“论两种不同正交异性楔弹性接触”中应力奇异性

THE STRESS SINGULARITIES IN THE ELASTIC CONTACT PROBLEM OF TWO DISSIMILAR ORTHOTROPIC WEDGES

一般楔形体受面力作用时,其应力及位移有时会变为无限大。本文继续[1]的工作,分析均匀正交异性楔和两种不同正交异性复合楔的应力奇异性问题。由于假定了G_(rθ)=((E_rE_θ)/(1/2))/(2(1+(μ_(rθ)μ_(θr))/(1/2)),可用解析法得到应力奇异阶次为γ^(-s)型。对于均匀正交异性楔s只与材料弹性模量比值平方根kl=(E_θ/E_r)/(1/2)有关;对于正交异性复合楔,当k＇=k＇＇,s与复合楔中材料剪切模量比值e(=G_(rθ)~＇/G_(rθ)~＇＇)是无关的。

For general wedges being subjected to traetions, the stresses and displace ments of which sometimes may become infinite. This paper gives a research after the paper [1] to analyse the singularties of the contact stress field of two homogeneous and orthotropic wedges as well as two dissimilar orthotropic composite wedges. On the supposition G_(rθ)=(E_rE_θ)^(1/2)/2(1+(μ_(rθ)μ_(θr)^(1/2)) singularities of the type r^(-s) may be obtained by use of the analytic method For homogeneous and orthotropic wedges, s is related to the square root of the ratio of moduli of elasticity of the material in the principal directions (E_θ/E_r)^(1/2)=K. For composite wedges of orthotropic materials,when K'= K', s is not related to the ratio of moduli of elasticity of shear in the principal directions G'_(rθ)/G'_(rθ)=e.