This paper presents a new method to efficiently approximate both linear buckling loads and associated mode shapes of finite element structures subject to perturbations. To achieve this, a coupling between a Reduced Order Model (ROM) based on the Homotopy Perturbation Method (HPM) and a Kriging model is presented here. The ROM maintains the link between eigenvalues, related eigenvectors and the dependencies between each eigenvector components, leading to a high precision level. The computational time is greatly reduced by the surrogate model which avoids the computation of modified finite element matrices for each prediction. Next, the capabilities of the method allow to efficiently handle the prediction, sensitivity and optimization steps of an uncertain propagation problem using fuzzy formalism. Additive Manufacturing is a powerful and impressive process but many factors can be responsible for relatively large discrepancies in the mechanical and geometrical characteristics of the manufactured structure. Lastly, a study shows how the proposed fuzzy strategy allows the prediction of the buckling variability of a set of lattice structures.

本文提出了一种新方法，可以有效地逼近线性屈曲载荷和受扰动的有限元结构的相关模式形状。为实现此目的，此处介绍了基于同伦摄动法（HPM）的降阶模型（ROM）与Kriging模型之间的耦合。ROM维护特征值，相关特征向量以及每个特征向量分量之间的依存关系之间的链接，从而实现了较高的精确度。代理模型极大地减少了计算时间，该代理模型避免了为每个预测计算修正的有限元矩阵。接下来，该方法的功能允许使用模糊形式主义有效地处理不确定传播问题的预测，敏感性和优化步骤。增材制造是一个功能强大且令人印象深刻的过程，但是许多因素可能是造成所制造结构的机械和几何特性差异较大的原因。最后，一项研究表明所提出的模糊策略如何允许预测一组晶格结构的屈曲变异性。