Integral equations with hypersingular kernels - Theory and applications to fracture mechanics

Youn Sha Chan; Albert C. Fannjiang; Glaucio H. Paulino

doi:10.1016/S0020-7225(02)00134-9

Integral equations with hypersingular kernels - Theory and applications to fracture mechanics

Youn Sha Chan, Albert C. Fannjiang, Glaucio H. Paulino

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

111 Scopus citations

Abstract

Hypersingular integrals were investigated for general integers α (positive) and m (nonnegative). The integrals were evaluated to calculate the stress intensity factors. Examples involving crack problems were given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. Analysis shows that as material property variation in space and higher order graded continuum theories are considered, the formulation of the crack problem and the associated kernels becomes quite involved.

Original language	English (US)
Pages (from-to)	683-720
Number of pages	38
Journal	International Journal of Engineering Science
Volume	41
Issue number	7
DOIs	https://doi.org/10.1016/S0020-7225(02)00134-9
State	Published - Apr 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Materials Science
Mechanics of Materials
General Engineering
Mechanical Engineering

Keywords

Asymptotic analysis
Chebyshev polynomials
Collocation method
Fredholm integral equation
Functionally graded materials
Hypersingular integrals
Integral equation method
Mode I crack
Mode III crack
Stress intensity factors

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10.1016/S0020-7225(02)00134-9

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@article{13a021c77d1e443eac22562fb54ce671,

title = "Integral equations with hypersingular kernels - Theory and applications to fracture mechanics",

abstract = "Hypersingular integrals were investigated for general integers α (positive) and m (nonnegative). The integrals were evaluated to calculate the stress intensity factors. Examples involving crack problems were given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. Analysis shows that as material property variation in space and higher order graded continuum theories are considered, the formulation of the crack problem and the associated kernels becomes quite involved.",

keywords = "Asymptotic analysis, Chebyshev polynomials, Collocation method, Fredholm integral equation, Functionally graded materials, Hypersingular integrals, Integral equation method, Mode I crack, Mode III crack, Stress intensity factors",

author = "Chan, {Youn Sha} and Fannjiang, {Albert C.} and Paulino, {Glaucio H.}",

note = "Funding Information: We acknowledge the support from the USA National Science Foundation (NSF) through grants CMS-9713798 (Mechanics & Materials Program) and DMS-9600119 (Applied Mathematics Program). ",

year = "2003",

month = apr,

doi = "10.1016/S0020-7225(02)00134-9",

language = "English (US)",

volume = "41",

pages = "683--720",

journal = "International Journal of Engineering Science",

issn = "0020-7225",

publisher = "Elsevier Ltd",

number = "7",

}

TY - JOUR

T1 - Integral equations with hypersingular kernels - Theory and applications to fracture mechanics

AU - Chan, Youn Sha

AU - Fannjiang, Albert C.

AU - Paulino, Glaucio H.

N1 - Funding Information: We acknowledge the support from the USA National Science Foundation (NSF) through grants CMS-9713798 (Mechanics & Materials Program) and DMS-9600119 (Applied Mathematics Program).

PY - 2003/4

Y1 - 2003/4

N2 - Hypersingular integrals were investigated for general integers α (positive) and m (nonnegative). The integrals were evaluated to calculate the stress intensity factors. Examples involving crack problems were given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. Analysis shows that as material property variation in space and higher order graded continuum theories are considered, the formulation of the crack problem and the associated kernels becomes quite involved.

AB - Hypersingular integrals were investigated for general integers α (positive) and m (nonnegative). The integrals were evaluated to calculate the stress intensity factors. Examples involving crack problems were given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. Analysis shows that as material property variation in space and higher order graded continuum theories are considered, the formulation of the crack problem and the associated kernels becomes quite involved.

KW - Asymptotic analysis

KW - Chebyshev polynomials

KW - Collocation method

KW - Fredholm integral equation

KW - Functionally graded materials

KW - Hypersingular integrals

KW - Integral equation method

KW - Mode I crack

KW - Mode III crack

KW - Stress intensity factors

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U2 - 10.1016/S0020-7225(02)00134-9

DO - 10.1016/S0020-7225(02)00134-9

M3 - Article

AN - SCOPUS:0037397139

SN - 0020-7225

VL - 41

SP - 683

EP - 720

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

IS - 7

ER -

Integral equations with hypersingular kernels - Theory and applications to fracture mechanics

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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