Exact stiffness-matrix of two nodes Timoshenko beam on elastic medium. An analogy with Eringen model of nonlocal Euler-Bernoulli nanobeams

The obtained analytical results are discussed in the light of nonlocal elasticity of Eringen differential type, applied to an Euler-Bernoulli beam model. As a result the stiffness-matrix and equivalent nodal loads of an Euler-Bernoulli nonlocal elastic beam, can be defined in analogy to those of a first order shear deformable beam. This conclusion allows handling the elastostatic problem of nanobeams, modelled according to Eringen's nonlocal elasticity, by slight modifications of the existing computational tools for the solution of the elastostatic problem of a local shear deformable beam.