An effective quadrilateral membrane finite element based on the strain approach

Rebiai, C.; Belounar, Lamine

doi:10.1016/j.measurement.2013.12.043

Cited by 17 publications

(6 citation statements)

References 16 publications

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“…Nevertheless, with the aim of conceiving a high-performance formulation, several potential improvements have been sought for in the literature. Among those, the introduction of corner rotational DOFs, initially explored by Allman [1], has been recognized as an attractive strategy to pursue intermediate accuracy between linear and quadratic elements with translations only [106,2,43,78,26,25,82,80]. On the other hand, drilling DOFs are associated to zero-energy spurious modes that need to be suppressed, via a modification of underlying variational formulation [41,44,69] or an adhoc treatment of the relevant interpolation [51].…”

Section: Interpolation Of Unknown Fieldsmentioning

confidence: 99%

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

Nodargi

2018

Arch Computat Methods Eng

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As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard displacement-based finite element formulations, attention is here focused on the use of mixed methods as approximation technique, within the small strain framework, for the mechanical problem of inelastic bidimensional structures. Despite a great flexibility characterizes mixed element formulations, several theoretical and numerical aspects have to be carefully taken into account in the design of a high-performance element. The present work aims at providing the basis for methodological analysis and comparison in such aspects, within the unified mathematical setting supplied by generalized standard material model and with special interest towards elastoplastic media. A critical review of the state-of-the-art computational methods is delivered in regard to variational formulations, selection of interpolation spaces, numerical solution strategies and numerical stability. Though those arguments are interrelated, a topic-oriented presentation is resorted to, for the very rich available literature to be properly examined. Finally, the performances of several significant mixed finite element formulations are investigated in numerical simulations.

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Section: Interpolation Of Unknown Fieldsmentioning

confidence: 99%

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

Nodargi

2018

Arch Computat Methods Eng

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“…The element compliance matrix H e is defined by the energy equivalence (9). Exploiting the properties of stress interpolation, the compliance matrix is conveniently obtained through Eq.…”

Section: Compliance and Compatibility Matricesmentioning

confidence: 99%

“…Research in developing high performance membrane finite elements, accurate for coarse meshes and less sensitive to geometry distortion, is even nowparticularly active [1][2][3][4][5][6][7][8][9]. Often, membrane elements are coupled with bending discretization to be used in linear and geometrically nonlinear analysis of folded plates, box structures also assembled with other type of element, as was given in [10,11].…”

Section: Introductionmentioning

confidence: 99%

A mixed isostatic 16 dof quadrilateral membrane element with drilling rotations, based on Airy stresses

Madeo¹,

Casciaro²,

Zagari³

et al. 2014

Finite Elements in Analysis and Design

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“…They analyzed the influence of the shell element with the different patterns of sampling points for interpolating different components of strains. Rebiai and Belounar [15] developed a new simple and efficient four-node quadrilateral membrane finite element with drilling rotation. Wang and Sun [16] developed a new 4node quadrilateral flat shell element for geometrically nonlinear analyses of thin and moderately thick laminated shell structures.…”

Section: Introductionmentioning

confidence: 99%

The stress analysis of a shear wall with matrix displacement method using rectangular finite element

Ergün¹,

Ateş²

2021

JSEAM

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The aim in this study is to numerically present some characteristic features of the rectangular finite element using the matrix displacement method and to show the utility of this element in plane stress problems compared to the finite element method. The paper consisted of three parts. In the first part, all of the finite element formulation steps from choosing the convenient coordinate system to creating element stiffness matrix are presented respectively. In the second part of the study, a static finite element analysis of the shear wall is also made by ANSYS Mechanical APDL. In the final part, the results (displacements, strains and stresses) obtained from the previous parts are compared with each other by the help of tables and graphics. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be conducted in order to indicate the efficiency of the matrix displacement method for the solution of different types of plane stress problems using different finite elements.

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An effective quadrilateral membrane finite element based on the strain approach

Cited by 17 publications

References 16 publications

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

A mixed isostatic 16 dof quadrilateral membrane element with drilling rotations, based on Airy stresses

The stress analysis of a shear wall with matrix displacement method using rectangular finite element

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