The element free Galerkin method has been used to solve linear
elastic fracture mechanics problems using least square
approximations, where the dependent variable at any point is
obtained by minimizing a weighted discrete -error norm involving
the nodal variable within a small domain surrounding the point.
Special techniques are presented for enriching the EFG
approximations near the crack tip such as extrinsic and intrinsic
enrichment. Extrinsic enrichment involves the addition of solution
form to the trial function, whereas the EFG basis is expanded to
include few terms from crack tip solution in intrinsic enrichment.
Apart from enrichment techniques, four basic techniques of
smoothing meshless approximations near nonconvex boundaries are
also presented such as diffraction, transparency, see through and
wedge model. These techniques are then used for the analysis of an
edge crack problem under mode-1 loading. Out of these used
techniques, the extrinsic PU enrichment technique was found to be
more accurate as compared to other used approaches. Extrinsic PU
enrichment technique has also been used for the analysis of a shear
edge crack problem.
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