Nonintrusive reduced order model for parametric solutions of inertia relief problems

This is the peer reviewed version of the following article: Cavaliere, F. [et al.]. Nonintrusive reduced order model for parametric solutions of inertia relief problems. "International journal for numerical methods in engineering", 30 Agost 2021, vol. 122, núm. 16, p. 4270-4291., which has been published in final form at DOI:10.1002/nme.6702. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a computational framework for the solution of unconstrained parametric structural problems with IR and the Proper Generalized Decomposition (PGD) method. First, the IR method is formulated in a parametric setting for both material and geometric parameters. A reduced order model using the encapsulated PGD suite is then developed to solve the parametric IR problem, circumventing the so-called curse of dimensionality. With just one offline computation, the proposed PGD-IR scheme provides a computational vademecum that contains all the possible solutions for a predefined range of the parameters. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial finite element (FE) packages. The applicability and potential of the developed technique is shown using a three-dimensional test case and a more complex industrial test case. The first example is used to highlight the numerical properties of the scheme, whereas the second example demonstrates the potential in a more complex setting and it shows the possibility to integrate the proposed framework within a commercial FE package. In addition, the last example shows the possibility to use the generalized solution in a multi-objective optimization setting. This project is part of the Marie Sk lodowska-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 Spanish Ministry of Economy and Competitiveness, Spain (Grant number: DPI2017-85139- C2-2-R) and by the Generalitat de Catalunya, Spain (Grant number: 2017-SGR-1278). Ruben Sevilla also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant number: EP/P033997/1).