考虑周长约束的圆柱薄壳初始几何缺陷随机场建模方法

Modeling initial geometrical imperfections of thin cylindrical shells by random field with perimeter constraints

利用随机场对圆柱薄壳结构的初始几何缺陷进行建模,并据此建立了一种用于含初始几何缺陷轴压圆柱薄壳屈曲分析的随机分析方法。首先,指出已有将圆柱薄壳初始几何缺陷表征为二维高斯随机场的方法会导致与实际不相符的初始几何缺陷,如圆柱周长显著增大或缩小的几何缺陷。其次,提出一种考虑周长不变约束的随机场建模方法,以剔除与实际不相符的随机几何缺陷。最后,基于所建立的初始几何缺陷随机场模型,利用非干涉多项式混沌展开法进行圆柱薄壳的随机屈曲分析,给出临界屈曲载荷的概率分布。数值试验结果表明,基于随机场理论的初始几何缺陷建模方法可有效刻画几何缺陷对结构承载能力的影响,而提出的约束随机场建模方法又能有效减小结果的分散性。

A novel random field approach is proposed to model the initial geometrical imperfections of thin cylindrical shell structures,based on which a stochastic analysis method for buckling analysis of thin cylindrical shells with initial geometrical imperfections is proposed.Firstly,it is pointed out that the existing method to characterize the initial geometrical imperfections of thin cylindrical shells as 2D Gaussian random field would lead to the initial geometrical imperfections inconsistent with the actual situation,for example,the cylinder circumference significantly increased or decreased geometrical imperfections.Secondly,a random field modeling method considering the perimeter invariant constraint is proposed to eliminate random geometrical imperfections which do not correspond to the reality.Finally,based on the initial imperfections random field model,a non-intrusive polynomial chaos expansion method is proposed for the stochastic buckling analysis of thin cylindrical shells,and the probability distribution results of critical buckling loads are given.Numerical results show that the initial geometrical imperfections modeling method based on random field theory can effectively describe the influence of the geometrical imperfections on the bearing capacity of structures,while the proposed constrained random field modeling method can reduce the dispersion of analysis results caused by random field model.