多孔有限大弹性薄板弯曲应力集中问题

Stress Concentration in Bending Lacunaris Finite Plate

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弹性薄板弯曲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,在外边界采用配点法来确定应力函数的未知系数,从而计算有限大弹性薄板的应力场。本文以外边界为矩形,内边界为任意多椭圆孔的有限薄板为例,编制了相应的计算程序,进行了算例分析。结果表明本方法对处理多孔有限大弹性平面问题是简单且行之有效的。

Following the theory of complex variable function, the multiple conformal transformation is adopted to obtain the expression of multiple complex variable stress in finite plate bending with random boles. Expanding Fourier series on the inner boundary , the unkown coefficient can be determined by collocation method on the outer boundary , thus the stress field of the plate is evaluated. A case of a rectangular plate with elliptic holes confirms the effectiveness.