Nonintrusive parametric solutions in structural dynamics

© 2022 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A nonintrusive reduced order method able to solve a parametric modal analysis is proposed in this work. The main objective is being able to efficiently identify how a variation of user-defined parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corresponding mode shapes. A parametric version of the inverse power method (IPM) is presented by using the proper generalised decomposition (PGD) rationale. The proposed approach utilises the socalled encapsulated PGD toolbox and includes a new algorithm for computing the square root of a parametric object. With only one offline computation, the proposed PGD-IPM approach provides an analytical parametric expression of the smallest (in magnitude) eigenvalue (or natural frequency) and corresponding eigenvector (mode shape), which contains all the possible solutions for every combination of the parameters within pre-defined ranges. A Lagrange multiplier deflation technique is introduced in order to compute subsequent eigenpairs, which is also valid to overcome the stiffness matrix singularity in the case of a free-free structure. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial finite element (FE) packages. Two numerical examples are shown to underline the properties of the technique. The first example includes one material and one geometric parameter. The second example shows a more realistic industrial example, where the nonintrusivity of the approach is demonstrated by employing a commercial FE package for assembling the FE matrices. Finally, a multi-objective optimisation study is performed proving that the developed method could significantly assist the decision-making during the preliminary phase of a new design process.This project is part of the Marie Skłodowska-Curie ITN-EJD ProTechTion funded by the European Union Horizon 2020 research and innovation program with Grant Number 764636. The work of Fabiola Cavaliere, Sergio Zlotnik and Pedro Díez is partially supported by the MCIN/AEI/10.13039/501100011033, Spain (Grant Number: PID2020-113463RB-C32, PID2020-113463RB-C33 and CEX2018-000797-S). Ruben Sevilla also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant Number: EP/P033997/1).Peer ReviewedPostprint (author's final draft

Nonintrusive parametric NVH study of a vehicle body structure

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Mechanics based design of structures and machines on 27/06/22, available online at: http://www.tandfonline.com/10.1080/15397734.2022.2098140A reduced order model technique is presented to perform the parametric Noise, Vibration and Harshness (NVH) study of a vehicle body-in-white (BIW) structure characterized by material and shape design variables. The ultimate goal is to develop a methodology which allows to efficiently explore the variation in the design space of the BIW static and dynamic global stiffnesses, such that the NVH performance can be evaluated already in the preliminary phase of the development process. The proposed technique is based on the proper generalized decomposition (PGD) method. The obtained PGD solution presents an explicit dependency on the introduced design variables, which allows to obtain solutions in 0.1 milliseconds and therefore opens the door to fast optimization studies and real-time visualizations of the results in a pre-defined range of parameters. The method is nonintrusive, such that an interaction with commercial software is possible. A parametrized finite element (FE) model of the BIW is built by means of the ANSA CAE preprocessor software, which allows to account for material and geometric parameters. A comparison between the parametric NVH solutions and the full-order FE simulations is performed using the MSC-Nastran software, to validate the accuracy of the proposed method. In addition, an optimization study is presented to find the optimal materials and shape properties with respect to the NVH performance. Finally, in order to support the designers in the decision-making process, a graphical interface app is developed which allows to visualize in real-time how changes in the design variables affect pre-defined quantities of interest.This project is part of the Marie Skłodowska-Curie ITN-EJD ProTechTion funded by the European Union Horizon 2020 research and innovation program with Grant Number 764636. The work of Fabiola Cavaliere, Sergio Zlotnik and Pedro D ıez is partially supported by the MCIN/AEI/10.13039/501100011033, Spain (Grant Number: PID2020-113463RB-C32, PID2020-113463RB-C33 and CEX2018-000797-S). Ruben Sevilla also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant Number: EP/T009071/1).Peer ReviewedPostprint (published version