Nelder–Mead Optimization of Elastic Metamaterials via Machine-Learning-Aided Surrogate Modeling

One of the fundamental challenges of structural optimization of elastic metamaterials (EMMs) with complex geometry lies within the high consumption of computational power associated with finite ele...

[1]  P. Sheng,et al.  Focusing of sound in a 3D phononic crystal. , 2004, Physical review letters.

[2]  Qing Hua Qin,et al.  Hybrid-Trefftz finite element method for Reissner plates on an elastic foundation , 1995 .

[3]  Sébastien Guenneau,et al.  Split-ring resonators and localized modes , 2004 .

[4]  Günter Rudolph,et al.  Replacing FEA for sheet metal forming by surrogate modeling , 2014 .

[5]  C. Sun,et al.  A chiral elastic metamaterial beam for broadband vibration suppression , 2014 .

[6]  Marco Antonio Luersen,et al.  Globalized Nelder-Mead method for engineering optimization , 2002 .

[7]  Louis J. Durlofsky,et al.  Error modeling for surrogates of dynamical systems using machine learning , 2017 .

[8]  M. Ruzzene,et al.  On the mechanism of bandgap formation in locally resonant finite elastic metamaterials , 2016 .

[9]  Sheng,et al.  Locally resonant sonic materials , 2000, Science.

[10]  Qing-Hua Qin,et al.  Trefftz Finite Element Method and Its Applications , 2005 .

[11]  M. Wegener,et al.  On three-dimensional dilational elastic metamaterials , 2013, 1310.3719.

[12]  Massimo Ruzzene,et al.  Phononic properties of hexagonal chiral lattices , 2009 .

[13]  P. Sheng,et al.  Hybrid elastic solids. , 2011, Nature materials.

[14]  Xiang Zhang,et al.  Method for retrieving effective properties of locally resonant acoustic metamaterials , 2007 .

[15]  Q. Qin,et al.  A closed crack tip model for interface cracks inthermopiezoelectric materials , 1999 .

[16]  Wei Sun,et al.  A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis , 2018, Journal of The Royal Society Interface.

[17]  Meiping Sheng,et al.  Multi-flexural band gaps in an Euler–Bernoulli beam with lateral local resonators , 2016 .

[18]  Q. Qin,et al.  Hybrid Trefftz finite-element approach for plate bending on an elastic foundation , 1994 .

[19]  Lixing Han,et al.  Implementing the Nelder-Mead simplex algorithm with adaptive parameters , 2010, Computational Optimization and Applications.

[20]  Demis Hassabis,et al.  Mastering the game of Go with deep neural networks and tree search , 2016, Nature.

[21]  P. Sheng,et al.  Locally resonant sonic materials , 2000, Science.

[22]  Dave Winkler,et al.  Bayesian Regularization of Neural Networks , 2009, Artificial Neural Networks.

[23]  Ananth Ranganathan,et al.  The Levenberg-Marquardt Algorithm , 2004 .

[24]  Matthias Troyer,et al.  Solving the quantum many-body problem with artificial neural networks , 2016, Science.

[25]  Q. Qin,et al.  An arbitrarily-oriented plane crack terminating at the interface between dissimilar piezoelectric materials , 1997 .

[26]  Sebastian Thrun,et al.  Dermatologist-level classification of skin cancer with deep neural networks , 2017, Nature.

[27]  S Mohammadi,et al.  Complete band gaps in two-dimensional phononic crystal slabs. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Q. Qin,et al.  A meshless method for generalized linear or nonlinear Poisson-type problems , 2006 .

[29]  Ian Stavness,et al.  TOWARDS FINITE-ELEMENT SIMULATION USING DEEP LEARNING , 2018 .

[30]  Yan Pennec,et al.  Two-dimensional phononic crystals: Examples and applications , 2010 .

[31]  Yi Xiao,et al.  Analysis of wave band gaps in mechanical metamaterial based on Nelder–Mead method , 2019, Engineering Analysis with Boundary Elements.

[32]  Guoliang Huang,et al.  Band Gaps in a Multiresonator Acoustic Metamaterial , 2010 .