A systematic development of ‘solid‐shell’ element formulations for linear and non‐linear analyses employing only displacement degrees of freedom

Hauptmann, R.; Schweizerhof, Karl

doi:10.1002/(sici)1097-0207(19980515)42:1<49::aid-nme349>3.3.co;2-u

Cited by 77 publications

(128 citation statements)

References 5 publications

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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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“…Linear example The linear shell problem is shown in figure 6. The shell consists of a pinched cylinder with rigid end diaphragms and has been analyzed, among others, in references [21,22,23,24]; these results are here reproduced for comparison. The point-load displacement is monitored.…”

Section: Examplesmentioning

confidence: 99%

A meshfree thin shell method for non‐linear dynamic fracture

Rabczuk

Areias

Belytschko

2007

Numerical Meth Engineering

446

135

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SUMMARYA meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straight forward.

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“…(10), leading to the residual, as well as the integrals in equations (14), (15), (16), leading to the consistent tangent matrix, have to be computed using one or another quadrature formulae. In the most common approach known as "node-to-surface" technique the value at the nodes from the finite element discretization of the "slave" part is taken directly.…”

Section: Computation Of the Contact Integralmentioning

confidence: 99%

“…The so-called 'Solid-Shell' formulation as described in [10] and e.g. [19], [17] is based solely on displacement degrees of freedom belonging to the upper and lower shell surfaces and thus the use of rotational degrees of freedom can be avoided.…”

Section: Introductionmentioning

confidence: 99%

Algorithmic aspects in large deformation contact analysis using ‘Solid-Shell’ elements

Harnau

Konyukhov

Schweizerhof

2005

Computers & Structures

Self Cite

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A special application for the so-called 'Solid-Shell' elements are sheet metal forming problems with high stretching and large local contact pressure where standard 2D-shells fail to converge resp. do not give reasonable results. To describe such kind of problems besides a full 3D continuum discretization appropriate contact formulations are necessary to introduce the contact condition of the metal sheets against the rigid tools. In this contribution a velocity description is taken for formulation of contact conditions. A penalty as well as an Augmented Lagrangian approach for frictionless contact is used as a first step in our developments. Special attention is paid to different numerical integration schemes of the contact integral and tangent matrices. As a result a series of different contact elements including various cases as "node-to-surface", "segment-to-segment" and "analytical rigid surface-to-segment" is considered under the unified description. For selected numerical examples the influence of the order of the quadrature formulae in a subdomain integration approach as well as the order of finite element interpolation used in the computations is discussed. The algorithms appear also to work well for friction type problems, which will be tested in a following paper.

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A systematic development of ‘solid‐shell’ element formulations for linear and non‐linear analyses employing only displacement degrees of freedom

Cited by 77 publications

References 5 publications

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

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

A meshfree thin shell method for non‐linear dynamic fracture

Algorithmic aspects in large deformation contact analysis using ‘Solid-Shell’ elements

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