大转动曲边柱壳非线性3-D动力学建模及分析

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,给出了一套高效三维动力学建模与数值求解方法.基于结构静动态变形关系,采用Lagrange方程推导建立了曲边柱壳多自由度三维动力学方程,通过线性化和降阶处理获得了曲边柱壳3-D动态膨胀数值解,与LS-DYNA有限元方法求解结果一致.计算结果表明:曲边柱壳动态响应行为与内压载荷轴向分布形式关系紧密,可以通过改变内压轴向分布形式来控制结构的动态变形模式;同时发现时间步是影响论文方法计算精度的重要因素.论文研究为后续含曲边柱壳复杂系统动力学响应研究提供了参考.

NONLINEAR 3-D DYNAMICS MODELING AND ANALYSIS OF CURVED BOUNDARY CYLINDRICAL SHELL WITH LARGE ROTATION

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.