The Generalized 2D Thermal -electro-elastic Solution for the Cracked- Half-Elliptical-Hole Problem in a Half Plane

摘要

In this paper,the half elliptical hole with an edge crack in a thermalpiezoelectric materials is studied,anda generalized 2D thermal-electro-elastic solution is derived by using the complex variable method.First,the mapping function which maps the outside of the elliptical hole and the crack in the right half planeinto the outside of a circular hole in a full plane is given by the method of conformal mapping.Then thecomplex potential functions for the temperature/mechanical/electric field,and the fields intensity factorsare presented based on the assumption that the surface of the crack and hole is adiabatic,electricallyimpermeable and traction-free,respectively.Numerical analysis is also made to discuss the influences ofthe crack length and the thermal/mechanical/electric loading on the fields intensity factors.Similar to thefull plane problem,some useful results can be found:the heat flux which perpendicular to the crack hasgreat effect on the stress intensity factors for the mode II cracks,but its influence on the stress intensityfactors for the mode I cracks and the intensity factors for the electric displacement is not significant.