Buckling Analysis of Sandwich Timoshenko Nanobeams with AFG Core and Two Metal Face-Sheets

This paper intends to introduce a new and simple technique to precisely assess the axial instability of a shear deformable sandwich nanobeam. The section of the considered beam element is composed of two metal face layers and an axially functionally graded (AFG) core. The power volume fraction law is utilized to describe the properties of spatially graded materials of the core. The coupled governing differential equations in terms of transverse displacement and angle of rotation due to bending are extracted within the context of first-order shear deformation theory and Eringen’s nonlocal elasticity model. The resulting equilibrium equations are then combined and transformed into a unique fifth-order differential equation. Then, the numerical differential quadrature technique is used to estimate the endurable axial critical loads. The most beneficial feature of the proposed technique is to simplify and decrease the essential computational efforts to obtain the endurable axial buckling loads of sandwich shear-deformable nano-scale beams with AFG core. In the case of an axially loaded Timoshenko nanobeam subjected to simply supported end conditions, the obtained results are compared with those accessible in the literature to confirm the correctness and reliability of the proposed approach. Eventually, comprehensive parameterization research is performed to investigate the sensitivity of linear buckling resistance to slenderness ratio, nonlocal parameter, volume fraction exponent, and thickness ratio. The numerical outcomes indicate obviously that the stability strength of sandwich Timoshenko nanobeam is significantly affected by these parameters.