The average equations of the dynamics of thin multilayered packets of arbitrary structure with contrasting directions of anisotropy in the elastic layers
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...
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| Published in | Journal of applied mathematics and mechanics Vol. 63; no. 1; pp. 93 - 100 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
1999
|
| Online Access | Get full text |
| ISSN | 0021-8928 |
| DOI | 10.1016/S0021-8928(99)00014-3 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Zakharov, D.D. |
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Mekh. – year: 1973 ident: BIB7 article-title: The Stability and Vibrations of Three-layered Shells – year: 1988 ident: BIB8 article-title: The Mechanics of Structures of Composite Materials – volume: 44 start-page: 669 year: 1977 end-page: 676 ident: BIB5 article-title: A high-order theory of plate deformation. P2. Laminated plates publication-title: Trans. ASME. J. Appl. Mech. – year: 1988 ident: BIB10 article-title: Multilayered Reinforced Shells. The Calculation of Pneumatic Tyres – year: 1988 ident: 10.1016/S0021-8928(99)00014-3_BIB10 – volume: 336 start-page: 50 year: 1994 ident: 10.1016/S0021-8928(99)00014-3_BIB18 article-title: Two-dimensional dynamic equations of a thin asymmetrically laminated elastic plate with a general form of anisotropy publication-title: Dok1 Ross. 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Mekh. – year: 1984 ident: 10.1016/S0021-8928(99)00014-3_BIB9 – volume: 32 start-page: 232 year: 1968 ident: 10.1016/S0021-8928(99)00014-3_BIB14 article-title: The construction of a theory of the bending of laminated plates publication-title: Prikl. Mat. Mekh. |
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| Title | The average equations of the dynamics of thin multilayered packets of arbitrary structure with contrasting directions of anisotropy in the elastic layers |
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