多孔有限弹性平面问题的研究

Study of finite elastic plane with multiple holes

应用弹性力学的复变函数理论,采用多保角变换的方法,推出了含有任意多孔有限大平板的多复变量应力函数的表达式.在内边界上进行复Fourier级数展开,在外边界上采用配点法确定应力函数的未知系数,从而计算有限大弹性板的应力场.以外边界为矩形,内边界为任意多椭圆孔的有限板为例,编制了相应的计算程序,进行了算例分析,给出了内外边界对孔边周向正应力影响的分布图.结果表明,本方法对处理多孔有限大弹性平面问题简单且行之有效.

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.