用计算复变函数法求解含圆孔板的应力场

Calculation of Stress Field in Plate with a Round Hole Using Computational Complex Function Method

采用保角映射技术将含有圆孔的外域变换为圆的内域,通过在边界配点来确定其边界条件,并应用弹性力学的复变函数理论及最小二乘法求解板内的应力场.为了比较本文方法的计算精度和计算效率,用Matlab语言编程并计算了含圆孔的有限板和无限板内的应力分布,结果表明用计算复变函数法求含孔板的应力场问题计算精度高,计算量小,具有应用的价值.

A plate with a round hole is transformed into a round domain by using conformal-mapping method. The boundary is settled by setting finite points. The complex function theory of elasticity mechanics and the least square method are applied to calculate the stress field in the plate. A computing code on the Matlab language is written to calculate and compare the stress distributions both in a finite and in an infinite plate with a round hole in order to test the precision and efficiency of this computing method. It is shown through the comparisons of the results that the computational complex function method is precise, efficient and applicable.