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基于泛复函的各向异性板裂纹尖端应力场解法
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Abstract:
本文介绍了泛复变函数的基本理论，利用特定的泛复变量建立求解各向异性材料弹性力学偏微分方程的广义复变函数方法。通过引入泛复变函数和极坐标代换方法解决了含裂纹各向异性板的应力边值问题。推导出I型裂纹端部应力场的实函数通解，有助于改进复合材料断裂力学的基本理论和研究方法。
The basic theory of pan-complex function is introduced, and the generalized complex function method to solve the partial differential equation of elastic mechanics for the anisotropic materials is built by the specific pan-complex variable. The pan-complex function and the polar coordinate re-place method are utilized with the aim of solving the stress boundary problems for the anisotropic plate with a crack. The general solution of Mode I crack-tip stress field is derived with real function variables. It is an aid to improve the basic theory and research method in the fracture mechanics to composite materials.
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