Parametrized reduced order modeling for cracked solids

[1]  Eleni Chatzi,et al.  Multiple crack detection in 3D using a stable XFEM and global optimization , 2018, Computational Mechanics.

[2]  I. Babuska,et al.  The design and analysis of the Generalized Finite Element Method , 2000 .

[3]  P Kerfriden,et al.  Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. , 2011, Computer methods in applied mechanics and engineering.

[4]  C. Farhat,et al.  Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity , 2008 .

[5]  Eric Blades,et al.  A fast mesh deformation method using explicit interpolation , 2012, J. Comput. Phys..

[6]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[7]  Gregory P. Phlipot,et al.  Locally enhanced reduced order modeling for the nonlinear geometric response of structures with defects , 2018 .

[8]  Anthony Gravouil,et al.  A global model reduction approach for 3D fatigue crack growth with confined plasticity , 2011 .

[9]  D. Ryckelynck,et al.  A priori hyperreduction method: an adaptive approach , 2005 .

[10]  P. Knupp.  Algebraic mesh quality metrics for unstructured initial meshes , 2003 .

[11]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[12]  C. Farhat,et al.  Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency , 2014 .

[13]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[14]  Raimondo Betti,et al.  A multiscale flaw detection algorithm based on XFEM , 2014 .

[15]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model , 2002 .

[16]  Danny C. Sorensen,et al.  Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..

[17]  W SederbergThomas,et al.  Free-form deformation of solid geometric models , 1986 .

[18]  T. Belytschko,et al.  New crack‐tip elements for XFEM and applications to cohesive cracks , 2003 .

[19]  Raimondo Betti,et al.  Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm , 2013 .

[20]  H. Bijl,et al.  Mesh deformation based on radial basis function interpolation , 2007 .

[21]  C. Farhat,et al.  Torsional springs for two-dimensional dynamic unstructured fluid meshes , 1998 .

[22]  Nirmal J. Nair,et al.  Transported snapshot model order reduction approach for parametric, steady‐state fluid flows containing parameter‐dependent shocks , 2018, International Journal for Numerical Methods in Engineering.

[23]  A. Guezlec,et al.  "Meshsweeper": dynamic point-to-polygonal mesh distance and applications , 2001 .

[24]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[25]  Simona Perotto,et al.  A POD‐selective inverse distance weighting method for fast parametrized shape morphing , 2017, International Journal for Numerical Methods in Engineering.

[26]  N. Moës,et al.  Improved implementation and robustness study of the X‐FEM for stress analysis around cracks , 2005 .

[27]  H. Waisman,et al.  A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method , 2015 .

[28]  M. P. Mignolet,et al.  Reduced Order Modeling with Local Enrichment for the Nonlinear Geometric Response of a Cracked Panel , 2019, AIAA Journal.

[29]  Haim Waisman,et al.  Experimental application and enhancement of the XFEM-GA algorithm for the detection of flaws in structures , 2011 .

[30]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[31]  Jiun-Shyan Chen,et al.  A decomposed subspace reduction for fracture mechanics based on the meshfree integrated singular basis function method , 2018, Computational Mechanics.

[32]  M. Duflot.  A study of the representation of cracks with level sets , 2007 .

[33]  Volker Mehrmann,et al.  The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena , 2015, SIAM J. Sci. Comput..

[34]  Anthony T. Patera,et al.  Reduced basis approximation and a posteriori error estimation for stress intensity factors , 2007 .

[35]  Dan Givoli,et al.  Crack identification by ‘arrival time’ using XFEM and a genetic algorithm , 2009 .

[36]  Charbel Farhat,et al.  A method for interpolating on manifolds structural dynamics reduced‐order models , 2009 .

[37]  Charbel Farhat,et al.  An Online Method for Interpolating Linear Parametric Reduced-Order Models , 2011, SIAM J. Sci. Comput..

[38]  Charbel Farhat,et al.  Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes , 2016, J. Comput. Phys..

[39]  Dan Givoli,et al.  XFEM‐based crack detection scheme using a genetic algorithm , 2007 .

[40]  Ertugrul Taciroglu,et al.  Modeling and identification of an arbitrarily shaped scatterer using dynamic XFEM with cubic splines , 2014 .

[41]  C. Farhat,et al.  Structure‐preserving, stability, and accuracy properties of the energy‐conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models , 2015 .

[42]  Ulrich Pinkall,et al.  Computing Discrete Minimal Surfaces and Their Conjugates , 1993, Exp. Math..

[43]  Xu-hao Han,et al.  An approach based on level set method for void identification of continuum structure with time-domain dynamic response , 2019, Applied Mathematical Modelling.

[44]  S Niroomandi,et al.  Real‐time simulation of surgery by reduced‐order modeling and X‐FEM techniques , 2012, International journal for numerical methods in biomedical engineering.

[45]  Joseph J. Hollkamp,et al.  Modeling vibratory damage with reduced-order models and the generalized finite element method , 2014 .

[46]  K. Willcox,et al.  Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis , 2009 .

[47]  Charbel Farhat,et al.  The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows , 2012, J. Comput. Phys..

[48]  Michel Lesoinne,et al.  Parameter Adaptation of Reduced Order Models for Three-Dimensional Flutter Analysis , 2004 .

[49]  P Kerfriden,et al.  A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics. , 2012, Computer methods in applied mechanics and engineering.

[50]  Haim Waisman,et al.  Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms , 2010 .

[51]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[52]  Charbel Farhat,et al.  A three-dimensional torsional spring analogy method for unstructured dynamic meshes , 2002 .

[53]  B. Haasdonk,et al.  REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS , 2008 .

[54]  Michel Salaün,et al.  High‐order extended finite element method for cracked domains , 2005 .