Accurate solution of traction free boundaries using hybrid stress membrane elements with drilling degrees of freedom

Groenwold, Albert A.; Xiao, Q. Z.; Theron, N.J.

doi:10.1016/j.compstruc.2003.10.030

Cited by 9 publications

(6 citation statements)

References 24 publications

(36 reference statements)

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“…Since then, many efforts have been put on developing membrane elements with drilling DOFs. Recent attempts include but are not limited to the literatures …”

Section: Introductionmentioning

confidence: 99%

“…Recent attempts include but are not limited to the literatures. [50][51][52][53][54][55] In the present work, a simple but robust unsymmetric 4-node low-order quadrilateral membrane element with the drilling DOFs is developed. First, the test function of this element is assumed as a new kind of 2-dimensional isoparametric-based displacement field enriched by the drilling DOFs.…”

Section: Introductionmentioning

confidence: 99%

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4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

Shang

Ouyang

2017

Numerical Meth Engineering

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Summary The unsymmetric finite element method is a promising technique to produce distortion‐immune finite elements. In this work, a simple but robust 4‐node 12‐DOF unsymmetric quadrilateral membrane element is formulated. The test function of this new element is determined by a concise isoparametric‐based displacement field that is enriched by the Allman‐type drilling degrees of freedom. Meanwhile, a rational stress field, instead of the displacement one in the original unsymmetric formulation, is directly adopted to be the element's trial function. This stress field is obtained based on the analytical solutions of the plane stress/strain problem and the quasi‐conforming technique. Thus, it can a priori satisfy related governing equations. Numerical tests show that the presented new unsymmetric element, named as US‐Q4θ, exhibits excellent capabilities in predicting results of both displacement and stress, in most cases, superior to other existing 4‐node element models. In particular, it can still work very well in severely distorted meshes even when the element shape deteriorates into concave quadrangle or degenerated triangle.

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“…Since then, many efforts have been put on developing membrane elements with drilling DOFs. Recent attempts include but are not limited to the literatures …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

Shang

Ouyang

2017

Numerical Meth Engineering

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“…The definition of the drilling DOFs proposed by Allman [3,4] can be treated as a milestone for this topic, in which a quadratic displacement approximation was introduced to supplement the drilling DOFs at element nodes. Based on Allman's work, numerous researches on plane elements with drilling degrees of freedom have been accomplished, such as the models proposed by Bergan and Felippa [5], Cook [6,7], MacNeal and Harder [8], Yunus et al [9], Hughes and Brezzi [10], Ibrahimbegovic et al [11], Iura and Atluri [12], Cazzani and Atluri [13], Piltner and Taylor [14], Geyer and Groenwold [15], Pimpinelli [16], Groenwold et al [17], Choi et al [18], Choo et al [19], Zhang and Kuang [20], Kugler et al [21], and Cen et al [22]. Long et al [23][24][25] presented a new definition on the drilling DOFs.…”

Section: Introductionmentioning

confidence: 99%

Four-Node Generalized Conforming Membrane Elements with Drilling DOFs Using Quadrilateral Area Coordinate Methods

Chen

Cen

Sun

et al. 2015

Mathematical Problems in Engineering

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Two 4-node generalized conforming quadrilateral membrane elements with drilling DOF, named QAC4 and QAC4 M, were successfully developed. Two kinds of quadrilateral area coordinates are used together in the assumed displacement fields of the new elements, so that the related formulations are quite straightforward and will keep the order of the Cartesian coordinates unchangeable while the mesh is distorted. The drilling DOF is defined as the additional rigid rotation at the element nodes to avoid improper constraint. Both elements can pass the strict patch test and exhibit better performance than other similar models. In particular, they are both free of trapezoidal locking in MacNeal's beam test and insensitive to various mesh distortions.

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“…Later in the 1990s, a series of successful studies was undertaken [17][18][19]. The recent studies in the subject area were reported by some researchers [20][21][22][23][24][25].All of these developments were done largely based on three-node triangle elements or fournode quadrilateral elements. However, for some special thick plate structures, such as transfer plates in tall buildings as mentioned before, high-order elements [26] should have a much better performance than linear triangle or bi-linear quadrilateral elements.The primary objective of this paper is to develop an eight-node arbitrary quadrilateral membrane element with drilling degrees of freedom using the compatible displacement interpolation within the element.…”

mentioning

confidence: 99%

“…Later in the 1990s, a series of successful studies was undertaken [17][18][19]. The recent studies in the subject area were reported by some researchers [20][21][22][23][24][25].…”

mentioning

confidence: 99%

Eight‐node membrane element with drilling degrees of freedom for analysis of in‐plane stiffness of thick floor plates

Zhang

Kuang

2008

Numerical Meth Engineering

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SUMMARYThe development of eight-node arbitrary quadrilateral membrane elements with drilling degrees of freedom is presented using the compatible displacement interpolation within the element. The element is considered to develop specifically for analysing the in-plane stiffness of thick floor plates in building systems, particularly the transfer plates in tall buildings as well as pile caps. With a new set of shape functions and following the displacement-based element procedure, the element stiffness and force vector are derived and nodal displacements are obtained after solving the simultaneous equations; the element stresses are then determined. A wide range of patch tests is conducted to evaluate the consistency and stability of the proposed element. The test results show very good agreement with the exact solutions of the beam theory. Numerical investigations are carried out, showing that the analyses using the proposed elements provide better results than those from the existing methods.

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Accurate solution of traction free boundaries using hybrid stress membrane elements with drilling degrees of freedom

Cited by 9 publications

References 24 publications

4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

Four-Node Generalized Conforming Membrane Elements with Drilling DOFs Using Quadrilateral Area Coordinate Methods

Eight‐node membrane element with drilling degrees of freedom for analysis of in‐plane stiffness of thick floor plates

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