表面效应影响的弹性条带状薄膜非线性尺寸相关屈曲行为

Nonlinear Size-dependent Buckling of Strip-like Elastic Film with Surface Effect

本文在非线性Von Karman板理论基础上,通过引入表面弹性研究了弹性条带状薄膜在简单支撑条件下的非线性尺度相关屈曲行为。按照Mindlin假设,用Hamilton变分原理导出带有表面效应影响的一般控制方程及非经典边界条件,同时引入了非零的正应力和大变形的影响。得到了平面应变情况下简单支撑薄膜的屈曲行为和准确解,并详细阐明了归因于表面效应的薄膜尺寸相关屈曲行为。

The size-dependent buckling of simply supported strip-like elastic film is investigated by incorporating surface elasticity into the conventional nonlinear Von Karman plate theory. Following Hamilton principle, the governing equations and boundary conditions of ultra-thin film including surface effects are derived under Mindlin assumption, where the effects of non-zero normal stress and large deflection are taken into account simultaneously. And the buckling of the simply supported thin film in plane strain state and the exact solutions are obtained. Subsequently, the size-dependent buckling behavior of the thin elastic film due to surface effects is well illustrated.