Continuum approximation in three-dimensional nonaxisymmetric problems of the stability theory of laminar compressible composite materials

Abstract

In the present work it has been rigorously proven that, for three-dimensional nonaxisymmetric stability problems of laminar compressible composite materials, forms of stability loss with a period along the axis ox3 larger than the period of the structure (the second and fourth forms) in the continuum approximation do not give results corresponding to internal instability; forms of stability loss with the period along the axis ox3 equal to the period of the structure (the first and third forms) in the continuum approximation give results corresponding to internal instability; the continuum theory of internal instability [2, 3] follows in the long-wave approximation, from the results corresponding to the first form of stability loss within the framework of the model of a piecewise-homogeneous medium (accurate formulation), and hence the continuum theory [2] is asymptotically accurate.