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Stress and displacement intensity factors of cracks in anisotropic media

Kuznetsov S., Karakozova A.

International Journal of Applied Mechanics and Engineering

2020

Vol. 25, no. 3

212--218

A relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.

Pseudo-differential equations and conical potentials: 2-dimensional case

Vasilyev Vladimir B.

Opuscula Mathematica

2019

Vol. 39, no. 1

109--124

We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.