A Stiffness Matrix for the Analysis of Thin Plates in Bending

Melosh, R. J.

doi:10.2514/8.8850

Cited by 66 publications

(15 citation statements)

References 4 publications

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“…This has led early on to the development of plate elements in most discretisation schemes. In the finite element method associated development started more than 50 years ago with the work of [8,17,24]. It was obvious that general forms of finite elements were not able to fulfill C 1 -continuity when using Kirchhoff-Love plate theory as starting point.…”

Section: Introductionmentioning

confidence: 99%

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

2021

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The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the $$C^1$$ C 1 -continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of $$C^1$$ C 1 -continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for $$C^0$$ C 0 -continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these $$C^1$$ C 1 -continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.

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Section: Introductionmentioning

confidence: 99%

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

2021

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“…al. did not make reference to variational considerations, rather, it took a "direct" approach, in which direct consideration was given to conditions of equilibrium and compatibility. Consequently, the paper stimulated numerous efforts to develop formulations for stiffness influence coefficients for a variety of different types of elements (Turner, 1959;Clough, 1960;Melosh, 1961;Melosh, 1963;Clough and Tocher, 1965 (Mallett and Marcal, 1968;Przemieniecki , 1968;Zienkiewicz, 1971;Desai and Abel, 1972). The method has been extended to deal with three-dimensional geometries using sub and superparametric elements, curvilinear elements, and account has been taken of inertia effects.…”

Section: Duresmentioning

confidence: 99%

Predicting Performance of Pipe Culverts Buried in Soil, Phase 1 : Interim Report

Leonards¹,

Roy²

1976

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“…The analysis of stress in a plane had been common usage since that time (Rayleigh, 1870;Hutton, 2004). During the period between 1960 and 1970, FEA was developed to the application in pressure vessels, shell bending, plate bending and general three-dimensional issue in the linear elastic analysis (Melosh, 1961;Melosh, 1963). During the year 1977, the finite element software CATIA was developed by Dassault Systèmes (Systemes, 2016).…”

Section: Introductionmentioning

confidence: 99%

Assessment of Stress Raiser Factor Using Finite Element Solvers

Fondjo¹,

Dzogbewu²

2019

ujme

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The stress raisers factor around circular holes in a plate exposed to uniform tensile load at the edges has been studied using Finite Element Analysis solvers. The effect of mesh quality on stress raisers factor, the maximum Von Mises stresses, the computing time, and the percentage error has been examined. 4 Node Quadrilateral Element and 8 Node Quadrilateral Element were utilized respectively as first-order component (4NQE) and higher-order component (8NQE) to assess the maximum Von Mises stress and the numerical stress raiser factor (Kn) at various mesh sizes. The maximum Von Mises stress and the stress raiser factor were determined using the following finite element solvers: ABAQUS, ANSYS, CATIA, STRAND 7, ALGOR, COSMOS/M, and FEMAP. The estimations of the numerical stress raiser factor (Kn) were compared with the theoretical stress raiser factor (Kt). There were discrepancies observed between the maximum Von Mises stresses of the FEA solvers.

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A Stiffness Matrix for the Analysis of Thin Plates in Bending

Cited by 66 publications

References 4 publications

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

Predicting Performance of Pipe Culverts Buried in Soil, Phase 1 : Interim Report

Assessment of Stress Raiser Factor Using Finite Element Solvers

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