Finite- and boundary-element linear and nonlinear analyses of shells and shell-like structures

Mackerle, Jaroslav

doi:10.1016/s0168-874x(01)00103-2

Cited by 16 publications

(3 citation statements)

References 303 publications

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“…These developments are mainly based on the classical first order shear deformation theory (FSDT), named Reissner–Mindlin for plates and Nagdhi for shells. In this research field, contributions on beam, plate, shell and three‐dimensional (3D) shell FE are too extensive to be reviewed here, but readers can refer for instance to the bibliography listed in . In this huge literature, different techniques have been developed to overcome or control transverse shear locking.…”

Section: Introductionmentioning

confidence: 99%

Robust C⁰ high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis

Polit¹,

Vidal²,

D′Ottavio³

2012

Numerical Meth Engineering

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SUMMARY This paper presents a new C0 eight‐node quadrilateral finite element (FE) for geometrically linear elastic plates. This finite element aims at modeling both thin and thick plates without any pathologies of the classical plate finite elements (shear and Poisson or thickness locking, spurious modes, etc). A C1 FE was previously developed by the first author based on the kinematics proposed by Touratier. This new FE can be viewed as an evolution towards three directions: (1) use of only C0 FE approximations; (2) modeling of thick to thin structures; and (3) capability in multifield problems. The transverse normal stress is included allowing use of the three‐dimensional constitutive law. The element performances are evaluated on some standard plate tests, and comparisons are given with exact three‐dimensional solutions for plates under mechanical and thermal loads. Comparisons are made with other plate models using C1 and semi‐C1 FE approximations as well as with an eight node C0 FE based on the Reissner–Mindlin model. All results indicate that the present element is highly insensitive to mesh distortion, has very fast convergence properties and gives accurate results for displacements and stresses. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Robust C⁰ high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis

Polit¹,

Vidal²,

D′Ottavio³

2012

Numerical Meth Engineering

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“…Many remedies have been proposed over the years: the literature is too extensive to be reviewed here. Refer for instance to the literature reviews [1,2].…”

Section: Introductionmentioning

confidence: 99%

Displacement‐based finite elements with nodal integration for Reissner–Mindlin plates

Castellazzi

Krysl

2009

Numerical Meth Engineering

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SUMMARYAn assumed-strain finite element technique is presented for shear-deformable (Reissner-Mindlin) plates. The weighted residual method (reminiscent of the strain-displacement functional) is used to enforce weakly the balance equation with the natural boundary condition and, separately, the kinematic equation (the strain-displacement relationship). The a priori satisfaction of the kinematic weighted residual serves as a condition from which strain-displacement operators are derived via nodal integration, for linear triangles, and quadrilaterals, and also for quadratic triangles. The degrees of freedom are only the primitive variables: transverse displacements and rotations at the nodes. A straightforward constraint count can partially explain the insensitivity of the resulting finite element models to locking in the thin-plate limit. We also construct an energy-based argument for the ability of the present formulation to converge to the correct deflections in the limit of the thickness approaching zero. Examples are used to illustrate the performance with particular attention to the sensitivity to element shape and shear locking.

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“…Ce travail pionnier a laissé place à un développement extraordinaire durant les trois dernières décennies, en matière d'éléments finis à cinématique particulière. Une synthèse bibliographique est résumée par (Kerber, 1990) et (Mackerle, 2002). Un grand nombre d'auteurs, comme Bathe, Hughes, Zienkiewich, Taylor, Dhatt, etc.…”

Section: Introductionunclassified

Formulation et évaluation d’un modèle d’élément fini discret au sens de Mindlin pour l’analyse des structures isotropes

Sakami¹,

Saberi²,

Ayad³

et al. 2008

TECM

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This work deals with a displacement formulation using local discrete hypothesises, to lead to a simple and accurate shell finite element. A first kinematic hypothesis allows introducing the transverse displacement in the 4 corner nodes. The other 4 mid-side nodes are eliminated using a 2nd mechanical hypothesis. The new element DMQS (Discrete Mindlin Quadrilateral for Shells) has 4 nodes and 6 dofs/node. Its numerical performances are analysed using some known standard tests. It can be considered as an alternative to thin structure finite elements without transverse shear, called Discrete Kirchooff Elements.

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Finite- and boundary-element linear and nonlinear analyses of shells and shell-like structures

Cited by 16 publications

References 303 publications

Robust C⁰ high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis

Robust C⁰ high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis

Displacement‐based finite elements with nodal integration for Reissner–Mindlin plates

Formulation et évaluation d’un modèle d’élément fini discret au sens de Mindlin pour l’analyse des structures isotropes

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Finite- and boundary-element linear and nonlinear analyses of shells and shell-like structures

Cited by 16 publications

References 303 publications

Robust C0 high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis

Robust C0 high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis

Displacement‐based finite elements with nodal integration for Reissner–Mindlin plates

Formulation et évaluation d’un modèle d’élément fini discret au sens de Mindlin pour l’analyse des structures isotropes

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Robust C⁰ high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis

Robust C⁰ high‐order plate finite element for thin to very thick structures: mechanical and thermo‐mechanical analysis