基于弧长法的南瓜型超压气球非线性后屈曲分析

Nonlinear Post-buckling Analysis of Pumpkin-shaped Super Pressure Balloon Based on Arc Length Method

稳定性研究是南瓜型超压气球设计面临的重要课题。针对南瓜球非线性屈曲过程,对含初始缺陷南瓜球的稳定性进行研究。首先,对南瓜球进行特征值屈曲分析,得到前8阶屈曲模态及线性屈曲临界载荷。然后,基于特征值分析的模态构型给出初始缺陷分布,进一步利用非线性有限元中的弧长法分别计算临界缺陷模态和组合缺陷模态下对应的屈曲临界载荷。结果表明,南瓜球对初始缺陷较敏感,缺陷的幅值和分布形式对承压能力和失稳形态均有影响,承压能力随缺陷幅值增大而降低,说明提高南瓜球稳定性需要提高气球的加工精度。同时,对已失稳南瓜球的应力分布进行分析,发现失稳状态下南瓜球高应力区的应力水平远高于相同载荷下未失稳南瓜球的应力水平。可见,失稳现象极大降低了气球的承压能力。

Stability study is an important subject in the design of the pumpkin-shaped super pressure balloon. Aiming at the nonlinear buckling process of pumpkin balloon, the stability of pumpkin balloon with initial imperfection was studied. Firstly, the eigenvalue buckling analysis of the pumpkin balloon is performed, and the first 8 buckling modes and the linear buckling critical load are obtained. Then, the initial imperfection distribution was given based on the modal configuration of eigenvalue analysis, and the buckling critical loads corresponding to critical imperfection mode and combined imperfection mode were calculated respectively by using the arc length method in nonlinear finite element method. The results show that the pumpkin balloon is sensitive to the initial imperfection, and the amplitude and distribution of imperfection have an effect on the bearing capacity and instability form. The bearing capacity decreased with the increase of imperfection amplitude, indicating that the processing accuracy of the balloon need to improve the stability of the pumpkin balloon. In the meantime, the stress distribution of the unstable pumpkin balloon was analyzed, and it is found that the stress level in the high stress area of the unstable pumpkin balloon is much higher than that of the non-unstable pumpkin balloon under the same load. It is concluded that the instability phenomenon greatly reduced the bearing capacity of the balloon.