Buckling of BDFG nanobeam

There are closed-form analytical equations that can be used to predict how bidirectional functionally graded (BDFG) nanobeams will buckle. These beams are made of materials that have different properties along their thickness and axial directions. The small-scale effects inherent in nanobeams are captured by Eringen's nonlocal elasticity theory and the displacement field of the nanobeam is assumed by the Euler-Bernoulli beam theory. The governing equations of motion are derived by applying Hamilton's principle. Analytical solutions to the governing equations are obtained by using the Mellin transform. Analytical expressions are derived as stability criteria for four distinct boundary conditions of nonlocal nanobeams