Remedies to rotational frame dependence and interpolation failure of US‐QUAD8 element

Ooi, Ean Tat; Rajendran, S.; Yeo, Joon Hock

doi:10.1002/cnm.1026

Cited by 28 publications

(57 citation statements)

References 27 publications

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“…Its numerical performance has been demonstrated using a series of analyses, namely: (i) a linear elastic plane stress cantilever, (ii) a three-dimensional finite deformation patch test, (iii) a soft elastic cantilever beam, (iv) an eccentrically loaded column and (v) an elasto-plastic double-notched plate. The proposed element was shown to be rotationally invariant and have similar distortion resistance to existing unsymmetric formulations [12,14,16,17,18]. Although element formulations based on Airy stress functions [2,3] have been shown to have superior distortion resistance, they can only be applied to a limited class of problems (currently, linear isotropic elasticity).…”

Section: Resultsmentioning

confidence: 99%

“…However, it is well known that these global metric derivatives produce element formulations that are dependent on the orientation of the element. In order to overcome this limitation, Ooi et al [14] proposed that the metric shape functions be reformulated based on a two-dimensional local coordinate system centred on the local coordinate system origin and aligned with one of the element edges. Although this did produce a formulation invariant to rigid body rotations, care must be taken to select an appropriate edge, and the extension to three-dimensions is not clear.…”

Section: Element Formulationmentioning

confidence: 99%

“…In 2008, Ooi et al [14] highlighted two defects associated with the US-QUAD8. These were its rotational frame dependence and interpolation failure under certain conditions.The remedy to its rotational frame dependence proposed in that paper was given by as rotating the local coordinate system to coincide with one of the element's edges.…”

Section: Introductionmentioning

confidence: 99%

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Rotationally invariant distortion resistant finite-elements

Cowan

Coombs

2014

Computer Methods in Applied Mechanics and Engineering

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe predictive capability of conventional iso-parametric finite-elements deteriorates with mesh distortion. In the case of geometrically non-linear analysis, changes in geometry causing severe distortion can result in negative Jacobian mapping between the local and global systems resulting in numerical breakdown. This paper presents a finite-element formulation that is resistant to irregular mesh geometries and large element distortions whilst remaining invariant to rigid body motion. The predictive capabilites of the family of finiteelements are demonstrated using a series of geometrically non-linear analyses including an elastic cantilever beam and an elasto-plastic double notched specimen.

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Section: Resultsmentioning

confidence: 99%

Section: Element Formulationmentioning

confidence: 99%

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Rotationally invariant distortion resistant finite-elements

Cowan

Coombs

2014

Computer Methods in Applied Mechanics and Engineering

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“…Because the displacement fields are incomplete cubic monomials, the element exhibits rotational frame dependence and interpolation failure under certain conditions [16]. Also, these defects cannot be avoided naturally by remedies proposed in [16].…”

Section: Construction Of the New 8-node Element Us-atfq8 By Unsymmetrmentioning

confidence: 99%

A shape‐free 8‐node plane element unsymmetric analytical trial function method

Cen

Zhou

2012

Numerical Meth Engineering

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SUMMARYThe unsymmetric FEM is one of the effective techniques for developing finite element models immune to various mesh distortions. However, because of the inherent limitation of the metric shape functions, the resulting element models exhibit rotational frame dependence and interpolation failure under certain conditions. In this paper, by introducing the analytical trial function method used in the hybrid stress-function element method, an effort was made to naturally eliminate these defects and improve accuracy. The key point of the new strategy is that the monomial terms (the trial functions) in the assumed metric displacement fields are replaced by the fundamental analytical solutions of plane problems. Furthermore, some rational conditions are imposed on the trial functions so that the assumed displacement fields possess fourthorder completeness in Cartesian coordinates. The resulting element model, denoted by US-ATFQ8, can still work well when interpolation failure modes for original unsymmetric element occur, and provide the invariance for the coordinate rotation. Numerical results show that the exact solutions for constant strain/stress, pure bending and linear bending problems can be obtained by the new element US-ATFQ8 using arbitrary severely distorted meshes, and produce more accurate results for other more complicated problems.

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“…In order to show that there is no rotational frame dependence [23] for the present HS-F element models, the approach of Spilker et al [37] is considered. As shown in Fig.…”

Section: Elementmentioning

confidence: 99%