Buckling Analysis of Nanobeams Resting on Viscoelastic Foundation

This paper uses analytical methods to analyze the buckling behavior of sandwich nanobeams composed of three layers of material, with the central layer including a hollow hole. This study is the first instance of using such analytical techniques for investigating the buckling response of these specific FGM (functionally graded material) nanobeams.

The calculation formulas have been derived using a novel third-order shear deformation theory. The equilibrium equation of the nanobeam is formulated based on the notion of virtual work. Analytical solutions have been used to get the precise answer for the ultimate load of the beam. Empirical evidence has substantiated the dependability of this particular approach.

This feature complicates the response of the beam and gives rise to several fascinating phenomena, including the idea of the virtual critical load which allows for the evaluation of the loss of the critical load. This research also looks at how the buckling behavior of the beam is affected by some geometric elements, material characteristics, hollow features of the intermediate layer, and viscous resistance-related parameters.

Based on the findings of this investigation, several inferences can be inferred. The third-order theory employed in this investigation exhibits commendable reliability in the computation of the buckling issue pertaining to sandwich beams experiencing substantial deformations. The presence of a viscoelastic foundation has a significant impact on the critical buckling load of the beam, resulting in the inclusion of both real and fictitious components. The critical buckling load is influenced by various factors, including the core thickness, foundation parameters, material composition ratio, and the number of hollows, nonlocal characteristics, and core layer material. These factors not only impact the actual magnitude of the critical buckling load, but also affect the rate at which it is lost. The findings of this study hold considerable importance for engineers in their calculations and designs of similar structures within the field of engineering. Moreover, this serves as the foundation for other forthcoming study avenues that can serve as valuable sources of reference.