Mechanical Engineering Journal
Online ISSN : 2187-9745
ISSN-L : 2187-9745
Solid Mechanics and Materials Engineering
Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading
Mutsumi MIYAGAWATakuo SUZUKIToru SASAKITakeshi TANE
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2018 Volume 5 Issue 6 Pages 18-00333

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Abstract

This paper presents theoretical solutions for cases of a two-dimensional isotropic elastic matrix containing two elliptical voids or rigid inclusions under anti-plane loading. These two ellipses have different long-axial radii, short-axial radii, inclining angles, and central points. Their geometries are arbitrary. The matrix is assumed to be subjected to arbitrary loading by, for example, uniform shear stresses, as well as to a concentrated force and screw dislocation at an arbitrary point. The solutions are obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential functions of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.

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© 2018 The Japan Society of Mechanical Engineers
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