On a stress resultant geometrically exact shell model. Part II: The linear theory; Computational aspects

Simo, J. C.; Fox, David; Rifai, M. S.

doi:10.1016/0045-7825(89)90098-4

Cited by 429 publications

(253 citation statements)

References 23 publications

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“…Linear example The linear shell problem is shown in figure 6. The shell consists of a pinched cylinder with rigid end diaphragms and has been analyzed, among others, in references [21,22,23,24]; these results are here reproduced for comparison. The point-load displacement is monitored.…”

Section: Examplesmentioning

confidence: 59%

A meshfree thin shell method for non‐linear dynamic fracture

Rabczuk

Areias

Belytschko

2007

Numerical Meth Engineering

444

135

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SUMMARYA meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straight forward.

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Section: Examplesmentioning

confidence: 59%

A meshfree thin shell method for non‐linear dynamic fracture

Rabczuk

Areias

Belytschko

2007

Numerical Meth Engineering

444

135

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“…Indeed, at the fixed end where the maximum bending moment is localized, there is a single Gauss point in the load direction P2 while there are five in the direction of load P1. Two other versions of this twisted beam problem can be found in the literature (Simo et al, 1989), (Batoz et al, 1992). These versions differ only by their lower thickness: 0.05 and 0.0032, which allows us to evaluate the effects of locking phenomena in the limit of high aspect ratios.…”

Section: Twisted Cantilever Beammentioning

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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“…In this section, we review the mechanics of thin shells [42,43], based on a geometrically exact formulation presented in [30,44]. We restrict our attention to the Kirchhoff-Love kinematical assumption of shells, which states that the material line orthogonal to the middle surface in the undeformed configuration remains straight, unstretched and always orthogonal to the middle surface during the deformations.…”

Section: Thin Shell Modelmentioning

confidence: 99%

Phase-field modeling of fracture in linear thin shells

Amiri

Millán

Shen

et al. 2014

Theoretical and Applied Fracture Mechanics

285

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We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximumentropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.

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On a stress resultant geometrically exact shell model. Part II: The linear theory; Computational aspects

Cited by 429 publications

References 23 publications

A meshfree thin shell method for non‐linear dynamic fracture

A meshfree thin shell method for non‐linear dynamic fracture

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

Phase-field modeling of fracture in linear thin shells

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