A well-posed Euler-Bernoulli beam model incorporating nonlocality and surface energy effect

This study shows that it is possible to develop a well-posed size-dependent model by considering the effect of both nonlocality and surface energy,and the model can provide another effective way of nanomechanics for nanostructures.For a practical but simple problem (an Euler-Bernoulli beam model under bending),the ill-posed issue of the pure nonlocal integral elasticity can be overcome.Therefore,a well-posed governing equation can be developed for the Euler-Bernoulli beams when considering both the pure nonlocal integral elasticity and surface elasticity.Moreover,closed-form solutions are found for the deflections of clamped-clamped (C-C),simply-supported (S-S) and cantilever (C-F) nano-/micro-beams.The effective elastic moduli are obtained in terms of the closed-form solutions since the transfer of physical quantities in the transition region is an important problem for span-scale modeling methods.The nonlocal integral and surface elasticities are adopted to examine the size-dependence of the effective moduli and deflection of Ag beams.