弹性介质中受轴向冲击载荷作用的圆柱壳的屈曲临界载荷计算分析  

Buckling Critical Load Calculation and Analysis of Axially Impacted Cylindrical Shells Embedded in Elastic Media

作　　者：桂夷斐 马建敏 GUI Yifei;MA Jianmin(Department of Aeronautics and Astronautics,Fudan University,Shanghai 200433,P.R.China)

机构地区：[1]复旦大学航空航天系,上海200433

出　　处：《应用数学和力学》2020年第4期353-366,共14页Applied Mathematics and Mechanics

摘　　要：建立并求解了弹性介质中圆柱壳的径向位移控制方程,考虑边界条件及相容条件,得到了应力波传播及反射过程中圆柱壳的动力屈曲分叉条件.通过计算得到了不同时间段屈曲临界载荷与应力波波阵面到达圆柱壳的位置、弹性介质的刚度、壳体未嵌入弹性介质部分的长度与总长之比的关系.数值计算结果表明,弹性介质中的圆柱壳发生轴对称屈曲和非轴对称屈曲趋势一致;嵌入弹性介质部分越深、弹性介质刚度越大圆柱壳越难屈曲;屈曲临界载荷随着弹性介质刚度的增大经历了增长缓慢、增长迅速以及增长较慢3个阶段;应力波反射前波阵面通过分界面后,屈曲仅发生在应力波传播区域,反射波波阵面通过分界面前,临界载荷较小时屈曲先发生在反射端部,随着轴向阶数增大,屈曲覆盖整个圆柱壳区域,反射波波阵面通过分界面后,壳体发生的屈曲始终覆盖整个圆柱壳区域.The radial governing equations for cylindrical shells embedded in elastic media were established and solved. The bifurcation conditions for dynamic buckling before and after stress wave reflection were obtained, in view of the boundary conditions and the consistency conditions. The relationships among the critical buckling load, the position of the wave front reaching the cylindrical shell, the elastic medium stiffness and the ratio of the non-embedded depth to the shell length were acquired through numerical calculation. The numerical results show that, there exists the same trend in axisymmetric and non-axisymmetric buckling modes of cylindrical shells embedded in elastic media. The larger the embedding depth and the elastic medium stiffness are, the harder the buckling will be. The critical buckling load experiences three stages of extremely slow growth, rapid growth and slow growth with stiffening of the elastic medium. Before stress wave reflection, buckling occurs only in the region of stress wave propagation. Before the reflected wave front goes through the interface, buckling occurs near the reflection end for a small critical load, and buckling covers the entire cylindrical shell as the axial mode order increases. After the reflected wave front goes through the interface, buckling always covers the entire cylindrical shell.

关 键 词：圆柱壳 弹性介质 轴向冲击 应力波 临界载荷 

分 类 号：O343.9[理学—固体力学]