Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D

Samuel Shannon; Victor Peron; Zohar Yosibash

doi:10.1016/j.engfracmech.2014.12.018

Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D

Samuel Shannon, Victor Peron, Zohar Yosibash

Department of Mechanical Engineering

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

6 Scopus citations

Abstract

Explicit asymptotic solutions are still unavailable for an elliptical crack or sharp V-notch in a three-dimensional elastic domain. Towards their derivation we first consider the Laplace equation. Both homogeneous Dirichlet and Neumann boundary conditions on the surfaces intersecting at the elliptical edge are considered. We derive these asymptotic solutions and demonstrate, just as for the circular edge case, that these are composed of three series with eigenfunctions and shadows depending on two coordinates.

Original language	English
Pages (from-to)	174-181
Number of pages	8
Journal	Engineering Fracture Mechanics
Volume	134
DOIs	https://doi.org/10.1016/j.engfracmech.2014.12.018
State	Published - 1 Jan 2015

Keywords

3-D singularities
Edge flux intensity functions
Elliptical singular edge

ASJC Scopus subject areas

General Materials Science
Mechanics of Materials
Mechanical Engineering

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10.1016/j.engfracmech.2014.12.018

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title = "Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D",

abstract = "Explicit asymptotic solutions are still unavailable for an elliptical crack or sharp V-notch in a three-dimensional elastic domain. Towards their derivation we first consider the Laplace equation. Both homogeneous Dirichlet and Neumann boundary conditions on the surfaces intersecting at the elliptical edge are considered. We derive these asymptotic solutions and demonstrate, just as for the circular edge case, that these are composed of three series with eigenfunctions and shadows depending on two coordinates.",

keywords = "3-D singularities, Edge flux intensity functions, Elliptical singular edge",

author = "Samuel Shannon and Victor Peron and Zohar Yosibash",

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AU - Shannon, Samuel

AU - Peron, Victor

AU - Yosibash, Zohar

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Y1 - 2015/1/1

N2 - Explicit asymptotic solutions are still unavailable for an elliptical crack or sharp V-notch in a three-dimensional elastic domain. Towards their derivation we first consider the Laplace equation. Both homogeneous Dirichlet and Neumann boundary conditions on the surfaces intersecting at the elliptical edge are considered. We derive these asymptotic solutions and demonstrate, just as for the circular edge case, that these are composed of three series with eigenfunctions and shadows depending on two coordinates.

AB - Explicit asymptotic solutions are still unavailable for an elliptical crack or sharp V-notch in a three-dimensional elastic domain. Towards their derivation we first consider the Laplace equation. Both homogeneous Dirichlet and Neumann boundary conditions on the surfaces intersecting at the elliptical edge are considered. We derive these asymptotic solutions and demonstrate, just as for the circular edge case, that these are composed of three series with eigenfunctions and shadows depending on two coordinates.

KW - 3-D singularities

KW - Edge flux intensity functions

KW - Elliptical singular edge

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DO - 10.1016/j.engfracmech.2014.12.018

M3 - Article

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SN - 0013-7944

VL - 134

SP - 174

EP - 181

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

ER -

Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D

Abstract

Keywords

ASJC Scopus subject areas

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