Na. Noda et T. Matsuo, Stress analysis of arbitrarily distributed elliptical inclusions under longitudinal shear loading, INT J FRACT, 106(1), 2000, pp. 81-93
This paper deals with an interaction problem of arbitrarily distributed ell
iptical inclusions under longitudinal shear loading. The problem is formula
ted as a system of singular integral equations with Cauchy-type or logarith
mic-type singularities, where unknown functions are the densities of body f
orces distributed in the longitudinal directions of infinite bodies having
the same elastic constants as those of the matrix and inclusions. In order
to satisfy the boundary conditions along the elliptical inclusions, four ki
nds of fundamental density functions are introduced in a similar way of pre
vious papers treating plane stress problems. Then the body force densities
are approximated by a linear combination of those fundamental density funct
ions and polynomials. In the analysis, elastic constants of matrix and incl
usion are varied systematically; then the magnitude and position of the max
imum stress are shown in tables and the stress distributions along the boun
dary are shown in figures. For any fixed shape, size and elastic constant o
f inclusions, the relationships between number of inclusions and maximum st
ress are investigated for several arrangements.