J. Helsing, AN INTEGRAL-EQUATION METHOD FOR ELASTOSTATICS OF PERIODIC COMPOSITES, Journal of the mechanics and physics of solids, 43(6), 1995, pp. 815-828
An interface integral equation is presented for the elastostatic probl
em in a two-dimensional isotropic composite. The displacement is repre
sented by a single layer force density on the component interfaces. In
a simple numerical example involving hexagonal arrays of disks the fo
rce density is expanded in a Fourier series. This leads to an algorith
m with superalgebraic convergence. The integral equation is solved to
double precision accuracy with a modest computational effort. Effectiv
e mod;li are extracted both for dilute arrays where previously three d
igit accurate results were available, and for dense arrays where previ
ously no results were available.