阶跃载荷下功能梯度材料圆柱壳的非线性动力稳定性

本文研究了阶跃轴压和阶跃侧压下功能梯度材料圆柱壳的非线性动力屈曲问题。非线性动力平衡方程由能量法推导，并采用变步长四阶Rugge-Kutta法进行求解，得到结构的响应曲线，结合B-R动力屈曲准则给出屈曲临界状态。数值结果表明：在阶跃载荷作用下，存在一结构变形的占优模态使得结构响应最早发生，且其幅值也最大。阶跃轴压和侧压载荷下结构的非线性动力屈曲载荷与其相应的线性静力屈曲载荷十分接近。在阶跃轴压载荷情况下，动力载荷可能激发比静力载荷更高阶的屈曲模态。此外，文中还讨论材料组分与多种热环境对动力屈曲的影响。

Nonlinear dynamic buckling of functionally graded cylindrical shells under step loads

Nonlinear dynamic buckling of functionally graded cylindrical shells under axial and lateral step loads was investigated in this paper. An energy method was resorted to obtain the nonlinear dynamic equilibrium equation which was then solved using the four-order Rugge-Kutta method of various step lengths. Thus the respond curves were then derived and they were combined with B-R dynamic buckling criterion used to give the buckling critical condition. Numerical results show that a dominating mode of structural deformation would arouse the earliest structural response with the largest amplitude. In both the axial and lateral step load cases, the nonlinear dynamic buckling loads are nearly close to their corresponding linear static buckling loads. Under the axial step load case, dynamic load tends to inspire a higher order buckling mode. Besides, the effects of material constituents and various thermal environments on dynamic buckling were also discussed.