Nonintrusive parametric solutions in structural dynamics
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hdl:2117/365282
Tipus de documentArticle
Data publicació2022-02-01
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
ProjecteProTechTion - Industrial decision-making on complex production technologies supported by simulation-based engineering (EC-H2020-764636)
INGENIERIA COMPUTACIONAL BASADA EN SIMULACION DE APRENDIZAJE AUTOMATICO (AEI-PID2020-113463RB-C32)
INGENIERIA COMPUTACIONAL BASADA EN SIMULACION DE APRENDIZAJE AUTOMATICO (AEI-PID2020-113463RB-C32)
Abstract
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.
Descripció
© 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/
CitacióCavaliere, F. [et al.]. Nonintrusive parametric solutions in structural dynamics. "Computer methods in applied mechanics and engineering", 1 Febrer 2022, vol. 381, núm. article 114336.
ISSN0045-7825
Versió de l'editorhttps://www.sciencedirect.com/science/article/pii/S0045782521006204
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