摘要对曲边柱壳受轴向非均匀内压作用下的大转动几何非线性3-D动力学行为进行了研究.基于Nayfeh and Pai[1]非线性壳体理论,给出了考虑几何非线性的3-D混合型（含内力与位移）动力学模型.为了克服该强非线性模型难以求解的问题,依据分析获得的结构静动态变形关系,采用Lagrange方程推导建立了基于结构静态解的曲边柱壳多自由度3-D动力学方程,并对其进行了线性化与降阶处理,结合差分法获得了一套高效的求解算法.与LS-DYNA有限元结果的吻合,验证了本文方法的正确性.最后分析了单元数和计算时间步分别对有限元模型和本文方法的影响,发现求解精度随着计算时间步的减小不断提高直至趋于稳定.同时对采用本文方法获得的曲边柱壳动态变形模式的分析表明:结构动态响应与其所受内压载荷沿轴向的分布形式关系紧密,可以通过改变或者设计内压轴向分布形式来影响以及控制结构的动态变形模式,从而应用于曲边柱壳结构设计及优化的工程实际中.
Abstract：Considering geometric nonlinearity, the 3-D dynamic behavior of curved boundary cylindrical shell with large rotation under non-uniform internal pressure along its axial direction is studied. Based on Nayfeh and Pai’s[1] theoretical system of shell, the mixed nonlinear 3-D dynamics model with internal force and displacement variables is first derived. Then with the basic assumption about its static and dynamic deformation modes, the 3-D Multi-degree of Freedom governing equations based on the obtained static solution are established using Lagrange’s equation, and an efficient numerical method combined with difference method is developed after linearization and order reduction to the equations, which avoids the difficulty of solving the mixed model due to its strong nonlinearity. The present method is verified to be valid by comparing with results obtained from LS-DYNA. The influences of element number on the FEM and time step on our method are also investigated and find that precision is improved with the decrease of the computing time step and tends to be stable finally. Meanwhile, the 3-D dynamic deformation modes under a linear distribution load were obtained, which are closely related with the load distribution. So one can change or design the load distribution to realize different dynamic deformation modes, which is useful for structural design and optimization of the curved boundary cylindrical shell structure in engineering application.
2014, Vol. 35 
