具微孔柱体扭转问题的一个近似解

一.问题 自从圣维那(Saint、Venant)对扭转问题进行研究后,扭转问题已化为求一函数(亦即扭转函数)φ,并使适合下列条件: 1.φ必须是泊松方程的解,即:

AN APPROXIMATE SOLUTION OF TORSION PROBLEM OF PRISM WITH SMALL HOLE

In this paper, a method of superposition in given for the determination of approximate stress function of prisin with small hole in torsion. The approximate stress function consists of two parts. The first part is the solution of torsion problem for a simply connected region bounded by the exterior boundary of the given prism. The second part is the solution of Von-Neumann problem in the exterior region of the small hole.The boundary value of second part on the small hole is determined so that the superposition of these two solution gives free boundary condition on the surface of hole. It can be shown that the effect of second solution are concentrated in around the neighbourhood of the small hole.