Isogeometric analysis of size-dependent Bernoulli–Euler beam based on a reformulated strain gradient elasticity theory

Abstract

In this paper, we present an efficient and accurate numerical approach for static bending and free vibration analyses of microstructure-dependent Bernoulli-Euler beams. The current approach includes strain gradient, couple stress (rotation gradient) and velocity gradient effects simultaneously through a reformulated strain gradient elasticity, which applies only one material parameter for each gradient effect. Based on the Hamilton’s principle and an Isogeometric Analysis (IGA) approach, the governing equations are derived and solved, respectively, which effectively fulfills the higher continuity requirements in the present microstructure-dependent Bernoulli-Euler beam formulation. The static bending and free vibration analyses of simply supported microstructure-dependent beams are studied by directly applying the current approach and compared with the corresponding analytical solutions. The physical mesh convergence and numerical results prove the high performance and accuracy of the present numerical approach. In addition, the cantilever and clamped microbeams are also carried out to show the applicability of the present approach.