Curious convergence with hypostatic hybrid equilibrium models

Ramsay, A. C. A.; Almeida, J. P. B. Moitinho De; Maunder, E. A. W.

doi:10.1002/(sici)1099-0887(199707)13:7<541::aid-cnm79>3.0.co;2-3

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Spurious Modes and Super-elements1

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“…Non-simplicial elements are also possible, both in 2D and in 3D. The quadrilateral element may present 'curious convergence' [13], that is, the strain energy may remain constant for certain ranges of the degree of the element, rather than converging at a positive rate with the degree of the element.…”

Section: Spurious Modes and Super-elementsmentioning

confidence: 99%

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Hybrid equilibrium hexahedral elements and super‐elements

Pereira

2006

Commun. Numer. Meth. Engng.

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SUMMARYEquilibrated solutions, locally satisfying all the equilibrium conditions, may be obtained by using a special case of the hybrid finite element formulation. Unlike simplicial super-elements in 2D and 3D, which are free from spurious kinematic modes, and the quadrilateral super-element with diagonal subdivision, which has exactly one internal spurious kinematic mode, no hexahedral super-element free of external spurious kinematic modes is yet known as far as the author is aware.

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Section: Spurious Modes and Super-elementsmentioning

confidence: 99%

“…Although the strain energy never remained constant for any increase in the degree of the approximation, the convergence rate appears somewhat erratic. This is similar to the 'curious convergence' of the quadrilateral element and the explanations given in Reference [13] would appear to be applicable here.…”

Section: Numerical Examplesmentioning

confidence: 99%