Three Node Triangular Bending Elements With One Degree of Freedom Per Node

Hampshire, J.K.; Topping, B. H. V.; Chan, H. P.

doi:10.1108/eb023848

Cited by 37 publications

(21 citation statements)

References 3 publications

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“…The membrane deformation may be expressed in terms of the Green-Lagrange (14) strain tensor or in terms of the metric tensor over the middle surface (6). The former may be written in the usual notation of the FEM as ⎡ ⎢ ⎢ ⎣…”

Section: Membrane Behaviour and Stiffness Matrixmentioning

confidence: 99%

A rotation‐free shell triangle for the analysis of kinked and branching shells

Flores

Oñate

2006

Numerical Meth Engineering

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SUMMARYThis paper extends the capabilities of previous BST and EBST rotation-free thin shell elements to the analysis of kinked and branching surfaces. The computation of the curvature tensor is first redefined in terms of the angle change between the normals at the adjacent elements. This allows to deal with arbitrary large angles between adjacent elements and to treat kinked surfaces. A relative stiffness between elements is introduced to consider non-homogeneous surfaces. This idea is latter generalized to deal with branching shells. Several linear and non-linear examples are presented showing that the formulation leads to the correct results.

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Section: Membrane Behaviour and Stiffness Matrixmentioning

confidence: 99%

A rotation‐free shell triangle for the analysis of kinked and branching shells

Flores

Oñate

2006

Numerical Meth Engineering

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“…Barnes [3] developed a simple three-node triangle with three nodal degrees of freedom, in which the curvatures were computed as functions of the normal rotations and the midside points that were determined from the nodal deflections of adjacent elements. This approach was extended by Hampshire et al [9] by assuming that the elements are hinged together at their common boundaries, and the bending stiffness was developed by incorporating a torsional spring that resists the rotations about the hinge lines. Brunet and Sabourin [5] derived three-node plate and shell triangles that involve out-of-plane degrees of freedom only in a study of sheet forming.…”

Section: Introductionmentioning

confidence: 99%

Local Instability and Free Vibration of Supported Plates Using the Basic Plate Triangle

2006

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This paper extends the numerical method, originally developed by Onate and his colleagues for the static analysis of plates, to enable modal (vibration) and bifurcative (buckling) analyses of plates to be undertaken. The procedure uses a rotation-free triangular element, and is based on combining the finite element method and the finite volume method so as to produce a triangular element with only three displacement degrees of freedom. Elastic stiffness, stability (geometric stiffness) and mass matrices are developed using the mixed formulation, and these are implemented in routine computer coding in order to demonstrate the validity and efficacy of the solution technique when compared with results reported by independent investigators. Natural frequencies and local buckling coefficients are given for plates with interior line supports, and these are used to illustrate the prowess of the numerical technique for the analysis of a wide class of plate buckling and vibration problems, whose analysis by non-discretisation techniques has found favour recently in deference to general finite element modelling which tends to introduce some inaccuracies. The element developed in this paper, however, is both accurate and has the attractive meshing characteristics of the finite element method for analysing more arbitrary geometric structural topologies.

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“…Among them was a plate element family called the "rotation-free" (RF) plate element. Their origins can be traced back to Nay and Utku [26], Hampshire et al [27] and Phaal and Calladine [28]. Most of these and related research were influenced by an element called "Morley Triangle" [29].…”

Section: Existing Rotation-free Triangular Plate Elementmentioning

confidence: 99%

“…If the yield line is inclined at an angle ( relative to the considered element side rather than the global axes as shown in Fig. (6), then, the quantities c 1 and s 1 can be expressed in the element local coordinate system as following: (27) Substituting these values into Eq. (25) results in the following expression for when is assumed to be zero:…”

Section: Adding Yield Lines To Element "S3"mentioning

confidence: 99%

Finite element lower bound “yield line” analysis of isotropic slabs using rotation-free elements

Al‐Sabah

Falter

2013

Engineering Structures

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A new lower bound finite element method for slab analysis is presented as a practical substitute to full, non-linear, finite element methods that require expert knowledge and long running times. The method provides a general, safe and efficient lower bound solution for the analysis of reinforced concrete slabs up to failure. As it is finite element based, the method is more general than the yield line and strip methods currently in use. Furthermore, its lower bound nature makes it safer than the yield line method. The method uses a rotation-free, plate finite element modified to allow plastic "yield lines" to pass through at any direction. Yield lines are generated at the principal moment directions when the plastic moment capacity is attained. The material is assumed to be elastic perfectly-plastic. Following the general spirit of yield line analysis, the effects of a yield line are projected to the sides of the triangular element and then used to calculate the bending curvatures. The method's efficiency is achieved by using rotation-free plate elements with a single degree of freedom per node and by the incremental solution that does not require iterations. The method's accuracy and convergence are assessed by comparing standard cases with known results. In all cases, results were close to the theoretical values with difference of less than 1%. It is also used to solve a practical sized flat slab problem in order to demonstrate the method's efficiency, convergence, and speed.

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Three Node Triangular Bending Elements With One Degree of Freedom Per Node

Cited by 37 publications

References 3 publications

A rotation‐free shell triangle for the analysis of kinked and branching shells

A rotation‐free shell triangle for the analysis of kinked and branching shells

Local Instability and Free Vibration of Supported Plates Using the Basic Plate Triangle

Finite element lower bound “yield line” analysis of isotropic slabs using rotation-free elements

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