On the convergence of a discrete Kirchhoff triangle method valid for shells of arbitrary shape

Bernadoua, Michel; Eiroa, Pilar Mato; Trouve, P.

doi:10.1016/0045-7825(94)90008-6

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…Indeed, there does not exist yet a ''uniformly optimal'' triangular shell element, and not even an element close to optimal. The motivation of this research comes from the fact that the development of optimal triangular shell elements is still a great challenge [10,12,[15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Development of MITC isotropic triangular shell finite elements

Lee

Bathe

2004

Computers & Structures

226

158

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Section: Introductionmentioning

confidence: 99%

Development of MITC isotropic triangular shell finite elements

Lee

Bathe

2004

Computers & Structures

226

158

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“…On the other hand, NURBS-based formulation, by construction, maintains tangent-continuity throughout the computational domain during deformation. We refer to [13] for numerical analysis of finite elements based on DK constraints in the linear case. The study of wrinkling in thin elastic sheets has attracted significant interest in the past two decades [25,24,72,64,74,46,62,61], and investigators have used a variety of two-dimensional models, numerical simulations, and even analytical treatments, to capture this phenomena.…”

Section: Point Indentation Of a Semi-cylindermentioning

confidence: 99%

Isogeometric Analysis of Elastic Sheets Exhibiting Combined Bending and Stretching using Dynamic Relaxation

Padhye¹,

Kalia²

2022

Preprint

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Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric formulation, based on classical Koiter nonlinear shell theory, to study instability problems like wrinkling and buckling in thin shells. The use of NURBS-basis provides rotation-free, conforming, higher-order spatial continuity, such that curvatures and membrane strains can be computed directly from the interpolation of the position vectors of the control points. A pseudo, dissipative and discrete, dynamical system is constructed, and static equilibrium solutions are obtained by the method of dynamic relaxation (DR). A high-performance computing-based implementation of the DR is presented, and the proposed formulation is benchmarked against several existing numerical, and experimental results. The advantages of this formulation, over traditional finite element approaches, in assessing structural response of the shells are presented.

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“…This implies that C 1 finite elements must be used to obtain a conforming discretization of the model, at least for the transverse component of the displacement. the DKT elements, see (Batoz, Bathe & Ho 1980, Bernadou, Mato Eiroa & Trouve 1994, Carrive, Le Tallec & Mouro 1995 and the references therein. In fact, a major reason for this preference can be seen by considering an example of C 1 -conforming finite element known as the Argyris triangle, see e.g.…”

Section: Discretizations Of Shell Mathematical Modelsmentioning

confidence: 99%

The Finite Element Analysis of Shells — Fundamentals

Chapelle

Bathe

2003

Computational Fluid and Solid Mechanics

197

104

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PrefaceSince the first developments of finite element methods for the analysis of shells, about half a century ago, the possibilities to analyze shells in designs and to study, in general, the behavior of shell structures have vastly increased. However, at the same time as shell finite element procedures were rapidly introduced in many everyday practices of engineering analysis, also, a large research effort was directed towards increasing the capabilities of shell finite element methods, for linear and nonlinear analyses. This research effort is still ongoing because of the great challenges in shell structural analyses. These challenges are largely due to the diversity of shell structural behaviors and the difficulties to solve for such behaviors in a reliable and uniformly effective, ideally optimal, manner. The difficulties are apparent when considering complex shells of arbitrary curvatures, material conditions, boundary supports, loading, and in particular of small thickness. Furthermore, these challenges have grown during the last decades, and probably will continue to grow, because increasingly more daring -but also more beautiful -shell structures have been designed and analyzed than previously thought possible.The earliest studies of shell structures using analytical methods were performed well over a century ago. At that time, and indeed until the development of the finite element method, researchers used all the available physical and mathematical understanding to formulate shell theories and solve shell problems. While the shell theories were quite general in nature, the actual solutions obtained to a shell problem were mostly very approximate, that is, when compared with the actual physical behavior of the shell considered.With the development of the modern finite element method, the approach towards the practical solution of shell problems changed. Finite element procedures were largely developed based on physical understanding without the use of mathematical shell theories. Indeed, various shell finite element methods were proposed by simply superimposing plate bending and plane stress membrane behaviors. With this approach many shell structures were successfully analyzed, but of course only to a certain level of accuracy. In fact, the significant limitations of such element formulations became also apparent and, to some extent, recourse to the use of shell theories was sought to develop more powerful finite element methods. VI PrefaceThe effective study of shell structures clearly requires a deep physical understanding of shell structural behaviors. The development of more powerful finite element methods requires in addition a strong knowledge of mathematical theories. Indeed, it is clearly the synergy between physical and mathematical understanding that will advance our knowledge of shell structural behaviors and the development of finite element methods. This, in fact, corresponds to the approach taken many years ago in the study of shell structures, but is now a path more difficult to follow. N...

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On the convergence of a discrete Kirchhoff triangle method valid for shells of arbitrary shape

Cited by 9 publications

References 14 publications

Development of MITC isotropic triangular shell finite elements

Development of MITC isotropic triangular shell finite elements

Isogeometric Analysis of Elastic Sheets Exhibiting Combined Bending and Stretching using Dynamic Relaxation

The Finite Element Analysis of Shells — Fundamentals

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