Problems of stability of laminar composites in the conditions of plane strain and piecewise-homogeneous basic stressed state have been considered. Two-dimensional spectral problems are reduced to one-dimensional ones by variables division. Formulas are obtained for the eigenvalues of the initial problems including qudrature from eigen functions of unidimensional problem of eigenvalues. It was shown that the Ritz method in the considered case leads to exact decision of the problem.
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