孔边位移边界条件下的应力分析

The Stress Analysis around a Hole with Various Displacement Boundary Conditions

根据自然边界元方法给出的圆外弹性问题应力解答,利用Poisson积分公式和自然边界积分方程求出多种形式位移边界条件下的位移场、应变场和应力场,并分析了位移边界条件对应力场的影响。同时与其他计算方法相比较,在边界位移为常数时其结果与文献[2]的解答一致。从本文的算例中不难发现,采用自然边界元方法计算圆外问题时,可以克服一般解析方法只能求解少数特殊位移边值问题的缺点。由于其结果仍为解析解,因此精度也优于数值解答。

In this paper, according to the elastic solution in an exterior circle domain from the natural boundary element method, we analyze displacement fields, strain fields and stress fields with any displacement boundary conditions, and compare them with theory solutions. From the examples given in this paper, we can find that the natural boundary element method can solve various elastic problems in an exterior circle domain with complex displacement boundary conditions, and the results are more accurate than numerical solutions.