柱体自由扭转时的最优横截面形式

Optimal cross section of a torsion bar

当柱体自由扭转时,柱体的抗扭性能与横截面形式有关,针对单连通域下的具有最优抗扭性能的横截面形式问题,本文建立了相应的最优形式控制模型,并通过变分法求解得到:在横截面面积相等的情况下,圆截面是所有截面中使结构整体应变能最小和扭转刚度最大的截面形式,这与圣维南所给的一般性结论是一致的。

Optimal control model of a torsion bar was established with control varia ble of structural form.An op-timal cross section of a torsion bar was obtained by the presented model,w hich was coincide with Saint -Venant ' s result,i.e.,round section makes a torsion bar has minimum strain energ y and maximum torsion stiffness.