多孔弹性平板弯曲或扭转的应力集中

Lacunaris Elastic Plane Bending and Torsion Stress Concentration Problem

针对含有任意多孔无限大弹性平板弯曲或扭转应力集中的计算问题,应用弹性力学的复变函数理论,采用多保角变换的方法,推出了多复变量应力函数的表达式。在边界上进行复Fou-rier级数展开,用待定系数法确定应力函数的未知系数,从而计算弹性板的应力场。以含有任意多圆孔的无限板为例,进行了算例分析,给出了各种载荷下孔距对应力集中的影响因素和孔边周向弯矩的分布图。结果表明:该方法对处理多孔弹性平板弯曲或扭转问题是行之有效的。

Based on the complex variable function theory of elastic mechanics, using multiple conformal mapping change to get the expression of multiple complex variable stress function about infinite elastic plane bending and torsion problem with arbitrary holes. Fourier series on every boundary are extended, the unknown coefficients are confirmed by undetermined coefficients method, and the stress field of elastic plane is computed. Taking arbitrary circle holes in infinite plane as an example, this paper gives the influencing effects of the hole distance in the condition of every load on stress concentration and the bending moment distribution maps around holes. The result proves this method is effective to analyze lacunaris elastic plane bending or torsion problems.