In this paper, the static and dynamic analysis of the higher-order shear deformation nanobeam is investigated within the framework of the two-phase local/nonlocal integral model, in which, the stress is described as the integral convolution form between the strain field and a decay kernel function to address the long-range force interactions in the domain. Based on the principle of minimum potential energy, the finite element formulation of the nonlocal higher-order shear deformation theory nanobeams is derived in a general sense through finite element method (FEM). The explicit expressions of the stiffness, geometric stiffness and mass stiffness matrix of the higher-order shear deformation theory nanobeams are derived directly. The efficiency and accuracy of the developed finite element model of higher-order shear deformation nanobeam are validated by conducting a comparation with the existing analysis results in the researches. Furthermore, under different loading and supported conditions, the effect of nonlocal parameter, nonlocal phase parameter and slenderness ratio on the bending, buckling and free vibration responses of higher-order shear deformation theory nanobeams is investigated in detail.

本文在两相局部/非局部积分模型的框架内研究了高阶剪切变形纳米梁的静态和动态分析，其中应力被描述为应变场和用于解决域中远程力相互作用的衰减核函数。基于最小势能原理，通过有限元法（FEM）推导了一般意义上的非局部高阶剪切变形理论纳米梁的有限元公式。直接推导了高阶剪切变形理论纳米梁的刚度、几何刚度和质量刚度矩阵的显式表达式。通过与现有研究分析结果的比较，验证了所建立的高阶剪切变形纳米梁有限元模型的效率和准确性。此外，在不同载荷和支撑条件下，详细研究了非局部参数、非局部相位参数和长细比对高阶剪切变形理论纳米梁的弯曲、屈曲和自由振动响应的影响。