纳米力学中的表面效应及相关问题(英文)

对载荷作用在边界和无穷远处的含有纳米圆孔弹性平面薄板问题进行了分析,给出了其边界值问题的解.假设全表面应力作用于孔的边界上,基于古沙-科洛索夫复势和Muskhelishvili’s技术,问题可简化为一个未知表面应力的超奇异积分方程的解.结果表明:由于表面应力存在,边界上的应力集中取决于材料表面和体内的弹性性质,也与孔的半径相关.

Surface Effects and Problems of Nanomechanics

A boundary value problem on a circular nanometer hole in an elastic plane loaded at the boundary and infinity is solved.It is assumed that complementary surface stresses are acting at the boundary of the hole.Based on Goursat-Kolosov’s complex potentials and Muskhelishvili’s technique,the solution of the problem is reduced to a hypersingular integral equation in an unknown surface stress.The solution of the problem shows that,due to an existence of the surface stresses,the stress concentration at the boundary depends on the elastic properties of a surface and bulk material,and also on the radius of the hole.