Bending Moment Mixed Method for the Kirchhoff--Love Plate Model

Amara, Mohamed; Capatina-Papaghiuc, Daniela; Chatti, Amna

doi:10.1137/s0036142900379680

Cited by 17 publications

(35 citation statements)

References 5 publications

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“…We follow an approach introduced and analyzed in [1] to deal with the load problem for Kirchhoff plates, adapted to the spectral problems of the previous section. Since the adaptation to the buckling problem presents several additional difficulties which must be tackled, we will describe this case in more detail and only summarize the analogous results for the vibration problem.…”

Section: Formulation Of the Spectral Problems In Terms Of Bending Mommentioning

confidence: 99%

“…To obtain a weak formulation of problem (2.9) we proceed as in [1]. First note that the operator C is invertible, its inverse being given by…”

Section: Formulation Of the Spectral Problems In Terms Of Bending Mommentioning

confidence: 99%

“…With this purpose, we follow once more the arguments proposed in [1] to obtain a convenient decomposition of the space X 0 . Consider the following space:…”

Section: Equivalent Variational Formulationsmentioning

confidence: 99%

“…Another low-order method was introduced much more recently by Amara et al in [1] to deal with the load problem for a Kirchhoff-Love plate subject to arbitrary boundary conditions. This method is based on a standard discretization by loworder conforming elements of a bending moment formulation.…”

Section: Introductionmentioning

confidence: 99%

“…We recall the mixed formulation in terms of bending moments and a third equivalent formulation considered in [1], which allows using standard finite elements for its discretization. In Section 3 we develop the numerical analysis of the buckling problem.…”

Section: Introductionmentioning

confidence: 99%

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A piecewise linear finite element method for the buckling and the vibration problems of thin plates

Mora¹,

Rodrı́guez²

2009

Math. Comp.

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Abstract. The aim of this paper is to analyze a piecewise linear finite element method to approximate the buckling and the vibration problems of a thin plate. The method is based on a conforming discretization of a bending moment formulation for the Kirchhoff-Love model. The analysis restricts to simply connected polygonal clamped plates, not necessarily convex. The method is proved to converge with optimal order for both spectral problems, including an improved order for the eigenvalues. Numerical experiments are reported to assess its performance and to compare it with other low-order finite element methods.

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Section: Formulation Of the Spectral Problems In Terms Of Bending Mommentioning

confidence: 99%

“…To obtain a weak formulation of problem (2.9) we proceed as in [1]. First note that the operator C is invertible, its inverse being given by…”

Section: Formulation Of the Spectral Problems In Terms Of Bending Mommentioning

confidence: 99%

“…With this purpose, we follow once more the arguments proposed in [1] to obtain a convenient decomposition of the space X 0 . Consider the following space:…”

Section: Equivalent Variational Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A piecewise linear finite element method for the buckling and the vibration problems of thin plates

Mora¹,

Rodrı́guez²

2009

Math. Comp.

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A reduced local C⁰ discontinuous galerkin method for Kirchhoff plates

Huang

2014

Numerical Methods Partial

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We propose and analyze a reduced local C0 discontinuous Galerkin (reduced LCDG) method with minimal penalization for Kirchhoff plate bending problems. The resulting linear system of the method can be solved efficiently by Gaussian elimination. Based on the key observation that the reduced LCDG method can be viewed as the localization of Hellan–Herrmann–Johnson method, we are inspired to use the techniques for dealing with the latter method to derive the well‐posedness and a priori error estimates of the reduced LCDG method. With the help of Zienkiewicz–Guzmán–Neilan element space, the a posteriori error analysis is also developed. Some numerical results are provided to demonstrate the theoretical estimates.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1902–1930, 2014

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Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system

Geredeli,

Kunwar,

Lee

2024

Numerical Methods Partial

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We consider the finite element approximation of a coupled fluid‐structure interaction (FSI) system, which comprises a three‐dimensional (3D) Stokes flow and a two‐dimensional (2D) fourth‐order Euler–Bernoulli or Kirchhoff plate. The interaction of these parabolic and hyperbolic partial differential equations (PDE) occurs at the boundary interface which is assumed to be fixed. The vertical displacement of the plate dynamics evolves on the flat portion of the boundary where the coupling conditions are implemented via the matching velocities of the plate and fluid flow, as well as the Dirichlet boundary trace of the pressure. This pressure term also acts as a coupling agent, since it appears as a forcing term on the flat, elastic plate domain. Our main focus in this work is to generate some numerical results concerning the approximate solutions to the FSI model. For this, we propose a numerical algorithm that sequentially solves the fluid and plate subsystems through an effective decoupling approach. Numerical results of test problems are presented to illustrate the performance of the proposed method.

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Bending Moment Mixed Method for the Kirchhoff--Love Plate Model

Cited by 17 publications

References 5 publications

A piecewise linear finite element method for the buckling and the vibration problems of thin plates

A piecewise linear finite element method for the buckling and the vibration problems of thin plates

A reduced local C⁰ discontinuous galerkin method for Kirchhoff plates

Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system

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Bending Moment Mixed Method for the Kirchhoff--Love Plate Model

Cited by 17 publications

References 5 publications

A piecewise linear finite element method for the buckling and the vibration problems of thin plates

A piecewise linear finite element method for the buckling and the vibration problems of thin plates

A reduced local C0 discontinuous galerkin method for Kirchhoff plates

Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system

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A reduced local C⁰ discontinuous galerkin method for Kirchhoff plates