广义重调和算子的研究和应用

Research and application of the generalized re-harmonic operator

研究了zj平面上解析函数的柯西-黎曼条件、求导公式以及一类广义重调和算子,探索复变函数方法在复合材料界面断裂力学上的应用,给出了正交异性双材料半无限界面裂纹尖端在判别式Δ1<0,Δ2<0时的应力场.其成果对广义重调和算子在工程中的应用具有现实意义.

Cauchy-Riemann conditions of the analytic functions,derivative formula and a class of generalized re-harmonic operator on the flat of zj were studied.The application of the complex function method in fracture mechanics of the composite material interface were explored.Finally,the stress field of semi-infinite interface crack tip of double dissimilar orthotropic composite materials was given when the discriminant Δ1〈0,Δ2〈0.The result has the important practical significance for the application of generalized re-harmonic operator in the engineering.