Bending-Dominated Deformation of Thin Spherical Shells: Analysis and Finite-Element Approximation

Kirmse, Andreas

doi:10.1137/0730053

Cited by 10 publications

(3 citation statements)

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“…But as we have a stable method, the treatment of the boundary layers should be done by a proper mesh re nement and this is a problem of approximation theory. The biggest shortcoming for the method we present, and also for the methods that have been mathematically studied in previous works 2, 49,28], is that they do not perform properly when they are applied to membrane dominated shells. Hence, we are still far from having \the shell element".…”

Section: Introductionmentioning

confidence: 93%

Stabilized Finite Element Formulations for Shells in a Bending Dominated State

Chapelle¹,

Stenberg²

1998

SIAM J. Numer. Anal.

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Section: Introductionmentioning

confidence: 93%

Stabilized Finite Element Formulations for Shells in a Bending Dominated State

Chapelle¹,

Stenberg²

1998

SIAM J. Numer. Anal.

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“…The inf-sup condition should be verified in several well-chosen test cases. Plate elements tend to show parasitic states in bending-dominated problems, as showed in literature [16,17,18,19,20], therefore this type of benchmarks is presented in this paper.…”

Section: Introductionmentioning

confidence: 96%

Plate Finite Element with Physical Shape Functions: Correctness of the Formulation

Gilewski

Sitek

2017

Archives of Civil Engineering

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The formulation of a plate finite element with so called 'physical' shape functions is revisited. The derivation of the 'physical' shape functions is based on Hencky-Bollé theory of moderately thick plates. The considered finite element was assessed in the past, and the tests showed that the solution convergence was achieved in a wide range of thickness to in-plane dimensions ratios. In this paper a holistic correctness assessment is presented, which covers three criteria: the ellipticity, the consistency and the inf-sup conditions. Fulfilment of these criteria assures the existence of a unique solution, and a stable and optimal convergence to the correct solution. The algorithms of the numerical tests for each test case are presented and the tests are performed for the considered formulation. In result it is concluded that the finite element formulation passes every test and therefore is a good choice for modeling plate structural elements regardless of their thickness.

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“…The mathematical analysis of shell ®nite element formulations which were designed to overcome locking is still in its beginning stages. We mention the initiatives of Pitk aranta [11], Arnold and Brezzi [12], Kirmse [13] and Chapelle and Stenberg [14] which, although restricted in their applicability, are very important since they constitute the basis for future developments.…”

Section: Introductionmentioning

confidence: 99%