A Unified Technique for Stability Analysis of an Embedded FG Porous Nano/Microbeam Via Modified Couple Stress Theory

Abstract

In this study, modified couple stress theory-dependent stability analysis of functionally graded porous nano/microbeams under deformable support conditions, for the first time, is carried out via a solution method based on the Fourier series and Stokes’ transform. The modified couple stress theory is used as a size-dependent elasticity theory including the small-scale effect. The functionally graded material formulation is based on the power-law distribution found in the literature. The governing equation of the problem and especially the force boundary conditions are determined and the appropriate solution technique is selected. Fourier sine series is chosen as the lateral displacement function of functionally graded porous nano/microbeam under axial loads. Accordingly, the Fourier coefficients are found by substituting this function in the governing equation. Then, these coefficients and the Stokes’ transformation are applied to the force boundary conditions to construct general eigenvalue problems for the stability analysis. The results are compared with the rigid boundary conditions and it is shown that an excellent agreement is achieved. Then, several examples are solved for the functionally graded porous nanobeams and the effects of different parameters are analyzed and presented in a series of graphs and tables.