考虑高阶表面效应的非局部纳米板屈曲分析

Buckling Analysis of Nanoplates with High-order Surface Stress Effect Via Nonlocal Elasticity

基于Kirchhoff板理论,非局部弹性理论,得到了矩形纳米板双轴屈曲的一般控制方程。用Navier方法解得了四边简支的矩形板的屈曲载荷的解析解。讨论了非局部效应和高阶表面效应对纳米板屈曲载荷的影响。非局部效应会减小纳米板的屈曲载荷,而表面效应会增大纳米板的屈曲载荷,且高阶表面效应对纳米板的屈曲载荷的影响显著大于常规表面效应。非局部效应和高阶表面效应对纳米板屈曲载荷的影响还与板的几何尺寸有关。

The general governing equation for biaxial buckling of rectangular nanoplate is formulated on the basis of the Kirchhoff plate theory and the nonlocal elastic theory. The closed form solution for buckling load of the rectangular nanoplate with simply supported boundary conditions is obtained by employing Navier ’s approach. The nonlocal effect and the influence of high-order surface stress on buckling load of the nanoplate are discussed. The nonlocal effect can lower down the value of buckling load,whereas the surface stress effect can raise its value. The effect of the high-order surface stress on buckling load is much more significant than that of the conventional surface stress. The nonlocal effect and the influence of high-order surface stress on buckling load are dependent upon the geometrical dimensions of the nanoplate.