Abstract
The focus of the present work is to present an analytical approach for buckling and free vibrations analysis of thick functionally graded nanoplates embedded in a Winkler-Pasternak medium. The equations of motion are derived according to both the third-order shear deformation theory, proposed by Reddy, and the nonlocal elasticity Eringen's model. For the first time, the equations are solved analytically for plates with two simply supported opposite edges, the solutions also turning helpful as shape functions in the analysis of structures with more complex geometries and boundary conditions. Sensitivity analyses are finally performed to highlight the role of nonlocal parameters, aspect and side-to-thickness ratios, boundary conditions, and functionally graded material properties in the overall response of plates and cylindrical shells. It is felt that the proposed strategy could be usefully adopted as benchmark solutions in numerical routines as well as for predicting some unexpected behaviors, for instance, in terms of buckling load, in thick nanoplates on elastic foundations.
Highlights
In the last years, a new class of composites known as Functionally Graded Materials (FGMs) has been subjected to extensive research activities
The first three dimensionless fundamental natural frequencies, obtained for different numbers of half-waves m in x-direction, are reported in Table 3 for rectangular plates with four different boundary conditions and compared with those obtained in [25] by Hosseini et al The results show that, by increasing the nonlocal parameter, the reduction of the frequency ratios is more pronounced for higher frequencies
In the present study, buckling and vibration of thick FGM nano-plates embedded in elastic Winkler-Pasternak media were studied
Summary
A new class of composites known as Functionally Graded Materials (FGMs) has been subjected to extensive research activities. In a FGM the microstructural variation of the material composition is intentionally designed to build up new composites with optimal physical performance under specific functional requirements Their superior properties make them applicable in a wide range of engineering fields. The formulation is based on an updated Mindlin plate theory, which includes nonlocal elasticity, first-order shear deformation, and plate-foundation interaction. This model was adopted in further works [17, 18] to analyze the. In [25], the authors studied the small-scale effects on the buckling and vibration of rectangular nanoplates based on the Reddy plate theory. The influence of different parameters such as aspect ratio, boundary conditions, and power-law index of FGMs on buckling and vibration is investigated and discussed, by highlighting how the comparison of the obtained outcomes with results available in the literature suggests effectiveness and robustness of the proposed strategy
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