Field‐ and edge‐consistency synthesis of A 4‐noded quadrilateral plate bending element

Prathap, Gangan; Somashekar, BR

doi:10.1002/nme.1620260803

Cited by 37 publications

(8 citation statements)

References 15 publications

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“…About the reduced integration technique, Prathap and Vishwanath [18] have mentioned that the integration type does not ensure the absence of shear locking. The 'Consistent ÿeld' approach they have proposed [19] suggested an optimal strategy with (2 × 1) and (1 × 2) Gauss integration of the terms 2 yz and 2 xz , respectively. The derived QUAD4-CC element is free of locking and has a proper rank.…”

Section: Synthesis Of Quadrilateral ÿNite Elements For Plate Bending=mentioning

confidence: 99%

An improved four‐node hybrid‐mixed element based upon Mindlin's plate theory

Ayad

Rigolot

2002

Numerical Meth Engineering

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SUMMARYBased on the mixed shear projected (MiSP) approach (Reference [54]: Int. J. Numer. Meth. Engng 1998; 42:1149-1179, an enhanced bending approximation for homogeneous isotropic plates is presented. Some hard benchmark tests, such as the skew plate (30 • ) problem, have often shown poor convergence when low-order elements (3-or 4-node element) are developed using linear approximations for kinematic variables. To put right this weakness, we propose a high-order interpolation for rotational dofs which results in more rich bending curvatures. The mid-side rotational nodes are eliminated using a combination of local discrete kinematic and constitutive Mindlin hypotheses. The derived 4-node quadrilateral element, called MiSP4+, is free of shear locking and passes all patch tests for thick and thin plates in an arbitrary mesh.

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Section: Synthesis Of Quadrilateral ÿNite Elements For Plate Bending=mentioning

confidence: 99%

An improved four‐node hybrid‐mixed element based upon Mindlin's plate theory

Ayad

Rigolot

2002

Numerical Meth Engineering

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“…Another concern for the finite element based on FSDT is the presence of shear locking phenomenon for thin plates. This problem has, however, been attempted to be alleviated by different methods such as the selective integration [5], assumed strain approach [4] and field consistent approach [8].…”

Section: Introductionmentioning

confidence: 99%

A new discrete Kirchhoff quadrilateral element based on the third-order theory for composite plates

Kulkarni

Kapuria

2005

Comput Mech

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A new discrete Kirchhoff quadrilateral element based on the refined third-order theory is developed for the analysis of composite plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid-surface. The inplane displacements and the shear strains are interpolated using bilinear interpolation functions and the mid-surface rotations are interpolated using bi-quadratic functions based on the discrete Kirchhoff technique. The element stiffness matrix and the consistent load vector are developed using the principle of virtual work. The finite element formulation is validated by comparing the results for simplysupported plate with the analytical Navier solution. Comparison of the present results with those using other available elements based on the TOT establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The element is free from shear locking.

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“…The displacement field is given by + a~( w i 9 @xz)q + @3(8x,)5 + a4(ex,)5~ (20) A similar expression can be obtained for y, by simply interchanging x and 5 by y and q.…”

Section: Four Node Rectangular Reissner-mindlin Plate Elementmentioning

confidence: 88%

“…For the bilinear rectangular plate element we can write, after observation of the initial strain field (see equation (20)),…”

Section: Choice O F Substitute Strain Fieldsmentioning

confidence: 99%

A general methodology for deriving shear constrained Reissner‐Mindlin plate elements

Oñate

Zienkiewicz

Suárez

et al. 1992

Numerical Meth Engineering

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SUMMARYIn this paper the necessary requirements for the good behaviour of shear constrained Reissner-Mindlin plate elements for thick and thin plate situations are re-interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re-formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.

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Field‐ and edge‐consistency synthesis of A 4‐noded quadrilateral plate bending element

Cited by 37 publications

References 15 publications

An improved four‐node hybrid‐mixed element based upon Mindlin's plate theory

An improved four‐node hybrid‐mixed element based upon Mindlin's plate theory

A new discrete Kirchhoff quadrilateral element based on the third-order theory for composite plates

A general methodology for deriving shear constrained Reissner‐Mindlin plate elements

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