Numerical Green's Functions for Finite-Sized Composites

摘要

In this paper, a semi-analytical approach is presented to derive Green's functions for a finite/infinite-sized medium that may contain a second phase (inclusion). In order to achieve this goal, permissible functions that satisfy the homogeneous boundary condition and the continuity conditions across different phases are derived analytically. These functions are assembled to construct the eigenfunctions for the Sturm-Liouville type differential equation whose differential operator is the principal part of the governing equations for the physical field (displacement in elasticity, temperature in heat conduction). The Green's functions are expressed by the eigenfunctions and the eigenvalues in series format. This procedure is analytical in nature except for determining the eigenvalues and eigenvectors numerically and has not been fully explored despite its importance.