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材料力学中的开口薄壁杆自由扭转的公式,一般是根据“刚周边假设”,直接引用弹性力学中矩形截面杆扭转的结果导出的。这在实用上是简便易行的;但缺乏必要的理论分析,而且与初等扭转理论相脱节。本文用能量法建立自由扭转时的“剪应力环流定理”,并以这个定理为基础导出开口薄壁杆自由扭转公式。这样就把开口与闭合薄壁截面杆的扭转理论紧密联系起来,建立起自由扭转初等理论的统一观点。
The formula for free torsion of thin-walled bars with open ends in material mechanics is derived directly from the result of torsion of rectangular section bars in elastic mechanics, based on the assumption of just the periphery. This is practically easy to use; however, it lacks the necessary theoretical analysis and is out of step with the elementary twist theory. In this paper, the “shear stress circulation theorem” in free torsion is established by energy method. Based on this theorem, the free torsion formula of thin-walled open-ended rod is deduced. This closely correlates the opening with the torsional theory of the closed thin section rod and establishes a unified view of the elementary theory of free torsion.