Elastic equilibrium of a half plane containing a finite array of elliptic inclusions

An accurate analytical method has been proposed to solve for stress in a half plane containing a finite array of elliptic inclusions, the last being a model of near-surface zone of the fibrous composite part. The method combines the Muskhelishvili’s method of complex potentials with the Fourier integral transform technique. By accurate satisfaction of all the boundary conditions, a primary boundary-value elastostatics problem for a piece-homogeneous domain has been reduced to an ordinary well-posed set of linear algebraic equations. A properly chosen form of potentials provides a remarkably simple form of equations and thus an efficient computational algorithm. The theory developed is rather general and can be applied to solve a variety of elastostatics problems. Up to several hundred interacting inclusions can be considered in this way in practical simulations which makes the model of composite half plane realistic and flexible enough to account for the microstructure statistics. The stress concentration factors and effective thermoelastic properties of random structure composites with dilute concentration of fibers are estimated in the vicinity of a free edge. The numerical examples are given showing accuracy and numerical efficiency of the developed method and disclosing the way and extent to which the nearby free or loaded boundary influences the local and mean stress concentration in the fibrous composite.