Stress analysis and the interaction between hole and straight crack in plane elasticity.

Using complex variable methods, some criteria for homothetic transformation and rotation in an in¯nite plane elasticity are established. Maclaurin series is used to analyze the stresses when the pressure exerted on half plane is of the class L1(¡1;1). A vibration pressure on the edge of half plane is also considered and the stresses at every point on the half plane is obtained. The problems of two dimensional hole subjected to in¯nite plane elasticity are considered. These mechanical problems can be written in terms of mathematical boundary value problems. The holes are mapped onto a unit circle by a rational function, then the relevant boundary value problems are solved using modified complex potential (MCP). Analytical results for the stress intensity factor and displacement functions for hypocycloid holes are presented. A circular hole in in¯nite plane elasticity with a single straight crack outside the circle is considered. Crack opening displacement and stress intensity factor for the mentioned crack are found. Family of hypocycloid hole is considered in an in¯nite plane elasticity. The stress intensity factor at the cusp points and the displacement functions are obtained. Then a straight crack is considered outside of the hypocycloid hole. Stresses are obtained at every point outside the hole using the two Muskhelishvili complex potentials.

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