Modeling and analysis of nanobeams based on nonlocal-couple stress elasticity and surface energy theories

• A nonlocal Bernoulli–Euler model is developed based on couple stress and surface energy theories.
• Gurtin-Murdoch surface elasticity theory and modified couple stress theory are adopted.
• Effects of the local rotation and surface energy are studied in context of nonlocal elasticity.
• The Poisson’s effect is incorporated in the newly developed nanobeam model.
• Analytical solutions of the static bending and critical buckling load are derived.

This paper aims to develop a new non-classical Bernoulli–Euler model, taking into account the effects of a set of size dependent factors which ignored by the classical continuum mechanics. Among those factors are the microstructure local rotation, long-range interactions between a particle and the other particles of the continuum and the surface energy effects. The model used the modified couple-stress theory to study the effect of the local rotational degree of freedom of a specific particle. Furthermore, the surface elasticity model developed by Gurtin and Murdoch has been used to determine the surface energy effects on the behavior of the particle. The effects of the local rotation and surface energy are investigated in the framework of nonlocal elasticity theory, which is employed to study the nonlocal and long-range interactions between the particles. In addition, Poisson׳s effect incorporated in the newly developed beam model. The equations of equilibrium and complete boundary conditions of the new beam are derived using the principle of virtual work.The developed model is validated, by comparing the obtained results with benchmark results. To illustrate the new model, analytical solutions for the static bending and critical buckling load are obtained. Numerical results reveal the significant effects of the nonlocal, microstructure, surface energy, length-to-height ratio and Poisson on the static bending and critical buckling load of nanobeams.