Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements

R. K.L. Su; S. L. Fok

doi:10.1016/j.engfracmech.2006.09.009

Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements

R. K.L. Su
, S. L. Fok

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

This paper applies the fractal finite element method (FFEM) together with 9-node Lagrangian hybrid elements to the calculation of linear elastic crack tip fields. An explicit stabilization scheme is employed to suppress the spurious kinematic modes of the sub-integrated Lagrangian element. An extensive convergence study has been conducted to examine the effects of the similarity ratio, reduced integration and the type of elements on the accuracy and stability of the numerical solutions. It is concluded that (i) a similarity ratio close to unity should be used to construct the fractal mesh, (ii) sub-integrated Lagrangian elements with occasionally unstable behaviour should not be used, and (iii) the good accuracy (with differences less than 0.5% with existing available solutions) and stability over a wide range of numerical tests support the use of fractal hybrid finite elements for determining crack tip asymptotic fields.

Original language	English (US)
Pages (from-to)	1649-1664
Number of pages	16
Journal	Engineering Fracture Mechanics
Volume	74
Issue number	10
DOIs	https://doi.org/10.1016/j.engfracmech.2006.09.009
State	Published - Jul 2007
Externally published	Yes

Bibliographical note

Funding Information:
The work presented was fully supported by the University Research Grant, The University of Hong Kong through Small Project Funding (2006–2007). The kind assistance of Prof. KY Sze and Mr. KS Yeung in the development of the HS9 element is gratefully acknowledged.

Keywords

Crack tip asymptotic field
Fractal finite element method
Higher-order coefficients
Hybrid element
Reduced integration

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10.1016/j.engfracmech.2006.09.009

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title = "Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements",

abstract = "This paper applies the fractal finite element method (FFEM) together with 9-node Lagrangian hybrid elements to the calculation of linear elastic crack tip fields. An explicit stabilization scheme is employed to suppress the spurious kinematic modes of the sub-integrated Lagrangian element. An extensive convergence study has been conducted to examine the effects of the similarity ratio, reduced integration and the type of elements on the accuracy and stability of the numerical solutions. It is concluded that (i) a similarity ratio close to unity should be used to construct the fractal mesh, (ii) sub-integrated Lagrangian elements with occasionally unstable behaviour should not be used, and (iii) the good accuracy (with differences less than 0.5\% with existing available solutions) and stability over a wide range of numerical tests support the use of fractal hybrid finite elements for determining crack tip asymptotic fields.",

keywords = "Crack tip asymptotic field, Fractal finite element method, Higher-order coefficients, Hybrid element, Reduced integration",

author = "Su, \{R. K.L.\} and Fok, \{S. L.\}",

note = "Funding Information: The work presented was fully supported by the University Research Grant, The University of Hong Kong through Small Project Funding (2006–2007). The kind assistance of Prof. KY Sze and Mr. KS Yeung in the development of the HS9 element is gratefully acknowledged.",

year = "2007",

month = jul,

doi = "10.1016/j.engfracmech.2006.09.009",

language = "English (US)",

volume = "74",

pages = "1649--1664",

journal = "Engineering Fracture Mechanics",

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TY - JOUR

T1 - Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements

AU - Su, R. K.L.

AU - Fok, S. L.

N1 - Funding Information: The work presented was fully supported by the University Research Grant, The University of Hong Kong through Small Project Funding (2006–2007). The kind assistance of Prof. KY Sze and Mr. KS Yeung in the development of the HS9 element is gratefully acknowledged.

PY - 2007/7

Y1 - 2007/7

N2 - This paper applies the fractal finite element method (FFEM) together with 9-node Lagrangian hybrid elements to the calculation of linear elastic crack tip fields. An explicit stabilization scheme is employed to suppress the spurious kinematic modes of the sub-integrated Lagrangian element. An extensive convergence study has been conducted to examine the effects of the similarity ratio, reduced integration and the type of elements on the accuracy and stability of the numerical solutions. It is concluded that (i) a similarity ratio close to unity should be used to construct the fractal mesh, (ii) sub-integrated Lagrangian elements with occasionally unstable behaviour should not be used, and (iii) the good accuracy (with differences less than 0.5% with existing available solutions) and stability over a wide range of numerical tests support the use of fractal hybrid finite elements for determining crack tip asymptotic fields.

AB - This paper applies the fractal finite element method (FFEM) together with 9-node Lagrangian hybrid elements to the calculation of linear elastic crack tip fields. An explicit stabilization scheme is employed to suppress the spurious kinematic modes of the sub-integrated Lagrangian element. An extensive convergence study has been conducted to examine the effects of the similarity ratio, reduced integration and the type of elements on the accuracy and stability of the numerical solutions. It is concluded that (i) a similarity ratio close to unity should be used to construct the fractal mesh, (ii) sub-integrated Lagrangian elements with occasionally unstable behaviour should not be used, and (iii) the good accuracy (with differences less than 0.5% with existing available solutions) and stability over a wide range of numerical tests support the use of fractal hybrid finite elements for determining crack tip asymptotic fields.

KW - Crack tip asymptotic field

KW - Fractal finite element method

KW - Higher-order coefficients

KW - Hybrid element

KW - Reduced integration

UR - https://www.scopus.com/pages/publications/33847724629

UR - https://www.scopus.com/pages/publications/33847724629#tab=citedBy

U2 - 10.1016/j.engfracmech.2006.09.009

DO - 10.1016/j.engfracmech.2006.09.009

M3 - Article

AN - SCOPUS:33847724629

SN - 0013-7944

VL - 74

SP - 1649

EP - 1664

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

IS - 10

ER -

Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements

Abstract

Bibliographical note

Keywords

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