薄壁圆筒壳初始几何缺陷不确定性量化的极大熵方法

针对薄壁圆筒壳结构轴压屈曲载荷的缺陷敏感性以及真实几何缺陷的不确定性,提出一种基于实测缺陷数据和极大熵原理的初始缺陷建模与屈曲载荷预测方法。首先,将初始几何缺陷视为二维随机场,并利用实测缺陷数据和Karhunen-Loève展开法将初始缺陷的随机场建模转化为随机向量的建模;其次,利用极大熵方法确定随机向量的概率分布;最后,基于所构建的初始缺陷随机模型,利用MCMC抽样方法和确定性屈曲分析方法,进行随机屈曲分析并给出基于可靠度的屈曲载荷折减因子。数值算例表明,与直接假设随机场相关结构的方法相比,本文方法的结果是对薄壁圆筒壳屈曲载荷的一个更无偏估计。

A maximum entropy approach for uncertainty quantification of initial geometric imperfections of thin-walled cylindrical shell

To address the imperfection sensitivity of the axial compression buckling load of a thin-walled cylindrical shell structure and the uncertainty of real geometric imperfections,an initial imperfection modeling and buckling load prediction method based on measured imperfection data and the principle of maximum entropy are proposed.Firstly,the initial geometric imperfections are considered as a two-dimensional random field,and the random field modeling of the initial imperfections is transformed into the modeling of a random vector using the measured imperfection data and the Karhunen-Loève expansion method.Secondly,the probability distribution of this random vector is determined using the maximum entropy method.Finally,based on the constructed random model,and combined with MCMC sampling method and a deterministic buckling analysis method,the stochastic buckling analysis is carried out.Furthermore,the reliability-based buckling load knockdown factor is given.Numerical examples show that the results of this method provide a better coverage of the experimental results and are a more unbiased estimate of the buckling load for thin-walled cylindrical shells compared with the method that directly assumes a random field-related structure.