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“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

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【作者】 李昭银刘丽丽

【Author】 Li Zhaoyin Liu Lili(Ho-Hai University)

【机构】 河海大学河海大学

【摘要】 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=((ErEθ)/(1/2))/(2(1+(μμθr)/(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=(Eθ/Er)/(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/G')是无关的。

【Abstract】 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=(ErEθ1/2/2(1+(μμθr1/2) 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 (Eθ/Er1/2=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’/G"=e.

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