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Assessment of Reuss, Tamura, and LRVE models for vibration analysis of functionally graded nanoplates

Shahsavari Davood, Karami Behrouz

Archives of Civil and Mechanical Engineering

2022

Vol. 22, no. 2

art. no. e92, 1--13

Majority of structural analysis on functionally graded materials utilized Voigt and Mori-Tanaka micromechanical modelling. The current article is focused on free vibration response of inhomogeneous nano-size plate resting on elastic foundations against different micromechanical models (i.e., Reuss, Tamura, and LRVE). For the elastic foundation type, Winkler, Pasternak, and Kerr mediums are modelled one by one. The nanoplate is modelled based on a quasi-3D shear deformation plate theory which is in relation with general strain gradient theory by employing Hamilton principle, then the model is solved analytically via Navier solution procedure. This exact model determines fourfold coupled (stretching-axial-bending-shear) response with estimating softening-stiffness and hardening-stiffness mechanisms of nano-sized systems. Finally, numerical results are provided to represent the influence of size-dependent effects on vibrations of embedded nanoplate obtained through different micromechanical models.

Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels

Huang Yong, Karami Behrouz, Shahsavari Davood, Tounsi Abdelouahed

Archives of Civil and Mechanical Engineering

2021

Vol. 21, no. 4

39--53

The current work develops a size-dependent model to provide a comprehensive analysis of static stability in doubly curved micro-panels resting on an elastic foundation. The doubly curved panel is made of advanced composites which reinforced with carbon-based materials. A seven-unknown shear deformation theory in curvilinear coordinate is combined with a non-classical approach to obtain a suitable model to get an accurate result for mechanical performance of micro-size shells. To perform this aim, a virtual work of Hamilton statement is developed and then an analytical technique on the basis of double-Fourier series is implemented for the microshell with fully simply supported conditions in edges. Results show that, CNTs reinforced composite curved shells exhibit a hardening response under buckling. It is also showed that the greatest critical buckling load of the microshell is observed for the shell with spherical panel followed by elliptical, cylindrical, and hyperbolic panels, respectively. Moreover, change of CNTs weight fraction can significantly alter the static stability characteristics of CNTs reinforced composite curved size-dependent shells.