一维正交准晶中具有四条裂纹的椭圆孔口问题的解析解

Analytical Solutions to Problems of Elliptical Holes With 4 Edge Cracks in 1D Orthorhombic Quasicrystals

运用广义复变函数方法,通过构造适当的广义保角映射,研究了一维正交准晶中具有四条裂纹的椭圆孔口的平面弹性问题.通过引入应力函数,把平面弹性问题的基本方程简化为一个四阶偏微分方程,从而给出了各个应力分量在像平面的复表示,求得了裂纹尖端的应力强度因子的解析解.当描述缺陷的各参数发生变化时,该文的结果不仅可以还原已有文献中的结论,还可给出多种常见缺陷构型的应力强度因子,为工程力学分析提供了理论依据.

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.