一维正交准晶中具有四条裂纹的椭圆孔口问题的解析解

Abstract

The plane elastic problems of elliptical holes with 4 cracks in 1D orthorhombic quasicrystals were investigated through introduction of a new generalized conformal mapping with the generalized complex variable method. With the stress functions, the basic elasticity equations were reduced to 4th-order partial differential equations, the complex expression of stress components was derived in the image plane and the analytical solution of stress intensity factors (SIFs) at the crack tips was found out. With the change of parameters describing the defects, the results can not only reduce to the conclusions in previous literatures, but also give the SIFs of a variety of common defect configurations, which provides a theoretical basis for engineering mechanics analysis.