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.

在本文中，我们提出了一种有效且准确的数值方法，用于对与微观结构相关的伯努利-欧拉梁进行静态弯曲和自由振动分析。目前的方法包括应变梯度、耦合应力（旋转梯度）和速度梯度效应，通过重新制定的应变梯度弹性，对每个梯度效应仅应用一个材料参数。基于哈密顿原理和等几何分析 (IGA) 方法，分别推导出和求解控制方程，这有效地满足了当前依赖于微观结构的伯努利-欧拉梁公式中更高的连续性要求。通过直接应用当前方法并与相应的解析解进行比较，研究了简支结构相关梁的静态弯曲和自由振动分析。物理网格收敛和数值结果证明了当前数值方法的高性能和准确性。此外，还进行了悬臂和夹紧微梁，以显示本方法的适用性。