The mathematical shell model underlying general shell elements

Chapelle, Dominique; Bathe, Klaus‐Jürgen

doi:10.1002/(sici)1097-0207(20000520)48:2<289::aid-nme897>3.0.co;2-8

Cited by 66 publications

(38 citation statements)

References 9 publications

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“…This modiÿcation leads to a membrane-dominated problem, where pure bending is inhibited but still conducting to a well-posed problem (References [26][27][28][29]). …”

Section: Membrane-dominated Test I -Clamped Cylindrical Shellmentioning

confidence: 99%

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Development of shear locking‐free shell elements using an enhanced assumed strain formulation

Sá

Jorge

Valente

et al. 2001

Numerical Meth Engineering

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SUMMARYThe degenerated approach for shell elements of Ahmad and co-workers is revisited in this paper. To avoid transverse shear locking e ects in four-node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse shear terms of the strain ÿeld. In the ÿrst part of the work the analysis of the null transverse shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking e ects are then justiÿed by the inability of the null transverse shear strain subspace, implicitly deÿned by a given ÿnite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single-element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse shear strain subspace is provided by the EAS method, enforcing Kirchho hypothesis for low thickness values and leading to a framework for the development of shear-lockingfree shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation.

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“…This modiÿcation leads to a membrane-dominated problem, where pure bending is inhibited but still conducting to a well-posed problem (References [26][27][28][29]). …”

Section: Membrane-dominated Test I -Clamped Cylindrical Shellmentioning

confidence: 99%

“…Based on a detailed analysis of bending and membrane subspaces, those authors developed a class of benchmark tests for the behaviour characterization of shell elements, which will be used in this paper (for details see References [28][29][30]). …”

Section: Introductionmentioning

confidence: 99%

Development of shear locking‐free shell elements using an enhanced assumed strain formulation

Sá

Jorge

Valente

et al. 2001

Numerical Meth Engineering

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“…In this way, different shell mathematical models can be derived, but in practice by far most shell analyses are based on the finite element discretization of the basic shell model presented and analyzed by Chapelle and Bathe [3,6], see also Ref. [7].…”

Section: The Governing Shell Equationsmentioning

confidence: 99%

“…(6) and (7), and then the consistent nodal point force vectors by the usual interpolation and integration over the finite elements discretizing the shell surface. In the practical use of these norms, it is very important to employ, when the exact solutionũ is unknown, instead, a reliable reference mesh finite element solution,ũ ref , obtained using a very fine mesh with an element that satisfies the consistency condition.…”

Section: Error Measuresmentioning

confidence: 99%

Measuring the convergence behavior of shell analysis schemes

Bathe

Lee

2011

Computers & Structures

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a b s t r a c tWhile shells have been analyzed abundantly for many years in engineering and the sciences, improved finite element and related analysis methods are still much desired and researched. More general and effective finite element procedures are needed for complex shell structures, including for the analysis of composite shells and the optimization of shells. In this paper we discuss how finite element methods, and other analysis techniques, should be tested in order to identify their reliability and effectiveness. We summarize some important theoretical results, present appropriate test problems and convergence measures, and we illustrate our discussion through some novel numerical results. An important conclusion is that the testing has to be performed very carefully in order to obtain relevant results, and we show how this is accomplished in detail.

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“…The MITC elements can be formulated using a continuum representation or the 'basic shell model' identified by Chapelle and Bathe [1,2,10,11]. While the Reissner-Mindlin assumptions are widely applicable, they cannot model the application of shell surface stresses as needed in the analysis of a shell confined between solid media.…”

Section: Introductionmentioning

confidence: 99%

A 4-node 3D-shell element to model shell surface tractions and incompressible behavior

Kim

Bathe

2008

Computers & Structures

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a b s t r a c tWe present in this paper a shell element that models the three-dimensional (3D) effects of surface tractions, like needed when a shell is confined between other solid media. The element is the widely used MITC4 shell element enriched by the use of a fully 3D stress-strain description, appropriate throughthe-thickness displacements to model surface tractions, and pressure degrees of freedom for incompressible analyses. The element formulation avoids instabilities and ill-conditioning. Various example solutions are presented to illustrate the capabilities of the element.

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The mathematical shell model underlying general shell elements

Cited by 66 publications

References 9 publications

Development of shear locking‐free shell elements using an enhanced assumed strain formulation

Development of shear locking‐free shell elements using an enhanced assumed strain formulation

Measuring the convergence behavior of shell analysis schemes

A 4-node 3D-shell element to model shell surface tractions and incompressible behavior

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