A study of boundary layers in plates using Mindlin‐Reissner and 3‐D elements

Rao, N. Bheema; Özakça, Mustafa; Hinton, E.

doi:10.1002/nme.1620330613

Cited by 16 publications

(10 citation statements)

References 10 publications

(3 reference statements)

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“…For this series of elements, the shear strain in the global x-y co-ordinates is obtained by the transformation stated in equation (11). The inverse of the Jacobian matrix there is in general a rational function of the natural co-ordinates.…”

Section: Rate Of Convergence For the Assumed Strain Elementsmentioning

confidence: 99%

Automatic adaptive refinement for plate bending problems using Reissner-Mindlin plate bending elements

Lee

Hobbs

1998

Int. J. Numer. Meth. Engng.

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The influence of the presence of singular points and boundary layers associated with the edge effects in a Reissner-Mindlin (RM) plate in the design of an optimal mesh for a finite element solution is studied, and methods for controlling the discretization error of the solution are suggested. An effective adaptive refinement strategy for the solution of plate bending problems based on the RM plate bending model is developed. This two-stage adaptive strategy is designed to control both the total and the shear error norms of a plate in which both singular points and boundary layers are present. A series of three different order assumed strain RM plate bending elements has been used in the adaptive refinement procedure. The locations of optimal sampling points and the effect of element shape distortions on the theoretical convergence rate of these elements are given and discussed. Numerical experiments show that the suggested refinement procedure is effective and that optimally refined meshes can be generated. It is also found that all the plate bending elements used can attain their full convergence rates regardless of the presence of singular points and boundary layers inside the problem domain. Boundary layer effects are well captured in all the examples tested and the use of a second stage of refinement to control the shear error is justified. In addition, tests on the Zienkiewicz-Zhu error estimator show that their performances are satisfactory. Finally, tests of the relative effectiveness of the plate bending elements used have also been made and it is found that while the higher order cubic element is the most accurate element tested, the quadratic element tested is the most efficient one in terms of CPU time used.

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Section: Rate Of Convergence For the Assumed Strain Elementsmentioning

confidence: 99%

Automatic adaptive refinement for plate bending problems using Reissner-Mindlin plate bending elements

Lee

Hobbs

1998

Int. J. Numer. Meth. Engng.

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“…For instance, Selman et al , adopted the triangular Mindlin–Reissner elements to study the edge effect of plates with various shapes, in conjunction with using adaptive mesh refinement procedures; Rao et al. used the Mindlin–Reissner plate and 3D elements to predict the distributions of resultants in plates, along with a crude adaptive strategy. Although the use of an adaptive mesh refinement technique may help solve these difficulties in modeling the boundary layer, the existence of the edge effect will slow down the convergence rate greatly, especially for relatively thin plates.…”

Section: Introductionmentioning

confidence: 99%

An effective hybrid displacement function element method for solving the edge effect of Mindlin–Reissner plate

Shang

Cen

et al. 2015

Numerical Meth Engineering

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SummaryIn bending problems of Mindlin–Reissner plate, the resultant forces often vary dramatically within a narrow range near free and soft simply‐supported (SS1) boundaries. This is so‐called the edge effect or the boundary layer effect, a challenging problem for conventional finite element method. In this paper, an effective finite element method for analysis of such edge effect is developed. The construction procedure is based on the hybrid displacement function (HDF) element method [1], a simple hybrid‐Trefftz stress element method proposed recently. What is different is that an additional displacement function f related to the edge effect is considered, and its analytical solutions are employed as the additional trial functions for the first time. Furthermore, the free and the SS1 boundary conditions are also applied to modify the element assumed resultant fields. Then, two new special elements, HDF‐P4‐Free and HDF‐P4‐SS1, are successfully constructed. These new elements are allocated along the corresponding boundaries of the plate, while the other region is modeled by the usual HDF plate element HDF‐P4‐11 β [1]. Numerical tests demonstrate that the present method can effectively capture the edge effects and exactly satisfy the corresponding boundary conditions by only using relatively coarse meshes. Copyright © 2015 John Wiley & Sons, Ltd.

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“…One of the possible ways would be to utilize the Reissner-Mindlin (RM) (thick-) plate model which only requires C 0 ðxÞÀ elements and therefore is easier to implement. Several sources suggest that the RM model in a number of cases more adequately reflects the physical behavior [31] of thin structures and also when it comes to the reproduction of boundary layers [32,33]. Another way would be to employ one of the non-conforming approaches that have been proposed for the KL model which require that additional steps, undesirable for the use in general purpose software, have to been taken in order to reproduce the solution expected in the thin-plate limit.…”

Section: Fe-discretization Of the Coupled Multi-layered Plate Equationsmentioning

confidence: 99%

“…Using definition (32) and taking into account that integration over edges E in the domain interior occurs twice the above equation becomes…”

Section: Error Analysis For Coupled Thin-structure Fe-problemsmentioning

confidence: 99%

Adaptive error control in multi-physical thin-structure MEMS FE-simulation

Müller¹,

Korvink²

2004

Journal of Computational Physics

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A study of boundary layers in plates using Mindlin‐Reissner and 3‐D elements

Cited by 16 publications

References 10 publications

Automatic adaptive refinement for plate bending problems using Reissner-Mindlin plate bending elements

Automatic adaptive refinement for plate bending problems using Reissner-Mindlin plate bending elements

An effective hybrid displacement function element method for solving the edge effect of Mindlin–Reissner plate

Adaptive error control in multi-physical thin-structure MEMS FE-simulation

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