The Finite Element Analysis of Shells: Fundamentals

Chapelle, Dominique; Bath, K-J; Meyer, Carol H.

doi:10.1115/1.1760517

Cited by 33 publications

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“…The first one is characteristic of common metal plasticity models, where plastic deformation is taken to be isochoric or, in other words, incompressible [19]. The second one comes from the analysis of thin shells, were the limit between ''thick'' and ''thin'' geometries is somewhat difficult to establish, with the occurrence of locking not only strictly relying on thickness/length ratios, as demonstrated by Chapelle, Bathe and co-workers [11,12,29,30,31].In order to circumvent these parasitic phenomena, selective reduced integration (or, equivalently, u/p formulation, mean-dilatation technique and B-bar methods) -for volumetric locking -and the ''mixed interpolation of tensorial components''/assumed strain method -for transverse shear locking -had arisen as possible and successful techniques. In the literature see, for instance, references [4,45,53,54,61,68,69,74,85,86,96] for the grounds of computational treatment of incompressibility, in elastic and elastoplastic finite element cases, and also [9,38,56,67] for earlier works dealing with transverse shear locking.…”

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confidence: 98%

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confidence: 98%

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An enhanced strain 3D element for large deformation elastoplastic thin-shell applications

Valente

Sousa

Jorge

2004

Computational Mechanics

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In this work a previously proposed solid-shell finite element, entirely based on the Enhanced Assumed Strain (EAS) formulation, is extended in order to account for large deformation elastoplastic thin-shell problems. An optimal number of 12 enhanced (internal) variables is employed, leading to a computationally efficient performance when compared to other 3D or solid-shell enhanced elements. This low number of enhanced variables is sufficient to (directly) eliminate either volumetric and transverse shear lockings, the first one arising, for instance, in the fully plastic range, whilst the last appears for small thickness' values. The enhanced formulation comprises an additive split of the Green-Lagrange material strain tensor, turning the inclusion of nonlinear kinematics a straightforward task. Finally, some shell-type numerical benchmarks are carried out with the present formulation, and good results are obtained, compared to well-established formulations in the literature. Keywords Solid-shell elements, Enhanced strains, Volumetric and transverse shear lockings, Geometric and material nonlinearities, Thin shells 1 Introduction Finite element analysis of shell structures goes back in time until the onset of the so-called degenerated approach in works of Ahmad et al. [1] and Zienkiewicz et al. [101], as well as in early papers of Ramm [78], and afterwards with Hughes and Liu [55] and Hughes and Carnoy [57], among others. Soon it was verified that brick elements were prone to the appearance of volumetric and transverseshear locking effects. The first one is characteristic of common metal plasticity models, where plastic deformation is taken to be isochoric or, in other words, incompressible [19]. The second one comes from the analysis of thin shells, were the limit between ''thick'' and ''thin'' geometries is somewhat difficult to establish, with the occurrence of locking not only strictly relying on thickness/length ratios, as demonstrated by Chapelle, Bathe and co-workers [11,12,29,30,31].In order to circumvent these parasitic phenomena, selective reduced integration (or, equivalently, u/p formulation, mean-dilatation technique and B-bar methods) -for volumetric locking -and the ''mixed interpolation of tensorial components''/assumed strain method -for transverse shear locking -had arisen as possible and successful techniques. In the literature see, for instance, references [4,45,53,54,61,68,69,74,85,86,96] for the grounds of computational treatment of incompressibility, in elastic and elastoplastic finite element cases, and also [9,38,56,67] for earlier works dealing with transverse shear locking.In the specific case of shell elements, original planestress assumptions were enough to avoid or postpone incompressibility issues in the nonlinear material range [5,47,55,78,88], although at the expense of a rotation tensor inclusion. As more generality was needed, higher order theories including thickness change via extensible director fields and/or ''layerwise'' approaches were developed, including (or not) rotatio...

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confidence: 98%

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confidence: 98%

An enhanced strain 3D element for large deformation elastoplastic thin-shell applications

Valente

Sousa

Jorge

2004

Computational Mechanics

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“…When the shell is not inhibited, bending displacements are not described sufficiently accurately when the relative thickness ε is small [7,8,20] and the bending displacement is underestimated. Such phenomena also occur in the layers.…”

Section: The Numerical Procedures Of Resolution Using Anisotropic Adapmentioning

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“…3 The problem is sensitive and a pathological behaviour emerges progressively as ε tends towards zero. The solution of the limit problem is not contained anymore in the distribution space or in any Sobolev space, 4 and we have a complexification phenomenon: large oscillations corresponding to a new kind of instability appear on the free boundary [1,7,21].…”

Section: Introductionmentioning

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Singular perturbations generating complexification phenomena for elliptic shells

Béchet¹,

Sanchez‐Palencia²,

Millet³

2008

Comput Mech

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This paper deals with elliptic shell problems using the Koiter shell model. When the shell is well-inhibited, the limit membrane problem satisfies the Shapiro-Lopatinskii condition and we have a classical singular perturbation problem. In a previous paper, the existence of two kinds of singularities was put in a prominent position for this kind of problem. Conversely, for ill-inhibited shells (when a part of the boundary is free), the limit problem does not satisfy the Shapiro-Lopatinskii condition. Complexification phenomenon appears when the thickness approaches zero, leading to large oscillations corresponding to a new kind of instability on the free boundary. To complete the theoretical analysis, numerical simulations are performed with a finite element software coupled with an anisotropic adaptive mesh generator. This enables us to visualize precisely the singularities and the instabilities predicted by the theory with only a small number of elements.

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“…They can be directly applied to analysis of conforming finite elements [2,5,9,10], making many standard techniques of numerical analysis usable to shells. Such conforming methods, however, have not satisfactorily resolved the locking problem in shell computations, which severely undermines the accuracy of numerical solutions.…”

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confidence: 99%