用加权残数法解不减薄拉伸中的弹性回跳问题

SOLVING THE PROBLEM OF ELASTIC REBOUND IN NON-THINNING ELONGATION WITH THE METHOD OF WEIGHTED RESIDAULS

本文用加权残数法对不减薄拉伸中芦笋锅底弹性回跳问题作出解答。首先,给出满足边界条件的试函数。试函数中的待定系数可以由以下方法定出。由于试函数而产生的残数可以应用最小二乘法的误差平方值,平均分配于整个域内,用求极值的方法定出待定系数,从而获得解答。这个解就是所求的弹性回跳。依据此解,进而提出拉伸凸模的修形问题。最后,还讨论了将椭圆形底板推论为圆形板的情况。

This article aims to give an answer for solving the problem of elastic rebound of asparagusshaped pot-bottom in non-thinning elongation through the method of weighted residauls.First the trial function which meets with the requirement of boundary conditions is introduced and then the undetermined coefficient in the trial function can be dermined through the following procedure:the residauls from the trial function can equally be dis- tributed at all fields by means of the equal average value from the least square method and then by determining the undertermined coefficient through the extremaevaluating method;next,according to the obtained solution,i.e.the required elastic rebound value,the amendment problem on elongation terrace can be solved;lasly,this article makes an inference from ellipse bottom to round bottom.