Development of polygon elements based on the scaled boundary finite element method

Chiong, Irene; Song, Chongmin

doi:10.1088/1757-899x/10/1/012226

Cited by 11 publications

(6 citation statements)

References 10 publications

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“…In order to obtain the in-plane ansatz functions for an arbitrary polygon, the scaled boundary finite element method (SBFEM) can be employed. More explanations are available in [33,34,35].…”

Section: Prismatic Polyhedral Finite Elements For Glass Fragmentsmentioning

confidence: 99%

Numerical representation of fracture patterns and post-fracture load-bearing performance of thermally prestressed glass with polymer foil

Saputra

Behnke

Xing

et al. 2021

Engineering Structures

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Section: Prismatic Polyhedral Finite Elements For Glass Fragmentsmentioning

confidence: 99%

Numerical representation of fracture patterns and post-fracture load-bearing performance of thermally prestressed glass with polymer foil

Saputra

Behnke

Xing

et al. 2021

Engineering Structures

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“…They can be constructed following standard procedures as in the FEM. Alternatively, Gauss‐Lobatto‐Legendre shape functions can also be used .…”

Section: Overview Of the Scaled Boundary Femmentioning

confidence: 99%

“…Specifically for fracture analyses, the scaled boundary shape functions in a cracked polygon naturally include the necessary modes that enable any type of stress singularity emanating from cracks, notches and multi‐material junctions to be accurately modeled. These stress singularities can be modeled accurately using significantly coarser meshes than that required in the FEM .…”

Section: Introductionmentioning

confidence: 99%

Scaled boundary polygons with application to fracture analysis of functionally graded materials

Chiong

Ooi

Song

et al. 2014

Numerical Meth Engineering

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SUMMARYThis study presents a framework for the development of polygon elements based on the scaled boundary FEM. Underpinning this study is the development of generalized scaled boundary shape functions valid for any n‐sided polygon. These shape functions are continuous inside each polygon and across adjacent polygons. For uncracked polygons, the shape functions are linearly complete. For cracked polygons, the shape functions reproduce the square‐root singularity and the higher‐order terms in the Williams eigenfunction expansion. This allows the singular stress field in the vicinity of the crack tip to be represented accurately. Using these shape functions, a novel‐scaled boundary polygon formulation that captures the heterogeneous material response observed in functionally graded materials is developed. The stiffness matrix in each polygon is derived from the principle of virtual work using the scaled boundary shape functions. The material heterogeneity is approximated in each polygon by a polynomial surface in scaled boundary coordinates. The intrinsic properties of the scaled boundary shape functions enable accurate computation of stress intensity factors in cracked functionally graded materials directly from their definitions. The new formulation is validated, and its salient features are demonstrated, using five numerical benchmarks. Copyright © 2014 John Wiley & Sons, Ltd.

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“…This technique is flexible in meshing complex geometries, and the use of polygons to discretize the computational domain naturally complements the SBFEM. It uses the scaled boundary shape functions described in [64,65] and is applicable to polygons of any number of sides. Only the boundary of the polygon is discretized with one-dimensional elements using Gauss-Lobatto-Lagrange shape functions [66,65].…”

Section: Introductionmentioning

confidence: 99%

A scaled boundary polygon formulation for elasto-plastic analyses

Ooi

Song

Tin‐Loi

2014

Computer Methods in Applied Mechanics and Engineering

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Development of polygon elements based on the scaled boundary finite element method

Cited by 11 publications

References 10 publications

Numerical representation of fracture patterns and post-fracture load-bearing performance of thermally prestressed glass with polymer foil

Numerical representation of fracture patterns and post-fracture load-bearing performance of thermally prestressed glass with polymer foil

Scaled boundary polygons with application to fracture analysis of functionally graded materials

A scaled boundary polygon formulation for elasto-plastic analyses

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