Voronoi Polygonal Hybrid Finite Elements with Boundary Integrals for Plane Isotropic Elastic Problems

2017 ◽  
Vol 09 (03) ◽  
pp. 1750031 ◽  
Author(s):  
Hui Wang ◽  
Qing-Hua Qin
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Displacement Field ◽  
Voronoi Tessellation ◽  
Convex Polygons ◽  
Boundary Integrals ◽  
Polygonal Mesh ◽  
Patch Tests ◽  
Polygonal Finite Elements ◽  
Element Boundary

Polygonal finite elements with high level of geometric isotropy provide greater flexibility in mesh generation and material science involving topology change in material phase. In this study, a hybrid finite element model based on polygonal mesh is constructed by centroidal Voronoi tessellation for two-dimensional isotropic elastic problems and then is formulated with element boundary integrals only. For the present [Formula: see text]-sided polygonal finite element, two independent fields are introduced: (i) displacement and stress fields inside the element; (ii) frame displacement field along the element boundary. The interior fields are approximated by fundamental solutions so that they exactly satisfy the governing equations to convert element domain integral in the two-field functional into element boundary integrals to reduce integration dimension. While the frame displacement field is approximated by the conventional shape functions to satisfy the conformity requirement between adjacent elements. The two independent fields are coupled by the weak functional to form the stiffness equation. This hybrid formulation enables the construction of [Formula: see text]-sided polygons and extends the potential applications of finite elements to convex polygons of arbitrary order. Finally, five examples including patch tests in square domain, thick cylinder under internal pressure, beam bending and composite with clustered holes are provided to illustrate convergence, accuracy and capability of the present Voronoi polygonal finite elements.

Truss and Beam Finite Elements Revisited: A Derivation Based on Displacement-Field Decomposition

1996 ◽  
Vol 11 (4) ◽  
pp. 371-380 ◽  
Author(s):  
Alphose Zingoni
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Symmetry Group ◽  
Displacement Field ◽  
Three Dimensional ◽  
Beam Elements ◽  
Symmetry Properties ◽  
Mass Matrices ◽  
General Displacement

Where a finite element possesses symmetry properties, derivation of fundamental element matrices can be achieved more efficiently by decomposing the general displacement field into subspaces of the symmetry group describing the configuration of the element. In this paper, the procedure is illustrated by reference to the simple truss and beam elements, whose well-known consistent-mass matrices are obtained via the proposed method. However, the procedure is applicable to all one-, two- and three-dimensional finite elements, as long as the shape and node configuration of the element can be described by a specific symmetry group.

Thermo-Mechanical Stress near Apex of a Bi-Material Wedge by a Novel Finite Element Analysis

2012 ◽  
Vol 525-526 ◽  
pp. 93-96
Author(s):  
Xue Cheng Ping ◽  
Lin Leng ◽  
Si Hai Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Elements ◽  
Mechanical Stress ◽  
Displacement Field ◽  
Thermal Loading ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Element Analysis

A super wedge tip element for application to a bi-material wedge is develop utilizing the thermo-mechanical stress and displacement field solutions in which the singular parts are numerical solutions. Singular stresses near apex of an arbitrary bi-material wedge under mechanical and thermal loading can be obtained from the coupling between the super wedge tip element and conventional finite elements. The validity of this novel finite element method is established through existing asymptotic solutions and conventional detailed finite element analysis.

A formulation of membrane finite elements with true drilling rotation

2019 ◽  
Vol 37 (1) ◽  
pp. 203-236 ◽  
Author(s):  
Djamel Boutagouga
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Polynomial Interpolation ◽  
Normal Displacement ◽  
Geometric Transformation ◽  
Rotational Degree ◽  
Content Type ◽  
Corner Node

Purpose This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF). Design/methodology/approach The presented formulation incorporates the true drilling rotation provided by continuum mechanics into the displacement field by way of using the polynomial interpolation. Unlike the linked interpolation, that uses a geometric transformation between displacement and vertex rotations, in this work, the interpolation of the displacement field in terms of nodal drilling rotations is obtained following an unusual approach that does not imply any presumed geometric transformation. Findings New relationship linking the mid-side normal displacement to corner node drilling rotations is derived. The resulting new element with true drilling rotation is compatible and does not include any problem-dependent parameter that may influence the results. The spurious zero-energy mode is stabilized in a careful way that preserves the true drilling rotational degrees of freedom (DOFs). Originality/value Several works dealing with membrane elements with vertex rotational DOFs have been published with improved convergence rate, however, owing to the need for incorporating rotations in the finite element meshes involving solids, shells and beam elements, having finite elements with true drilling rotational DOFs is more appreciated.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

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