含有椭圆孔的各向异性体平面问题的通解

应用复变函数方法,给出了在椭圆孔外任一点作用任意一个集中力和集中力偶时的Green应力函数,即应力函数基本解.通过基本解的迭加,首次得到了在椭圆孔周围作用任意集中载荷或分布载荷时表达简洁的通解.为了验证该解的正确性并说明其应用,给出了当孔周作用一对平衡的集中力或均匀的分布力时的解,其结果与前人所得的结果一致.

GENERAL SOLUTIONS OF LOADED ANISOTROPIC PLANE WITH ELLIPTICAL HOLE

A fundamental solution of Green's stress function for the case of a concentrated force and a moment acting on an arbitrary point in an anisotropic plane with an elliptical hole was derived with a complex variable function method. By using the fundamental solution and the principle of superposition, very simple expressions of the general solutions for the case of arbitrary concentrated loads or distributed loads acting around an elliptical hole in an anisotropic plane were obtained. In order to verify the solutions and illustrate its application, the solutions were provided when the edge of an elliptical hole was subjected to two concentrated forces equal in magnitude and opposite in direction or uniformly distributed forces. The particular results coincided with those in early works.