Abstract
In this paper, a new nonlinear model of nanobeams made of bi-directional (2D) functionally graded material (FGM) is presented. The material properties are assumed to obey an exponential gradation along both the thickness and length directions. The equation of motion is derived based on Euler-Bernoulli beam theory, von Kármán geometric nonlinearity and non-local elasticity theory. The nonlinear bending, buckling and vibration of the nanobeams with size effect is investigated. Results show that the 2D FGM introduces an additional stiffness term in governing equation, so it cannot be solved by classical analytical methods. Therefore, the differential quadrature method (DQM) is used to solve the nonlinear problem. The size-dependent nonlinear critical load and frequencies are calculated. The effect of different material parameters, boundary conditions and size scale are discussed in details.
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