Abstract
The problem of a doubly periodic rectangular array of elastic filaments contained in an elastic matrix material has been formu lated using a theory of elasticity analysis. The filaments can be of arbitrary shape within the restriction of having two axes of symmetry. The composite is assumed to be subjected to normal stress components in directions perpendicular to the direction of the filament axes. A uniform temperature change can also be im posed. A finite difference representation of the governing equi librium and stress-displacement equations has been utilized in obtaining a solution by a systematic overrelaxation procedure. Numerical results have been obtained for various cross-sectional shapes, a number of filament and matrix material properties, and a range of filament spacings (filament volume contents) varying from filaments nearly in contact to extremely wide spacings in which interaction effects between filaments are essentially zero. Theoretical results have been compared with other methods of analysis and with the limited experimental data presently available.
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