Application of the 2-D constant strain assumption to FEM elements consisting of an arbitrary number of nodes

Peters, John F.; Heymsfield, Ernest

doi:10.1016/s0020-7683(02)00521-8

Cited by 11 publications

(12 citation statements)

References 13 publications

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“…Wachspress [3] proposed rational basis functions on polygonal elements, which has only received limited attention so far [4][5][6][7][8]. The advantages and potential benefits of using polygonal finite elements in computation are striking: greater flexibility (single algorithm suffices) in the meshing of arbitrary geometries such as those that arise in biomechanics [9,10]; better accuracy in the numerical solution (higher-order approximation) over that obtainable using triangular and quadrilateral meshes on a given nodal grid; useful as a transition element in finite element meshes [11,12]; suitable in material design [13] and in the modelling of polycrystalline materials [14]; and will have less sensitivity to lock (unlike lower-order triangular and quadrilateral elements which tend to be stiff) under volume-preserving deformation states which arise in incompressible elasticity as well as in von Mises plasticity. To this end, we explore the construction of robust and accurate finite element methods that are based on polygonal elements.…”

Section: Introductionmentioning

confidence: 99%

Conforming polygonal finite elements

Sukumar

Tabarraei

2004

Numerical Meth Engineering

423

386

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SUMMARYIn this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, recent advances in meshfree approximations, computational geometry, and computer graphics are used to construct different trial and test approximations on polygonal elements. A particular and notable contribution is the use of meshfree (natural-neighbour, nn) basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons. This numerical formulation enables the construction of conforming approximation on n-gons (n 3), and hence extends the potential applications of finite elements to convex polygons of arbitrary order. Numerical experiments on second-order elliptic boundary-value problems are presented to demonstrate the accuracy and convergence of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Conforming polygonal finite elements

Sukumar

Tabarraei

2004

Numerical Meth Engineering

423

386

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“…The topological restrictions attending the parent-to-physical element mapping thereby disappear, allowing elements to take arbitrary polyhedral form. Others have devised finite-element-like methods with a similar goal in mind [33,34]. However, the present formulation is unique in that basis functions with the requisite smoothness properties are explicitly formed.…”

Section: Closurementioning

confidence: 99%

A three‐dimensional finite element method with arbitrary polyhedral elements

Rashid

Selimotic

2006

Numerical Meth Engineering

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SUMMARYThe 'variable-element-topology finite element method' (VETFEM) is a finite-element-like Galerkin approximation method in which the elements may take arbitrary polyhedral form. A complete development of the VETFEM is given here for both two and three dimensions. A kinematic enhancement of the displacement-based formulation is also given, which effectively treats the case of near-incompressibility. Convergence of the method is discussed and then illustrated by way of a 2D problem in elastostatics. Also, the VETFEM's performance is compared to that of the conventional FEM with eight-node hex elements in a 3D finite-deformation elastic-plastic problem. The main attraction of the new method is its freedom from the strict rules of construction of conventional finite element meshes, making automatic mesh generation on complex domains a significantly simpler matter.

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“…The procedure for obtaining B is similar to that for suppressing zero-energy modes in under-integrated finite elements described in [14]. In that case, the zero-energy modes are deformation modes that are not resisted by internal stresses.…”

Section: Remark On Finite-element Stabilizationmentioning

confidence: 99%

Some fundamental aspects of the continuumization problem in granular media

Peters

2005

J Eng Math

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The central problem of devising mathematical models of granular materials is how to define a granular medium as a continuum. This paper outlines the elements of a theory that could be incorporated in discrete models such as the Discrete-Element Method, without recourse to a continuum description. It is shown that familiar concepts from continuum mechanics such as stress and strain can be defined for interacting discrete quantities. Established concepts for constitutive equations can likewise be applied to discrete quantities. The key problem is how to define the constitutive response in terms of truncated strain measures that are a practical necessity for analysis of large granular systems.

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Application of the 2-D constant strain assumption to FEM elements consisting of an arbitrary number of nodes

Cited by 11 publications

References 13 publications

Conforming polygonal finite elements

Conforming polygonal finite elements

A three‐dimensional finite element method with arbitrary polyhedral elements

Some fundamental aspects of the continuumization problem in granular media

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