The plane problem of the theory of end effects for a two-component composite weakly reinforced by fibers of square cross-section is considered. The composite is under conditions of uniform uniaxial loading. As a mathematical model, the equation of elasticity theory of piecewise-homo-geneous media is used. The approximate solution of the problem is searched for with the help of the method of finite differences with application of the concept of base scheme. For an actual composite, the analysis of the results obtained is carried out.

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