Structural analysis of nonlocal nanobeam via FEM using equivalent nonlocal differential model

In the present work, we developed a new FEM framework to simulate the mechanical responses of the Euler–Bernoulli beam with a two-phase local/nonlocal mixed model. The shape function is a fifth-order polynomial and constitutive boundary conditions (CBCs) are treated as external loads. The main advantages of the present model are the efficient of convergence, simplicity of expressions, and the flexibility on handling various boundary conditions as well as the external loads. Several numerical tests, including static bending, free vibration, and elastic bulking, are carried out to validate the FEM framework. The results showed the complete agreement with the exact solution from Laplace transformation and indicated a simple and reliable scheme to deal with complicated nanosystems.