Buckling analysis of functionally graded microplates incorporating nonlocal strain gradient theory and surface energy effects

• Published in: Advances in mechanical engineering Vol. 16; no. 10
• Main Authors: Van Hieu, Dang, Gia Phi, Bui
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01-10-2024; Sage Publications Ltd; SAGE Publishing
• Subjects: Aspect ratio; Boundary conditions; Buckling; Deformation effects; Equilibrium equations; Exact solutions; Functionally gradient materials; Material properties; Parameters; Potential energy; Power law; Shear deformation; Strain analysis; Surface energy; Thickness; surface elasticity theory; Higher-order shear deformation theory; buckling; functionally graded microplate; nonlocal strain gradient theory; minimum potential energy principle
• ISSN: 1687-8132; 1687-8140
• DOI: 10.1177/16878132241288327

The purpose of this work is to present a buckling analysis of functionally graded (FG) microplates by combining nonlocal strain gradient theory (NSGT) with the higher-order shear deformation plate theories (HSDPTs). The microplate is assumed to be composed of a combination of ceramic and metal materials, and the material properties are assumed to vary continuously in the thickness direction based on a simple power law. The equilibrium equations and the boundary conditions are derived using the principle of minimum potential energy. Analytical solutions are determined for the critical buckling loads of the rectangular FG microplates with different boundary conditions. The results obtained have been verified by comparison with existing findings in the literature. Furthermore, some numerical illustrations are provided to investigate the effects of nonlocal parameters, the material length scale parameter, shear deformation, aspect ratios, the power-law index, and the surface energy on the buckling response of the rectangular FG microplates.