Two interacting non-elliptical rigid harmonic inclusions loaded by couples

IF 0.7 Q4 MECHANICS
Xu Wang, P. Schiavone
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引用次数: 1

Abstract

We use conformal mapping techniques to design two interacting non-elliptical rigid inclusions, each of which is loaded by a couple, which ensure the so-called ?harmonic condition? in which the original mean stress in the matrix remains undisturbed after the introduction of the inclusions. We show that for prescribed Poisson?s ratio and corresponding geometric parameters, several restrictions are necessary on the external loadings to ensure the harmonic condition. It is seen from our analysis that: (i) the interfacial and hoop stresses are uniformly distributed along each of the inclusion-matrix interfaces; (ii) the interfacial normal and hoop stresses along the two interfaces are completely determined by the Poisson?s ratio and the constant mean stress in the matrix whilst the interfacial tangential stress along the two interfaces can be completely determined by the moments of the couples and the areas of the two inclusions; (iii) the existence of the applied couples will influence the non-elliptical shapes of the two rigid harmonic inclusions when the moment to area ratios for the two inclusions differ.
耦合载荷下两个相互作用的非椭圆刚性谐波包体
我们使用保角映射技术设计了两个相互作用的非椭圆刚性内含体,每个内含体都由一对载荷,从而保证了所谓的“谐波条件”。其中,在引入夹杂物后,基体中的原始平均应力保持不变。对于规定泊松?S比和相应的几何参数,需要对外载荷进行若干限制,以保证谐波条件。分析表明:(1)界面应力和环向应力沿包涵矩阵界面均匀分布;(ii)沿两个界面的界面法向应力和环向应力完全由泊松?S比和基体中恒定的平均应力,而沿两个界面的界面切向应力完全由偶矩和两个夹杂物的面积决定;(iii)当两个夹杂物的矩面积比不同时,施加的耦合的存在将影响两个刚性谐波夹杂物的非椭圆形状。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
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