Elastic equilibrium and effective elastic constants of a cross-reinforced fiber composite (Q1319706)

A solution of the problem on a stressed state of the cross-reinforced fibrous composite under condition of macroscopically uniform external loading is obtained. The initial tri-periodic problem is reduced to the problem for a layer whose displacement vector is presented as a series by especially constructed systems of inner and outer bi-periodical solutions of the Lamé equation. Using representations of partial solutions in different coordinate bases, the initial boundary problem is reduced to an infinite system of linear algebraic equations.