以Kirchhoff薄板理论解狭长矩形截面杆的约束扭转
On the Restricted Torsion of Narrow Rectangular Cross Section by Kirchhoff’s Thin Plate Theory
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摘要: 本文以Kirchhoff的薄板理论,解狭长矩形截面杆的约束扭转.这扭转问题,相当于在自由端作用扭矩的悬臂矩形板的弯曲.得到的结果,不仅证实了Timoshenko教授以能量法所得的扭转角,并且也给出应力的值.Abstract: Kirchhoff's thin plate theory is used to solve the restricted torsion of narrow rectangular cross section as this problem is equivalent to the bending of a rectangular cantilever plate by a twisting moment at the free end. The results obtained not only prove the angle of twist obtained by Prof. Timoshenko using the energy method put give us stresses.
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[1] Timoshenko,S,,Theory of Elasticity. [2] Timoshenko,S,,On the torsion of a prism,one of the cross section of which remains plane,Proceedings of the London Mathematical Society,Ser,2,(1922). [3] 张福范,《弹性薄板》,科学出版社,(1964). [4] 张福范,均布荷载下悬臂矩形板的弯曲,应用数学和力学,1.3,(1980). -
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