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

• Published in: Applied Mathematical Modelling Vol. 97; pp. 602 - 618
• Main Authors: Doan, V.T., Massa, F., Tison, T., Naceur, H.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.09.2021; Elsevier BV; Elsevier
• Subjects: Additive manufacturing; Approximation; Buckling; Computing time; Coupling; Eigenvalues; Eigenvectors; Engineering Sciences; Fuzzy sets; Lattice structure; Mechanics; Optimization; Perturbation methods; Reduced order model; Reduced order models; Surrogate model; Uncertainty; Fuzzy sets; Uncertainty; Surrogate model; Reduced order model; Buckling; Lattice structure
• ISSN: 0307-904X; 1088-8691; 0307-904X; 1872-8480
• DOI: 10.1016/j.apm.2021.04.005

•Comparison of experimental and numerical buckling variability of a set of additively manufactured lattice structures.•Reduction of computational time for prediction, sensitivity and optimization steps of an uncertain propagation problem.•Efficient coupling between a Reduced Order Model and a surrogate model.•Improvement of the calculation precision with projection basis composed of high order perturbed modes. 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.