On the numerical performance of three-dimensional thick shell elements using a hybrid/mixed formulation

Graf, W.; Chang, Tienchong; Saleeb, A. F.

doi:10.1016/0168-874x(86)90022-3

Cited by 10 publications

(4 citation statements)

References 19 publications

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“…Among the pioneering research dealing with thin structure modeling by means of threedimensional elements without rotational degrees of freedom, the work of Graf et al [53] is notable for developing 8,16, and 18-node three-dimensional elements based on hybrid/mixed formulations. Xu and Cai [54] proposed a 16-node displacement-based isoparametric element with 40 degrees of freedom and plane-stress assumptions.…”

Section: Introductionmentioning

confidence: 99%

An improved assumed strain solid–shell element formulation with physical stabilization for geometric non‐linear applications and elastic–plastic stability analysis

Abed‐Meraim

Combescure

2009

Numerical Meth Engineering

125

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SUMMARYIn this paper, the earlier formulation of the SHB8PS finite element is revised in order to eliminate some persistent membrane and shear locking phenomena. This new formulation consists of a solid-shell element based on a purely three-dimensional approach. More specifically, the element has eight nodes, with displacements as the only degrees of freedom, as well as an arbitrary number of integration points, with a minimum number of two, distributed along the 'thickness' direction. The resulting derivation, which is computationally efficient, can then be used for the modeling of thin structures, while providing an accurate description of the various through-thickness phenomena. A reduced integration scheme is used to prevent some locking phenomena and to achieve an attractive, low-cost formulation. The spurious zero-energy modes due to this in-plane one-point quadrature are efficiently controlled using a physical stabilization procedure, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the assumed strain method. In addition to the extended and detailed formulation presented in this paper, particular attention has been focused on providing full justification regarding the identification of hourglass modes in relation to rank deficiencies. Moreover, an attempt has been made to provide a sound foundation to the derivation of the co-rotational coordinate frame, on which the calculations of the stabilization stiffness matrix and internal load vector are based. Finally to assess the effectiveness and performance of this new formulation, a set of popular benchmark problems is investigated, involving geometric non-linear analyses as well as elastic-plastic stability issues.

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Section: Introductionmentioning

confidence: 99%

An improved assumed strain solid–shell element formulation with physical stabilization for geometric non‐linear applications and elastic–plastic stability analysis

Abed‐Meraim

Combescure

2009

Numerical Meth Engineering

125

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“…It verifies whether an arbitrary patch of assembled elements reproduce exactly the behaviour of an elastic solid material when subjected to boundary displacements consistent with constant straining Babuska (1971Babuska ( , 1973 Ellipticity, and inf-sup condition Irons & Razzaque (1972) Experiences with the patch test Brezzi (1974) Ellipticity, and inf-sup condition Veubeke (1974) Variational interpretation of patch test Sander & Beckers (1977) The influence of choice of connectors in FEM Oliveira (1977) The patch test and the general convergence criteria Stummel (1980) Limitations of patch test: examples of non-conforming finite elements that passed the patch test of Irons (1966) and Strang & Fix (1973) but did not converge Hayes (1981) Stability test for under integrated and selectively integrated elements is proposed Irons & Loikkanen (1983) Convergence criterion is proved for all eligible FE formulations. Patch test is proved to be universal when it is combined with adequate test of stability MacNeal & Harder (1985) Standard set of problems to test finite element accuracy Belytschko et al (1985) Scordelis-Lo roof, hemispherical shell without holes, pinched cylinder Taylor et al (1986) Patch test and convergence Razzaque (1986) Patch tests Zienkiewicz et al (1986) Patch test for mixed formulations Graf et al (1986) Three dimensional thick shell elements using a hybrid/mixed formulation Noor & Babuska (1987) Techniques for assessing the reliability of finite element. Techniques for a posteriori error estimation and the reliability of the estimators Verma & Melosh (1987) Redefined the convergence requirements for finite element models.…”

Section: Author(s) Remarksmentioning

confidence: 99%

A set of pathological tests to validate new finite elements

Rao

Shrinivasa

2001

Sadhana

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The finite element method entails several approximations. Hence it is essential to subject all new finite elements to an adequate set of pathological tests in order to assess their performance. Many such tests have been proposed by researchers from time to time. We present an adequate set of tests, which every new finite element should pass. A thorough account of the patch test is also included in view of its significance in the validation of new elements.

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“…Among the pioneering research work dealing with thin structure modeling by means of three-dimensional elements without rotational degrees of freedom, we can mention (Graf et al, 1986) who developed 8, 16 and 18-node three-dimensional elements based on hybrid/mixed formulation. Xu et al, (1993) proposed a 16-node displacement-based isoparametric element with 40 degrees of freedom and planestress assumptions.…”

Section: Introductionmentioning

confidence: 99%

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

Abed‐Meraim

Combescure

2007

European Journal of Computational Mechanics

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On the numerical performance of three-dimensional thick shell elements using a hybrid/mixed formulation

Cited by 10 publications

References 19 publications

An improved assumed strain solid–shell element formulation with physical stabilization for geometric non‐linear applications and elastic–plastic stability analysis

An improved assumed strain solid–shell element formulation with physical stabilization for geometric non‐linear applications and elastic–plastic stability analysis

A set of pathological tests to validate new finite elements

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

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