Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method

Abstract

In the present study, the buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study is made of functionally graded materials in the longitudinal direction and the cross-section of the microcolumn varies continuously throughout the axial direction. The Bernoulli–Euler beam theory in conjunction with modified strain gradient theory are employed to model the structure by considering the size effect. The Rayleigh–Ritz numerical solution method is used to solve the eigenvalue problem for various conditions. The influences of changes in the cross-section and Young’s modulus, size dependency, and non-classical boundary conditions are examined in detail. It is observed that the size effect becomes more pronounced for smaller sizes and differences between the classical and non-classical buckling loads increase by increasing the taper ratios.