Navier Solution for Buckling Analysis of Size-Dependent Functionally Graded Micro-Plates

Abstract

In the present paper, buckling analysis of functionally graded rectangular micro-plates, on the basis of strain gradient theory with one length scale parameter is studied. Considering the Kirchhoff plate theory and the principle of minimum total potential energy, governing equations of micro-plate subjected to in-plane loads are extracted. In accordance with functionally graded distribution of material properties through the thickness, higher order governing equation of sixth order is derived. Consequently, the stability equation is solved analytically for simply supported micro-plates and the effects of material properties, micro-structure parameters, dimensions and loading conditions are expounded on the critical buckling load. Developing the strain gradient theory for buckling analysis of micro-plates made of functionally graded material is a significant novelty of the presented study.

Strain gradient theory-based vibration analyses for functionally graded microbeams reinforced by GPL

“…Many researchers have studied mechanical characteristic of the graphene nanoplatelets reinforced composite structures by microscopic theory. For example, the Navier method was used to analyze the bending, buckling and forced vibration of the GPL reinforced FG composite beams or plates [18,19]. Wang et al [20], analyzed the vibration of the GPL reinforced micro-shells based on MCST, in which the Navier method was used to solve the natural frequencies of the simply supported boundary, and the Galerkin method was used to other boundaries.…”

Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

“…In [53] using the third order shear deformation plate theory, the bending, buckling, free and forced vibration behavior of a nonlocal composite microplate is analyzed. Functionally graded microplates using Kirchhoff plate's theory and straing gradient theory with only one length scale parameter are studied in [54]. In [55] theory of elasticity including surface stresses is used to study behaviour of shells with nano-scaled thickness.…”

Mechanical Buckling Analysis of Functionally Graded Plates Using an Accurate Shear Deformation Theory

“…Shi-Rong Li et al have study correspondence relations between deflection, buckling load, and frequencies of thin functionally graded material plates and those of corresponding homogeneous plates [24]. H. Farahmand et al to develop with Navier's solutions the size effect that a study expressed by Navier solution for buckling analysis of sizedependent functionally graded micro-plates [25]. A theory of transverse shear deformation for homogeneous monoclinic plates has been studied by [26].…”