Isogeometric analysis for non-classical Bernoulli-Euler beam model incorporating microstructure and surface energy effects

Abstract The non-classical Bernoulli-Euler beam model contains a material length scale parameter to account for the microstructure effect on the bulk material and three surface elasticity constants to capture the distinguished material properties on a surface. The present work is dedicated to develop a new effective computational approach for the non-classical Bernoulli-Euler beam model based on the isogeometric analysis (IGA) with high-order continuity basis functions of non-uniform rational B-splines (NURBS), which effectively fulfills the higher continuity requirements in the non-classical Bernoulli-Euler beam. To verify the new approach, the numerical results obtained from the new developed approach of the two applications for both simply supported and cantilever beams are compared with the corresponding analytical results available in the literature. Eventually, the approach verified is further utilized to explore the effects of microstructure and surface energy on beam deflection and natural frequency. For the static bending problem, it is detected that both the microstructure and surface energy effects enhance the beam bending stiffness. And for the free vibration problem, it is found that both the microstructure and surface energy effects increase the beam natural frequency. Furthermore, it is seen that the effect of microstructure on the natural frequency is more significant than the surface energy effect at nanoscale.