Abstract
The present research is dedicated to the stability analysis of nonlinearly elastic highly porous plates. The mechanical properties and behavior of these plates are described using the model of an inhomogeneous micropolar (Cosserat) medium. Such approach allows for a more precise modeling and detailed analysis of the buckling process for constructional elements made of highly porous materials. In the framework of a general stability theory for three-dimensional bodies, we have studied the stability of a circular micropolar plate subject to radial compression. It is assumed that elastic properties of the plate vary through the thickness. Using the linearization method in a vicinity of a basic state, the neutral equilibrium equations are derived, which describe the perturbed state of a plate. For a special case of axisymmetric buckling modes this linearized equilibrium equations are reduced to the system of three ordinary differential equations. It is also shown that if elastic properties of a plate are symmetric through the thickness then the stability analysis is reduced to solving two independent linear homogeneous boundary-value problems for the half-plate.
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Acknowledgments
This work was supported by the Russian Foundation for Basic Research (grant 12-01-91262-RFG-z and 11-08-01152-a) and German Academic Exchange Service (DAAD) (program “Forschungsaufenthalte für Hochschullehrer und Wissenschaftler”).
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Sheydakov, D.N. (2013). Buckling of Inhomogeneous Circular Plate of Micropolar Material. In: Altenbach, H., Forest, S., Krivtsov, A. (eds) Generalized Continua as Models for Materials. Advanced Structured Materials, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36394-8_17
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DOI: https://doi.org/10.1007/978-3-642-36394-8_17
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