A theoretical analysis is made of the optimal interference for fitting elastic fibres into the two-periodic system of holes of an isotropic elastic binder. The principles of equal strength and the minimization of stress intensity factors are used. The binder of the composite is weakened by a doubly periodic system of rectilinear cracks. A criterion and methods for solving the problem of the prevention of fracture of a composite reinforced with unidirectional fibres are suggested. A closed system of algebraic equations that allows one to obtain the solution of the problem of the optimal design of a composite body depending on the mechanical and geometrical characteristics of a binder and fibre is constructed. The found interference provides an increase of the load-bearing capacity of the composite. The results of the considered theoretical work open new possibilities for the optimal design of the composite bodies (composites) at the expense of the choice of interference of the binder and fibre joint.
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