm Shellmentioning

confidence: 99%

Section: Hemispherical Fgm Shell With 18° Holementioning

confidence: 99%

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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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“…Numerical solutions for the isotropic case may be found in Refs . [13,10,3,45,46,47]. We employ uniform and arbitrarily curved quadrilateral shell elements consisting of 4 elements with the 8 = p…”

mentioning

confidence: 99%

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Vallala

Reddy

2013

MCA

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Abstract-This study deals with the use of high-order spectral/hp approximation functions in finite element models of various of nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. For many of these classes of problems, the high-order (typically, polynomial order 4  p ) spectral/hp finite element technology offers many computational advantages over traditional low-order (i.e., 3 < p ) finite elements. For instance, higher-order spectral/hp finite element procedures allow us to develop robust structural elements such as beams, plates, and shells in a purely displacement-based setting, which avoid all forms of numerical locking. For fluid flows, when combined with least-squares variational principles, the higher-order spectral/hp technology allows us to develop efficient finite element models that always yield a symmetric positive-definite (SPD) coefficient matrix and, hence, robust iterative solvers can be used. Also, the use of spectral/hp finite element technology results in a better conservation of physical quantities like dilatation, volume, and mass, and stable evolution of variables with time for transient flows. The present study considers the weak-form based displacement finite element models elastic shells and the least-squares finite element models of the Navier-Stokes equations governing flows of viscous incompressible fluids. Numerical solutions of several nontrivial benchmark problems are presented to illustrate the accuracy and robustness of the developed finite element technology.

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“…For these reasons, full integration scheme is more frequently used for the development of 3D finite elements such as in the case of solid-shell elements (e.g. [5,6,[16][17][18][19]) even if it suffers from several locking pathologies. In order to reduce these locking effects, several techniques are available in the literature for low-order fully integrated solid and solid-shell formulations.…”

Section: Introductionmentioning

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 eight‐node hybrid‐stress solid‐shell element for geometric non‐linear analysis of elastic shells

Cited by 143 publications

References 29 publications

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

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

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

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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