Using the modified strain gradient theory to investigate the size-dependent biaxial buckling analysis of an orthotropic multi-microplate system

On the basis of the modified strain gradient theory, this research presents an analytical approach to analyze elastic instability of an orthotropicmulti-microplate system (OMMPS) embedded in a Pasternak elastic medium under biaxial compressive loads. Kirchhoff plate theory and the principle of total potential energy are applied to obtain the partial differential equations and corresponding boundary conditions. Various types of "chain" boundary conditions for the ends of the microplates system are assumed such as "Clamped-Chain," "Free-Chain" and "Cantilever-Chain" systems. In order to analytically obtain the buckling load of the OMMPS, we use Navier's approach which satisfies the simply supported boundary conditions and trigonometric method. In order to show the dependability of the presented formulation in this paper, several comparison studies are carried out to compare with existing data in the literature. Numerical results are presented to reveal variations of the buckling load of OMMPS corresponding to various values of the number of microplates, the length scale parameter (h/l), aspect ratio, Pasternak elastic medium parameters and the thickness of the microplate and the biaxial compression ratio. Some numerical results of this paper illustrate that when the number of microplates is small, especially becoming 2, there is an important difference between buckling loads obtained for "Clamped-Chain," "Free-Chain" and "Cantilever-Chain" systems. Also, it is shown that by increasing the number of microplates in the system, the influence of the Pasternak elastic medium on the buckling load of system is reduced. It is anticipated that the results reported in this work are applied as a benchmark in future microstructure issues.