The average equations of the dynamics of thin multilayered packets of arbitrary structure with contrasting directions of anisotropy in the elastic layers

• Published in: Journal of applied mathematics and mechanics Vol. 63; no. 1; pp. 93 - 100
• Main Author: Zakharov, D.D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1999
• ISSN: 0021-8928
• DOI: 10.1016/S0021-8928(99)00014-3

Using the three-dimensional dynamical theory of elasticity, the asymptotic method [1, 2] is used to derive two-dimensional equations and elasticity relations for a packet with an arbitrary anisotropy and arrangement of the layers. It is assumed that the contact between layers is ideal and the packet is subject to stresses on the face surfaces with certain boundary conditions at the ends. It is also assumed that in addition to the usual small parameter e = h L ⪡ 1 for a long-wave approximation ( h is the half-thickness and L is the scale of the process in a longitudinal direction), the ratios of the elastic moduli in different directions in each layer can generate additional small parameters of the form ε p p > 0, ε → +0. Similar contrasting differences are permitted between groups of layers. The results are classified in terms of the contrast characteristics and types of anisotropy.