Size-dependent buckling analysis of nanobeams resting on two-parameter elastic foundation through stress-driven nonlocal elasticity model

The instability of nanobeams rested on two-parameter elastic foundations is studied through the Bernoulli–Euler beam theory and the stress-driven nonlocal elasticity model. The size-dependency is incorporated into the formulation by defining the strain at each point as an integral convolution in terms of the stresses in all the points and a kernel. The nonlocal elasticity problem in a bounded domain is well-posed and inconsistencies within the Eringen nonlocal theory are overcome. Excellent agreement is found with the results in the literature, and new insightful results are presented for the buckling loads of nanobeams rested on the Winkler and Pasternak foundations