TORSION OF ELASTIC SHAFT OF REVOLUTION EMBEDDED IN AN ELASTIC HALF SPACE

摘要

The problem of torsion of elastic shaft of revolution embedded in an elastic half spaceis studied by the Line-Loaded Integral Equation Method(LLIEM).The problem isreduced to pair of one-dimensional Fredholm integral equations of the first kind due to thedistributions of the fictitious loads“Point Ring Couple(PRC)”and“Point Ring Couple inHalf Space(PRCHS”on the axis of symmetry in the interior and external ranges of theshaft occuied respectively.The direct discrete solution of this integral equations may beunstable,i.e.an ill-posed case occurs.In this paper,such an ill-posed Fredholm integralequation of first kind is replaced by a Fredholm integral equation of the second kind withsmall parameter,which provides a stable solution.This method is simpler and easier tocarry out on a computer than the Tikhonov’s regularization method for ill-posed problems.Numerical examples for conical,cylindrical,conical-cylindrical,and parabolic shafts aregiven.