扭转弹性杆Lagrange假设的验证
Confirmation of Lagrange Hypothesis for Twisted Elastic Rod
摘要：
结构优化作为一门精确科学的历史可能始于著名的拉格朗日问题：找到一条曲线，该曲线通过绕其平面内的轴旋转来确定最大效率的杆。在欧拉屈曲问题中，放弃了最优杆具有等截面的拉格朗日假设。本文证明了拉格朗日假设对格林希尔扭矩屈曲问题是成立的。相应的等周不等式得到了肯定。
英文摘要：
The history of structural optimization as an exact science begins possibly with the celebrated Lagrange problem: to find a curve which by its revolution about an axis in its plane determines the rod of greatest efficiency. The Lagrange hypothesis, that the optimal rod possesses the constant cross-section was abandoned for Euler buckling problem. In this Article the Lagrange hypothesis is proved to be valid for Greenhill's problem of torque buckling. The corresponding isoperimetric inequality is affirmed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
