Nonintrusive Stochastic Finite Elements for Crashworthiness with VPS/Pamcrash

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]  Eric Florentin,et al.  Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems , 2012 .

[2]  Ibrahim Rawabdeh,et al.  An Application of Finite Element Method and Design of Experiments in the Optimization of Sheet Metal Blanking Process , 2008 .

[3]  Mehmet Tolga Taner,et al.  Taguchi's experimental design method on improvement of medical image quality. , 2007, Leadership in health services.

[4]  H. Najm,et al.  A stochastic projection method for fluid flow II.: random process , 2002 .

[5]  O. Knio,et al.  Quantifying uncertainties in fault slip distribution during the Tōhoku tsunami using polynomial chaos , 2016, Ocean Dynamics.

[6]  D. Xiu.  Fast numerical methods for stochastic computations: A review , 2009 .

[7]  Lee Margetts,et al.  Practical Application of the Stochastic Finite Element Method , 2016 .

[8]  Danny Lathouwers,et al.  Uncertainty quantification for criticality problems using non-intrusive and adaptive Polynomial Chaos techniques , 2013 .

[9]  M. Eldred,et al.  Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos. , 2008 .

[10]  Wing Kam Liu,et al.  Probabilistic finite elements for nonlinear structural dynamics , 1986 .

[11]  Xiangting Su,et al.  Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials , 2009 .

[12]  George Stefanou,et al.  Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields , 2007 .

[13]  Hermann G. Matthies,et al.  Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations , 2005 .

[14]  Tien-Tsin Wong,et al.  Sampling with Hammersley and Halton Points , 1997, J. Graphics, GPU, & Game Tools.

[15]  K. Phoon,et al.  Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion , 2005 .

[16]  J. Hammersley.  MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS , 1960 .

[17]  Roger Ghanem,et al.  Stochastic model reduction for chaos representations , 2007 .

[18]  Roger Ghanem,et al.  Numerical solution of spectral stochastic finite element systems , 1996 .

[19]  Bruno Sudret,et al.  Computing derivative-based global sensitivity measures using polynomial chaos expansions , 2014, Reliab. Eng. Syst. Saf..

[20]  Thomas A. Zang,et al.  Stochastic approaches to uncertainty quantification in CFD simulations , 2005, Numerical Algorithms.

[21]  M. Lemaire,et al.  Stochastic finite element: a non intrusive approach by regression , 2006 .

[22]  H. Niederreiter.  Quasi-Monte Carlo methods and pseudo-random numbers , 1978 .

[23]  Andrea Barth,et al.  Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients , 2011, Numerische Mathematik.

[24]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[25]  Yongbo Peng,et al.  Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes , 2017 .

[26]  Anthony C. Atkinson,et al.  Optimum Experimental Designs, with SAS , 2007 .

[27]  D. Xiu.  Numerical Methods for Stochastic Computations: A Spectral Method Approach , 2010 .

[28]  A. Nouy.  Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations , 2009 .

[29]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[30]  R. Askey,et al.  Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials , 1985 .

[31]  Hans Petter Langtangen,et al.  Chaospy: An open source tool for designing methods of uncertainty quantification , 2015, J. Comput. Sci..

[32]  G. Schuëller.  A state-of-the-art report on computational stochastic mechanics , 1997 .

[33]  R. Rifkin,et al.  Notes on Regularized Least Squares , 2007 .

[34]  Francisco Herrera,et al.  A geometrical robust design using the Taguchi method: application to a fatigue analysis of a right angle bracket , 2018 .

[35]  M. Eldred.  Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design , 2009 .

[36]  M. Shinozuka,et al.  Simulation of Stochastic Processes by Spectral Representation , 1991 .

[37]  K. Sepahvand,et al.  Spectral stochastic finite element vibration analysis of fiber-reinforced composites with random fiber orientation , 2016 .

[38]  G. Stefanou.  The stochastic finite element method: Past, present and future , 2009 .

[39]  A. Doostan,et al.  Least squares polynomial chaos expansion: A review of sampling strategies , 2017, 1706.07564.

[40]  Ranjit K. Roy,et al.  Design of Experiments Using The Taguchi Approach: 16 Steps to Product and Process Improvement , 2001 .

[41]  Elisabeth Ullmann,et al.  Computational aspects of the stochastic finite element method , 2007 .

[42]  Bruno Sudret,et al.  Polynomial chaos expansions and stochastic finite element methods , 2015 .

[43]  Mircea Grigoriu,et al.  Evaluation of Karhunen–Loève, Spectral, and Sampling Representations for Stochastic Processes , 2006 .

[44]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[45]  S. Kamaruddin,et al.  Practical Applications of Taguchi Method for Optimization of Processing Parameters for Plastic Injection Moulding: A Retrospective Review , 2013 .

[46]  Cristian Caizar,et al.  Application of Taguchi method to selection of optimal lubrication and cutting conditions in face milling of AlMg3 , 2011 .

[47]  B. Mondal,et al.  TAGUCHI METHOD AND ANOVA: AN APPROACH FOR PROCESS PARAMETERS OPTIMIZATION OF HARD MACHINING WHILE MACHINING HARDENED STEEL , 2009 .

[48]  Ivan G. Graham,et al.  Modern Monte Carlo Variants for Uncertainty Quantification in Neutron Transport , 2017, 1702.03561.

[49]  Michael B. Giles,et al.  Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..

[50]  Samuel P. Marin,et al.  A computational design-of-experiments study of hemming processes for automotive aluminium alloys , 2005 .

[51]  John E. Mottershead,et al.  A review of robust optimal design and its application in dynamics , 2005 .

[52]  Michał Kleiber,et al.  The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation , 1993 .

[53]  Louis J. M. Aslett,et al.  Multilevel Monte Carlo for Reliability Theory , 2016, Reliab. Eng. Syst. Saf..

[54]  Tom Dhaene,et al.  Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits , 2018 .

[55]  Saurav Datta,et al.  Grey-based taguchi method for optimization of bead geometry in submerged arc bead-on-plate welding , 2008 .

[56]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[57]  Wing Kam Liu,et al.  Random field finite elements , 1986 .

[58]  Kwok-Leung Tsui,et al.  AN OVERVIEW OF TAGUCHI METHOD AND NEWLY DEVELOPED STATISTICAL METHODS FOR ROBUST DESIGN , 1992 .