The unified gradient elasticity theory with applications to nano-mechanics of torsion is examined. The Reissner stationary variational principle is invoked to detect the differential and boundary conditions of equilibrium along with the consistent form of the constitutive laws. An efficient meshless numerical approach is established by making recourse to the Reissner variational functional wherein independent series solution of the kinematic and kinetic field variables are proposed. Suitable forms of the coordinate functions, in terms of the Chebyshev polynomials, are introduced to fulfill a set of kinematic and higher-order boundary conditions in the elastic torsion of nano-bars with practical kinematic constraints. Torsional behavior of the unified gradient elastic bar is studied for structural schemes of applicative interest. An excellent agreement between the torsional responses of the nano-bar detected based on the established meshless method and obtained exact analytical solution is realized. The proposed meshless numerical approach is confirmed to have a fast convergence rate and an admissible convergence region in determination of the torsional rotation field with high accuracy. The introduced meshless method is demonstrated to be highly efficacious in characterizing both the softening and stiffening structural behaviors at nano-scale. The presented numerical approach therefore paves the way ahead in mechanics of nano-structures.

研究了应用于纳米扭转力学的统一梯度弹性理论。调用 Reissner 平稳变分原理来检测平衡的微分和边界条件以及本构律的一致形式。通过求助于 Reissner 变分泛函建立了一种有效的无网格数值方法，其中提出了运动学和动力学场变量的独立级数解。根据切比雪夫多项式，引入了坐标函数的合适形式，以在具有实际运动学约束的纳米杆弹性扭转中满足一组运动学和高阶边界条件。针对具有应用意义的结构方案，研究了统一梯度弹性杆的扭转行为。基于建立的无网格方法检测到的纳米棒的扭转响应与获得的精确解析解之间实现了极好的一致性。所提出的无网格数值方法被证实在高精度确定扭转旋转场时具有快速的收敛速度和可接受的收敛区域。引入的无网格方法被证明在表征纳米尺度的软化和硬化结构行为方面非常有效。因此，所提出的数值方法为纳米结构力学铺平了道路。所提出的无网格数值方法被证实在高精度确定扭转旋转场时具有快速的收敛速度和可接受的收敛区域。引入的无网格方法被证明在表征纳米尺度的软化和硬化结构行为方面非常有效。因此，所提出的数值方法为纳米结构力学铺平了道路。所提出的无网格数值方法被证实在高精度确定扭转旋转场时具有快速的收敛速度和可接受的收敛区域。引入的无网格方法被证明在表征纳米尺度的软化和硬化结构行为方面非常有效。因此，所提出的数值方法为纳米结构力学铺平了道路。