偏心环域应力极值的逼近

本文用近似方法对圆板偏心开孔的安全性作了探讨。其方法是首先通过分析确定危险点,然后再设法找一个弯曲位移的近似函数,使其满足边界位移条件和薄板微分程。再通过近似变分,并在危险点限制其误差,使这个近似解在危险点逼近精确值,从而得该点应力值的一个上界,并以它作为判别的根据。

Approxmation of Maximum Stress on an Eccentie Annulus

Researches on the safety of a hole, drilled eccentricly on round plate materials, are done by using an approximative method. The dangerous point on the plate is found through analyzing the complex boundary state. Then, obtained is the displacement function which coresponds to both the boundary displacement condition, and the thin plate differential question. Using Rits calculus of variations and restraining errors at the dangerous point, we can further obtain an approximate solution which is the upper bound of the exact value and is regarded as criterion determining whether the round plate is safe, or not.