推导并得到了任意形状的位移边界条件下在集中角位错作用下的薄板弯曲问题的封闭形式的应力函数解。在求解过程中利用了复变函数及有理型的保角映射的方法。并针对相应的边界条件采取了解析接续的技术以直接得到应力函数的解。为不失一般性,提供了在固定的边界条件下针对一个菱形孔的一些计算结果。得到的应力函数可作为格林函数模拟裂纹等情况下的外界作用。 The closed-form stress function solution of sheet bending problem under the action of concentrated angular dislocation under the displacement boundary condition with arbitrary shape is deduced and obtained. In the process of solving, the method of conformal mapping of complex functions and rational type is used. In order to get the solution of the stress function directly, the analytical technique of continuation is adopted for the corresponding boundary conditions. Without loss of generality, some computations for a diamond hole under fixed boundary conditions are provided. The resulting stress function can be used as a Green’s function to simulate the external effects such as cracks.