嵌在弹性半空间的刚性变直径圆轴的扭转<sup>*</sup>

嵌在弹性半空间的刚性变直径圆轴的扭转^*

基金项目: * 国家自然科学基金

Department of Mathematics and Mechanics, South China Institute of Technology, Guangzhou

摘要: 本文用线载荷积分方程法(LLIEM)研究嵌在弹性半空间的刚性变直径圆轴的轴对称扭转.利用将“半空间的点环力偶”(PRCHS)这一虚的基本载荷沿对称轴的圆轴区间中分布就能使本问题归结为一个一维的非奇异的Ferdholm第一种积分方程,且很易用数值求解.文中给出刚性圆锥,圆柱,圆锥柱嵌在弹性半空间的扭转的数值计算的例并和他人的已知结果相比较.文中也给出了刚性半球嵌在弹性半空间的扭转的精确解.

Abstract: The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLJEM), where the problem is formulated by distributions of ficitious fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically. Numerical examples oftorsin of rigid conic, cylinder, conical-cylinder embedded in an elastic half space are given and compared with the known result obtained, by the others. The exact solution of torsion of rigid half sphere embedded in an elastic half space is also presented.

[1]	Luco, J.E., Torsion of a rigid cylinder embedded in an elastic half space, J. Appl. Mech. ASME, 43(1976), 419-423.
[2]	Yun T.Q., An integral equation method for solving the torsion problem of revolution bodies, J.H.I.T., 1(1979), 82-97.(English edition)
[3]	Yun, T.Q., Pile analysis by simple integral equation method, Appl. Math. and Mech., 2, 3(1981), 331-349.(English edition)
[4]	Yun, T.Q., U.C. Shao and C.G.Qiu, Analysis of ellipsoid compressed by two axial concentrated forces at two ends, Appl. Math. and Mech., 2, 6(1981), 699-710.(English edition.)
[5]	云天拴,水平刚性岩基上的弹性层表面受垂直集中力间题的积分方程解法,固体力学学报,3(1983), 376-382.
[6]	云天拴,嵌在倾斜半空间的轴向受力刚性桩的线载荷积分方移法的分析,固体力学学报,1(1986), 64-68.
[7]	云天锉、张进敏,竖井的近似分析,上海力学, 1 (1986), 50-54.
[8]	云天锉,线载荷积分方程法分析嵌在非均匀平空问的轴向受力桩,第16届国际理论与应用力学大会(ICTAM)中国学者论文集锦(上册),中国力学学会编,大连工学院出版社(1986),63-74.
[9]	云天拴,包含一受扭迥转轴的半空间的性质,应用数学和力学,9, 6 (1988).
[10]	Mindlin, R.D., Force at a point in the interior of a semi-infinite solid, J. of Physics, 77(1936), 195.