TY - JOUR
T1 - Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D
AU - Shannon, Samuel
AU - Peron, Victor
AU - Yosibash, Zohar
N1 - Publisher Copyright:
© 2014 Elsevier Ltd.
PY - 2015/1/1
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
UR - http://www.scopus.com/inward/record.url?scp=84921031575&partnerID=8YFLogxK
U2 - 10.1016/j.engfracmech.2014.12.018
DO - 10.1016/j.engfracmech.2014.12.018
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AN - SCOPUS:84921031575
SN - 0013-7944
VL - 134
SP - 174
EP - 181
JO - Engineering Fracture Mechanics
JF - Engineering Fracture Mechanics
ER -