Generic Substitute Imperfection Patterns for the GMNIA of Tanks and Silos made of Steel or Aluminium

In EN 1993-1-6, several methods are offered for the stability design of shell structures. Most elaborate results are found by a GMNIA (“full analysis”, EN 1993-1-6:2017 8.8) where geometric substitute imperfections and material non-linearities are accounted for in the numerical model. Typically, radial shape deviations are used, which represent a governing eigenmode, see EN 1993-1-6 8.8.2 (13) and (15). Rules for the maximum amplitude of the imperfection pattern are given in Tab. 8.5. In practical design however, it is more convenient to use imperfection patterns, the shape of which is known a priori. E.g. Rotter/Teng (1989) presented an analytical description for an idealized circumferential weld depression, which has been proven to be sufficient for a realistic description of the resistance under axial compression. For other load cases and other manufacturing methods, such as joining the plates by bolted overlaps, these a priori imperfections have not been described so far. In the present paper, a set of generic imperfection patterns for different load cases and different methods of manufacture is described by means of truncated double Fourier series. The patterns are investigated by exemplary GMNIA, so that the imperfection sensitivity of the different patterns can be demonstrated. Using this generic imperfection patterns, the structural engineer is able to script a universal imperfection generator. For each individual project, the Fourier coefficients of the relevant generic imperfection pattern are introduced. Thus, the aim of the paper is to simplify the handling of imperfection patterns with GMNIA.在EN 1993-1-6标准中，针对壳体结构的稳定性设计提供了多种方法。其中最精细的分析结果可通过GMNIA（即全分析，详见EN 1993-1-6:2017第8.8条）获得，该方法在数值模型中考虑了几何替代缺陷与材料非线性效应。通常采用代表主导特征振型的径向形状偏差，具体参见EN 1993-1-6第8.8.2条的(13)与(15)款，缺陷模式的最大幅值规则详见表8.5。但在实际工程设计中，采用形状已知的先验缺陷模式会更为便捷。例如，Rotter与Teng（1989年）针对理想化周向焊缝凹陷提出了解析描述方法，经证实该方法可准确描述轴向受压工况下的结构抗力。但针对其他荷载工况及其他制造工艺（如采用螺栓搭接连接钢板），此类先验缺陷模式至今仍未被系统描述。本文通过截断双傅里叶级数，提出了一套适用于不同荷载工况及不同制造工艺的通用缺陷模式。通过典型GMNIA分析对上述缺陷模式进行研究，可验证不同模式的缺陷敏感性。借助这套通用缺陷模式，结构工程师可编写通用缺陷生成程序，针对每个具体工程项目，仅需代入对应通用缺陷模式的傅里叶系数即可适配使用。因此，本文的研究目标为简化采用GMNIA进行结构稳定性设计时，缺陷模式的处理流程。