阶跃荷载下功能梯度材料圆柱壳的非线性动力稳定性

针对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,由能量原理推导非线性动力平衡方程,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:阶跃荷载下结构变形存在一占优模态,该模态相应的结构响应发生最早,且幅值最大;阶跃轴压和侧压荷载下结构的非线性动力屈曲荷载与其相应的线性静力屈曲荷载十分接近;在阶跃轴压荷载情况下,动力荷载将激发比静力荷载更高阶的屈曲模态;增加陶瓷组分含量将提高结构的动力屈曲荷载;线性温度分布与实际热传导温度场得到的临界荷载较为接近.

Nonlinear Dynamic Stability of Functionally Graded Cylindrical Shells Under Step Loads

This paper deals with the nonlinear dynamic buckling of functionally graded cylindrical shells under axial and lateral step loads. In the investigation, a nonlinear dynamic equilibrium equation is deduced using an energy method and is then solved by means of the four-order Rugge-Kutta method with various step lengths. Thus, the res-ponse curves of the shell structure are derived, which are combined with the B-R dynamic buckling criterion to determine the critical buckling condition. Numerical results show that (1) there is a dominating mode of structural deformation under step loads, which aroused the earliest structural response with maximum amplitude;(2) in the case of axial and lateral step loads, the nonlinear dynamic buckling loads are quite close to the corresponding linear static ones;(3) under axial step loads, the dynamic load would inspire a buckling mode with higher order;(4) the dynamic buckling load of the structure increases with the content of ceramic constituent;and (5) the critical load in the linearly-distributed temperature field is close to that in the actual thermal-conduction temperature field.