Nonintrusive Stochastic Finite Elements for Crashworthiness with VPS/Pamcrash
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ORIGINAL PAPER
Nonintrusive Stochastic Finite Elements for Crashworthiness with VPS/ Pamcrash M. Rocas1,2 · A. García‑González1,3 · X. Larráyoz2 · P. Díez1,3 Received: 22 November 2019 / Accepted: 27 December 2019 © CIMNE, Barcelona, Spain 2020
Abstract Crashworthiness analysis remains an important concern for the design of safety structures. In this context, uncertainties play an essential role in the response of a crash problem with non linear behavior. With this statement at hand, in this work it is presented a review of uncertainty quantification (UQ) techniques, with intrusive and non-intrusive approaches in stochastic finite element methods for crashworthiness. The well-known deterministic finite element solver VPS/Pamcrash is used to illustrate the currently available methods, developing a comparative analysis of these techniques in crashworthiness UQ. Finally, relevant non-intrusive methods are applied to analyze the behavior of a specific quantity of interest in a dynamic crash model.
1 Introduction Models in Computational Mechanics provide the response of physical systems by solving mathematical problems, depending on specific input parameters. Input data is often subject to uncertainty or lack of knowledge. Thus, uncertainty quantification (UQ) via stochastic analysis is of great importance to assess the credibility of the output [57]. Developments in stochastic analysis are implemented in several physical applications [9, 10, 25, 34, 49, 50, 53]. Specifically, in crash analysis the structured behavior after impact is analyzed to quantify stress, strain and displacements. In automotive industry, the stochastic response is a robust and powerful tool, to quantify the variation of the outputs of the simulations and therefore allows reducing the number of experimental tests. This paper focuses on summarizing a review of intrusive and non-intrusive methods for stochastic crash analysis. The most relevant methods are applied through the solver
* A. García‑González [email protected] 1
Laboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, Barcelona, Spain
2
SEAT, Martorell, Barcelona, Spain
3
International Centre for Numerical Methods in Engineering, CIMNE, Barcelona, Spain
VPS(Pamcrash), an explicit finite element code for transient dynamics, popular in the automotive industry. Usually, in industry, UQ is developed through classical Monte Carlo [30]. However, this method is computationally unaffordable for simulating a whole vehicle. Nevertheless, alternative approaches are available to reduce computational costs. Here we review those methods considered suitable for crashworthiness UQ, divided in two main groups: (i) Intrusive approaches, where the source code of the used solver VPS requires to implement modifications of the FE formulation, such that Perturbation method based on Taylor series [2, 35], Galerkin Polynomial Chaos (PC) based on orthogonal polynomials [11], Spectral stochastic finite element method based on Karhunen–Loeve expansion
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