Study of finite elastic plane with multiple holes

The expressions of multiple complex variable stress function of a finite plane with random holes were derived using the theory of complex variable functions and multiple conformal mapping transformation. The inner boundary was processed with complex Fourier series and the outer boundary was processed with collocation method, through which the unknown factors of the stress functions were obtained to calculate the stress field of the finite elastic plane. For a plane with rectangular outer boundary and random ellipse holes, a program was designed to calculate the stress distribution around the holes, and the diagram of the circumferential stress distribution affected by the inner and outer boundaries was obtained. The results show that this processing method is an effective way to deal with the problem of finite elastic plane with multiple holes.