Coupling of Homotopy Perturbation Method and Kriging surrogate model for an efficient fuzzy linear buckling analysis: Application to additively manufactured lattice structures

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. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper presents a new method that efficiently approximates linear buckling loads and mode shapes of finite element structures by coupling a ROM based on HPM with a Kriging model, achieving high precision and reduced computational time. The method is capable of handling uncertain propagation problems using fuzzy formalism, and is also applicable for predicting and optimizing structural characteristics in the field of Additive Manufacturing.