The <i>h</i>–<i>p</i>‐version of the finite‐element method in the plate modelling problem

Babuška, Ivo; Li, L.

doi:10.1002/cnm.1630080104

Cited by 25 publications

References 5 publications

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Plates and Shells: Asymptotic Expansions and Hierarchic Models

Dauge

Faou

Yosibash

2004

Encyclopedia of Computational Mechanics

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Concerning thin structures such as plates and shells, the idea of reducing the equations of elasticity to twodimensional models defined on the mid-surface seems relevant. Such a reduction was first performed thanks to kinematical hypotheses about the transformation of normal lines to the mid-surface. As nowadays, the asymptotic expansion of the displacement solution of the three-dimensional linear model is fully known at least for plates and clamped elliptic shells, we start from a description of these expansions in order to introduce the twodimensional models known as hierarchical models: These models extend the classical models, and pre-suppose the displacement to be polynomial in the thickness variable, transverse to the mid-surface. Because of the singularly perturbed character of the elasticity problem as the thickness approaches zero, boundary-or internal layers may appear in the displacements and stresses, and so may numerical locking effects. The use of hierarchical models, discretized by higher degree polynomials (p-version of finite elements) may help to overcome these severe difficulties.

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Plates and Shells: Asymptotic Expansions and Hierarchic Models

Dauge

Faou

Yosibash

2004

Encyclopedia of Computational Mechanics

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Plates and Shells: Asymptotic Expansions and Hierarchical Models

Dauge

Faou

Yosibash

2017

Encyclopedia of Computational Mechanics Second Edition

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Concerning thin structures such as plates and shells, the idea of reducing the equations of elasticity to two‐dimensional models defined on the mid‐surface seems relevant. Such a reduction was first performed thanks to kinematical hypotheses about the transformation of normal lines to the mid‐surface. As the asymptotic expansion of the displacement solution of the three‐dimensional linear model is fully known, at least for plates and clamped elliptic shells, we start from a description of these expansions in order to introduce the two‐dimensional models known as hierarchical models: These models extend the classical models, and pre‐suppose the displacement to be polynomial in the thickness variable, transverse to the mid‐surface. Because of the singularly perturbed character of the elasticity problem as the thickness approaches zero, boundary‐ or internal layers may appear in the displacements and stresses, and so may numerical locking effects. The use of hierarchical models, discretized by higher degree polynomials (‐version of finite elements) may help to overcome these severe difficulties.

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