Buckling Analyses of Spherical Shells by the Finite Element Method Based on the Willis-Form Equations
Buckling Analyses of Spherical Shells by the Finite Element Method Based on the Willis-Form Equations
复制标题
基于威利斯型方程的有限元法球壳屈曲分析
DOI：
10.1142/s1758825119500911
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发表时间：
2019-12
影响因子：
3.5
通讯作者：
Zhihai Xiang
中科院分区：
文献类型：
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作者：
Yixiao Sun;Zhihai Xiang
球壳在外压作用下的屈曲分析是机械工程和航空航天工程中的一个重要问题。众所周知，用经典方法得到的屈曲载荷远高于实验结果。造成这种差异的主要原因通常是由于初始几何缺陷，而加载过程中的应力不均匀分布的影响通常被忽略。为了研究这个被忽略的因素的影响，几个球壳的屈曲载荷进行了分析的几何非线性有限元法（FEM）的基础上的威利斯形式的方程，其中显式包含在前一个加载步骤的应力梯度。结果表明，Willis形式有限元的屈曲载荷比经典有限元的屈曲载荷低10%左右。这一发现可以更好地理解近似完美球壳的理论和实验结果之间的差异，并可能有助于获得更准确的屈曲载荷的初始几何缺陷的壳。
Buckling analysis of spherical shells under external pressure is a crucial problem in mechanical and aerospace engineering. It is widely known that the buckling loads obtained by classical methods are much higher than experimental results. The main reason for this large discrepancy is customarily attributed to initial geometrical imperfections, and the impact of inhomogeneously distributed stresses during loading process is usually ignored. In order to investigate the effect of this ignored factor, the buckling loads of several spherical shells are analyzed by the geometrically nonlinear finite element method (FEM) based on the Willis-form equations, which explicitly contain the stress gradients at previous loading step. It can be shown that the buckling loads from the Willis-form FEM are about 10% lower than the values from classical FEM. This finding may give better understandings to the differences between theoretical and experimental results for nearly perfect spherical shells and may be helpful to obtain more accurate buckling loads for shells with initial geometrical imperfections.