Large displacement analysis of thin plates and shells using a flat facet finite element formulation

Meek, J.L.; Ristic, Svetlana

doi:10.1016/s0045-7825(96)01220-0

Cited by 10 publications

(4 citation statements)

References 16 publications

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“…The nonlinear response of the spherical shell is illustrated by the load-vertical displacement curve of the central point, represented in (Figure 12). We refer to the analytical solution extracted from the reference (Meek et al, 1997). The present solution obtained by the "Qdrill" element is in good agreement with the analytical solution for shallow shells.…”

Section: Spherical Shell Under Concentrated Loadingsupporting

confidence: 73%

Geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom

Boutagouga¹,

Gouasmia²,

Djeghaba³

2010

TECM

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We present in this research article, the improvements that we made to create a four nodes flat quadrilateral shell element for geometrically nonlinear analysis, based on corotational updated lagrangian formulation. These improvements are initially related to the improvement of the in-plane behaviour by incorporation of the in-plane rotational degrees of freedom known as “drilling degrees of freedom” in the membrane displacements field formulation. In the second phase, a co-rotational spatial local system of axes which adapts well to the problems of quadrilateral elements is adopted, while ensuring simplicity and effectiveness at numerical level. The required goal being mainly to have a robust thin shell element associated with a simplified formulation. The obtained element remains economic, and showing a robust behaviour in delicate situations of tests.

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Section: Spherical Shell Under Concentrated Loadingsupporting

confidence: 73%

Geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom

Boutagouga¹,

Gouasmia²,

Djeghaba³

2010

TECM

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“…Three discrete Kirchho at shell elements for shell analysis with large geometric non-linearity were developed by Talbot and Dhatt [11] and a six-node triangular plate=shell element DLTP [12] was developed for geometric and material non-linear analysis. Meek and Ristic [13] developed a 24-d.o.f. triangular at shell element and large rotation was included by removing the rigid-body motion.…”

Section: Introductionmentioning

confidence: 99%

A refined non‐linear non‐conforming triangular plate/shell element

Zhang

Cheung

2003

Numerical Meth Engineering

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SUMMARYA reÿned non-conforming triangular plate=shell element for geometric non-linear analysis of plates=shells using the total Lagrangian=updated Lagrangian approach is constructed in this paper based on the reÿned non-conforming element method for geometric non-linear analysis. The Allman's triangular plane element with vertex degrees of freedom and the reÿned triangular plate-bending element RT9 are used to construct the present element. Numerical examples demonstrate that the accuracy of the new element is quite high in the geometric non-linear analysis of plates=shells.

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“…This shell is shown in Figure 8 (Meek and Ristic, 1997;Boutagouga et al, 2010). Owing to the symmetry, only one-quarter of the structure is analyzed with 200 shell elements.…”

Section: The Shallow Spherical Capmentioning

confidence: 99%

Geometrically nonlinear analysis of shells by various dynamic relaxation methods

Rezaiee‐Pajand

Estiri

2017

WJE

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Purpose Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. To achieve this task, 12 famous approaches are briefly introduced. The differences among these schemes are between the estimation of the time step, the mass and the damping matrices. In this study, several benchmark structures are analyzed by using these 12 techniques. Based on the number of iterations and the analysis duration, their performances are graded. Numerical findings reveal the high efficiency of the kinetic DR (kdDR) approach and Underwood’s strategy. Design/methodology/approach Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells have not been investigated. In this paper, 12 famous DR methods have been used for solving these structures. It should be noted that the difference between these approaches is in the estimation of the fictitious parameters. The aforementioned techniques are used to solve several numerical samples. Then, the performances of all schemes are graded based on the number of iterations and the analysis duration. Findings The final ranking of each strategy will be obtained after studying all numerical examples. It is worth emphasizing that the number of iterations and that of convergence points of the arc length algorithms are dependent on the value of the initial arc length. In other words, a slight change in the magnitude of the arc length may lead to the wrong responses. Contrary to this behavior, the analyzer’s role in the dynamic relaxation techniques is considerably less than the arc length method. In the DR strategies when the answer approaches the limit points, the iteration number increases automatically. As a result, this algorithm can be used to analyze the structures with complex equilibrium paths. Research limitations/implications Numerical experiences reveal that the DR method performances are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. Practical implications Geometric nonlinear analysis of shells is a sophisticated procedure. Consequently, extensive research studies have been conducted to analyze the shells efficiently. The most important characteristic of these structures is their high resistance against pressure. This study demonstrates the performances of various DR methods in solving shell structures. Originality/value Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells are not investigated.

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Large displacement analysis of thin plates and shells using a flat facet finite element formulation

Cited by 10 publications

References 16 publications

Geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom

Geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom

A refined non‐linear non‐conforming triangular plate/shell element

Geometrically nonlinear analysis of shells by various dynamic relaxation methods

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