This paper analyzes the mechanical behavior of a Kirchhoff thin nanoplate with surface stresses containing a thickness-through rigid line inclusion. Based on the bulk and surface elasticity, a rigid line inclusion problem of a prescribed displacement is reduced to an associated mixed boundary value problem. By using the Fourier transform, the problem is converted to dual integral equations, then to a weakly singular integral equation with the logarithmic kernel. An exact solution for a rigid line inclusion with an off-nanoplate rigid rotation is obtained and full elastic fields including the deflection, bending moments, and effective shear forces at any position of the nanoplate are determined explicitly in terms of the elementary functions. The singularity coefficients of the bending moments and effective shear forces near the tip of the rigid line inclusion are evaluated. The obtained results show that the bending moments and the stress components exhibit an $r^{-3/2}$ singularity near the rigid line inclusion tip, where $r$ is the distance from the rigid line inclusion tip. The effective shear forces have an $r^{-5/2}$ singularity. The influence of surface elasticity on the singularity coefficients is examined.

本文分析了具有表面应力的基尔霍夫薄纳米板的力学行为，该表面应力包含通过厚度计入的刚性线夹杂物。基于体积和表面弹性，将规定位移的刚性线夹杂问题减少为相关的混合边界值问题。通过使用傅立叶变换，将问题转换为对偶积分方程，然后将其转换为具有对数核的弱奇异积分方程。获得了具有非纳米板刚性旋转的刚性线夹杂物的精确解，并根据基本函数明确确定了包括纳米板的任何位置处的挠曲，弯曲力矩和有效剪切力在内的全弹性场。评估了弯矩的奇异性系数和刚性线夹杂物尖端附近的有效剪切力。所得结果表明，弯矩和应力分量呈现出${\mathrm{[R}}^{-3/\mathrm{2个}}$ 刚性线夹杂点附近的奇点，其中 $\mathrm{[R}$是到刚性线夹杂物尖端的距离。有效剪切力有一个${\mathrm{[R}}^{-5/\mathrm{2个}}$奇点。研究了表面弹性对奇异系数的影响。