Application of Polygonal Finite Elements in Linear Elasticity

Tabarraei, Alireza; Sukumar, N.

doi:10.1142/s021987620600117x

Cited by 69 publications

(53 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a regular n-gons all the vertex nodes lie on the same circumcircle, and hence all the nodes of the element are natural neighbors of any interior point of the reference element. Closed-form expressions for Laplace shape functions on reference elements are presented in Reference [12]. In Fig.…”

Section: Polygonal Finite Elementsmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Tabarraei

Sukumar

2007

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

Quadtree is a hierarchical data structure that is well-suited for h-adaptive mesh refinement. Due to the presence of hanging nodes, classical shape functions are non-conforming on quadtree meshes. In this paper, we use natural neighbor basis functions to construct conforming interpolants on quadtree meshes. To this end, the recently proposed construction of polygonal basis functions is adapted to quadtree elements. A fast technique for calculating stiffness matrix on quadtree meshes is introduced. Residual-based error estimators and material force technique are used to estimate the error on quadtree meshes. The performance of the adaptive technique is demonstrated through the solution of linear and nonlinear boundary-value problems.

show abstract

Section: Polygonal Finite Elementsmentioning

confidence: 99%

“…In this paper the method developed in Reference [9] is employed to resolve the problem associated with the presence of hanging nodes. This technique is based on the polygonal finite element method introduced in References [11,12].…”

Section: Introductionmentioning

confidence: 99%

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Tabarraei

Sukumar

2007

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…As a consequence, generalizations of FE methods to arbitrary polygonal or polyhedral meshes have gained increasing attention, both in computational physics [34,36,37] and in computer graphics [43,25]. For instance, when cutting a tetrahedron into two pieces, polyhedral FEM can directly process the resulting two elements, while standard FEM has to remesh them into tetrahedra first.…”

Section: Introductionmentioning

confidence: 99%

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Sieger

Alliez

Botsch

2010

Proceedings of the 19th International Meshing Roundtable

View full text Add to dashboard Cite

Summary. We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities-short edges in the Voronoi diagram. We evaluate our method on a 2D Poisson problem and demonstrate that our simple but effective optimization achieves a significant improvement of the stiffness matrix condition number.

show abstract

“…1.1.1 there are a few research groups that successfully applied polytope finite elements to a wide range of problem classes including structural mechanics [4,10,12,22,23], nonlinear analyses [6,[24][25][26][27], optimization [7,[28][29][30][31], crack propagation analysis [11,26,32,33] and fluid flow problems [34]. Noteworthy contributions that have advanced the application of polytope FEMs are discussed in the following paragraph.…”

Section: Applications Of Polygonal Finite Element Methodsmentioning

confidence: 99%

The finite cell method for polygonal meshes: poly-FCM

Duczek

Gabbert

2016

Comput Mech

View full text Add to dashboard Cite

In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.

show abstract

Application of Polygonal Finite Elements in Linear Elasticity

Cited by 69 publications

References 18 publications

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

The finite cell method for polygonal meshes: poly-FCM

Contact Info

Product

Resources

About