Quasi-3D integral model for thermomechanical buckling and vibration of FG porous nanoplates embedded in an elastic medium

摘要

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.