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

Conclusions

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.

The above conclusions corresponding to a three-dimensional nonaxisymmetric problem coincide completely with the conclusions of [5] obtained for plane problems.