Abstract
Mechanical buckling, thermal buckling and free vibration behaviors of functionally graded (FG) porous nanoplates embedded in an elastic medium are investigated via a nonlocal strain gradient theory. Two dimensional (2D) and quasi three dimensional (quasi-3D) sinusoidal shear deformation theories are used in this study. The proposed theories have a displacement field with integral terms which include the effects of both transverse shear and normal deformations. Porosity-dependent material properties of the porous nanoplate are defined via a modified power-law function. Equations of motion are derived based on Hamilton’s principle which includes the effect of the two-parameter elastic foundations. Numerical results are presented to verify the accuracy of the present 2D and quasi-3D shear deformation theories by comparing them with the solutions given in literature with different 2D, quasi-3D and 3D solutions. The effects of many parameters like porosity factor, nonlocal, length scale parameters, plate aspect ratio, side-to-thickness ratio and gradient index on the buckling, thermal buckling and vibration of FG porous nanoplates are all discussed.
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