ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

# 国际多尺度计算工程期刊

DOI: 10.1615/IntJMultCompEng.2017019518
pages 219-237

## MODELING OF THIN COMPOSITE LAMINATES WITH GENERAL ANISOTROPY UNDER HARMONIC VIBRATIONS BY THE ASYMPTOTIC HOMOGENIZATION METHOD

Yu. I. Dimitrienko
Computational Mathematics and Mathematical Physics Department, Bauman Moscow State Technical University, 2-nd Baumanskaya Str., 5, Moscow, 105005, Russia
I.D. Dimitrienko
Computational Mathematics and Mathematical Physics Department, Bauman Moscow State Technical University, 2-nd Baumanskaya Str., 5, Moscow, 105005, Russia

### ABSTRACT

A new approach to the asymptotic homogenization theory for thin composite laminates with general anisotropy of elastic modules under harmonic vibrations is suggested. The main purpose of the theory is to derive a closed explicit equation system for all six stress tensor components in composite laminates under vibrations, using 3D general equations for steady oscillations of elastic solids, by the asymptotic homogenization method. Unlike the classical homogenization analysis of 3D periodicity structures, our approach was applied to thin laminates with a constant thickness, but without any periodicity through the plate thickness. Recurrent chains of local vibration problems were deduced by the homogenization method, and closed-form solutions of these problems were found for thin laminates. This method allows us to compute all six stresses’ distributions in a plate including normal through-thickness and shear interlayer stresses for the case of general anisotropy in elastic modules. Unlike the classical plate theories, for the case of general anisotropy in elastic modules, when there are 21 elastic constants, the displacements’ distribution through a plate thickness is not linear. Longitudinal displacements proved to be linear functions of the coordinate along a plate thickness only for special anisotropy types — for monoclinic materials of plate layers, whose elastic modules’ symmetry plane is parallel to a middle plane of the plate. Computations by the developed method and by a 3D-?nite-element method solving the three-dimensional problem on free vibrations were compared, which showed a high accuracy of the developed method in calculation of natural frequencies and all six stresses in the plate.

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