Elastic stability of curved nanobeam based on higher-order shear deformation theory and nonlocal analysis by finite element approach

In the present work, elastic stability analysis of curved nanobeams is investigated using the differential constitutive law consequent to Eringen's strain-driven integral model coupled with a higher-order shear deformation theory accounting for through thickness stretching effect. The formulation developed here is general in the sense that it can be deduced to realise the influence of different structural theories and analyses of nanobeams. The governing equations derived are solved employing finite element method using a 3-nodes curved beam element. The model developed here is validated considering problems for which analytical/numerical solutions are available in the literature. For comparison purpose, results are also presented for various structural theories obtained from the present formulation. The influence of structural and material parameters such as thickness ratio, beam length, rise of the curved beam, boundary conditions, and size-dependent or nonlocal parameter are brought out on the buckling behaviours of curved nanobeams. It is observed that the type of buckling mode pertaining to the lowest critical value can be different depending on geometrical and internal material length scale parameter, and boundary conditions. •Curved beam models: higher order, stretching effect, 3D behaviour law.•Nonlocal elasticity using Eringen formulation.•Finite Element approach for buckling analysis.•Assessments with available reference results from the literature.•New reference solutions for thin/thick, shallow/deep curved nanobeams.