Several Treatments on Nonconforming Element Failed in the Strict Patch Test

Chen, Xiaoming; Cen, Song; Li, Yungui; Sun, Jianyun

doi:10.1155/2013/901495

Cited by 5 publications

(13 citation statements)

References 27 publications

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“…So, their convergence raised some queries and discussions [34,35]. Cen et al [29] and Chen et al [36] tried to make them pass the C 0 patch test, but the distortion resistance will be destroyed again for bending tests.…”

Section: For Past 60 Years Numerous Efforts Have Been Made To Improvmentioning

confidence: 99%

An unsymmetric 8‐node hexahedral element with high distortion tolerance

Zhou

Cen

Huang

et al. 2016

Numerical Meth Engineering

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SUMMARYAmong all 3D 8-node hexahedral solid elements in current finite element library, the 'best' one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8-node, 24-DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8-node tri-linear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US-ATFH8, contains no adjustable factor, and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first-order (constant stress/strain) patch test and the second-order patch test for pure bending, remove the volume locking, and provide the

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Section: For Past 60 Years Numerous Efforts Have Been Made To Improvmentioning

confidence: 99%

An unsymmetric 8‐node hexahedral element with high distortion tolerance

Zhou

Cen

Huang

et al. 2016

Numerical Meth Engineering

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“…Chen et al . imposed some constraints on the elements to make them pass the C 0 patch test, but the trapezoidal locking in bending comes back.…”

Section: Introductionmentioning

confidence: 99%

“…So, their convergence raised some queries and discussions [41][42][43]. Chen et al [44] imposed some constraints on the elements to make them pass the C 0 patch test, but the trapezoidal locking in bending comes back.…”

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confidence: 99%

An unsymmetric 4-node, 8-DOF plane membrane element perfectly breaking through MacNeal's theorem

Cen

Zhou

et al. 2015

Int. J. Numer. Meth. Engng

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Summary Among numerous finite element techniques, few models can perfectly (without any numerical problems) break through MacNeal's theorem: any 4‐node, 8‐DOF membrane element will either lock in in‐plane bending or fail to pass a C0 patch test when the element's shape is an isosceles trapezoid. In this paper, a 4‐node plane quadrilateral membrane element is developed following the unsymmetric formulation concept, which means two different sets of interpolation functions for displacement fields are simultaneously used. The first set employs the shape functions of the traditional 4‐node bilinear isoparametric element, while the second set adopts a novel composite coordinate interpolation scheme with analytical trail function method, in which the Cartesian coordinates (x,y) and the second form of quadrilateral area coordinates (QACM‐II) (S,T) are applied together. The resulting element US‐ATFQ4 exhibits amazing performance in rigorous numerical tests. It is insensitive to various serious mesh distortions, free of trapezoidal locking, and can satisfy both the classical first‐order patch test and the second‐order patch test for pure bending. Furthermore, because of usage of the second form of quadrilateral area coordinates (QACM‐II), the new element provides the invariance for the coordinate rotation. It seems that the behaviors of the present model are beyond the well‐known contradiction defined by MacNeal's theorem. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Most of these new elements formulated with quadrilateral area coordinate methods can present exact solution for patch test, but some of them are the same as Q6 element, Chen et al [11] researched different methods to make them pass the patch test. In this paper, a universal form of internal displacement field was formulated by using QACM-III based on generalized conforming theory.…”

Section: Introductionmentioning

confidence: 99%

A universal form of internal displacement field based quadrilateral area coordinate method QACM-III

Chen¹,

Jin²,

Li³

2017

Proceedings of the 2017 6th International Conference on Energy and Environmental Protection (ICEEP 2017)

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Abstract. By supplement appropriate internal displacement field on the nodal displacement of the element, the complementary of displacement polynomial can be increased, so the accuracy of element can be improved and the element may be more insensitive to mesh distortion. But in order to keep compatibility of source element, internal displacement field should be researched according to different source elements. In this paper, based on generalized conforming theory, the third quadrilateral area coordinate method QACM-III was used to develop universal form for plane elements. This universal internal displacement field can be used easily for those plane elements formulated with QACM-III.

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Several Treatments on Nonconforming Element Failed in the Strict Patch Test

Cited by 5 publications

References 27 publications

An unsymmetric 8‐node hexahedral element with high distortion tolerance

An unsymmetric 8‐node hexahedral element with high distortion tolerance

An unsymmetric 4-node, 8-DOF plane membrane element perfectly breaking through MacNeal's theorem

A universal form of internal displacement field based quadrilateral area coordinate method QACM-III

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