关于圆柱壳几何缺陷分析中傅立叶级数选取的探讨

圆柱壳屈曲一般对壳壁上微小几何缺陷的型式和幅值均十分敏感.为了能将缺陷的不同分量和圆柱壳的结构特征联系起来以及研究缺陷各分量对壳屈曲强度的影响,缺陷通常采用傅立叶级数分解.然而,大多数先前的研究选取不适当的傅立叶级数得到不正确的结果.本文首先考察傅立叶级数的数学描述基础,进而讨论不同傅立叶级数在描述不同型式几何缺陷的表现,从而得出如何选取适当的傅立叶级数用来描述圆柱壳几何缺陷的结论.采用这些适当的傅立叶级数,能更好地了解圆柱壳几何缺陷的特征分量以及这些分量对壳体屈曲强度的影响.

On selection of Fourier series in analysis of geometric imperfections in cylindrical shells

Buckling behavior of cylindrical shells is often highly sensitive to both the form and amplitude of minor geometric imperfections in the shell walls. In order to connect different components of the imperfections with structural features and their effect on shell buckling strength, the imperfections are generally decomposed using Fourier series. Most of previous studies suffer from choosing improper Fourier series, leading to some incorrect results. This paper first examined the mathematical basis of a Fourier series representation and then discussed the performance of various forms of the series in representing different forms of geometric imperfections, Conclusions were then drawn on selection of an appropriate Fourier series to represent the imperfections so that to obtain a better understanding of the characteristic components of the geometric imperfections in cylindrical shells and their effect on shell buckling strength.