Component-wise reduced order model lattice-type structure design

McBane, Sean; Choi, Youngsoo

doi:10.1016/j.cma.2021.113813

Component-wise reduced order model lattice-type structure design

Journal Article · Mon Apr 19 00:00:00 EDT 2021 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2021.113813· OSTI ID:1818413

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Univ. of Texas, Austin, TX (United States). Oden Inst. for Computational Engineering & Sciences
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling as introduced in Huynh et al. (2013); Eftang and Patera (2013), which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of 1%. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. Furthermore, the sensitivity of the compliance with respect to the particular parameterization is derived solely at the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of 1% and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for the displacement field, compliance, and compliance sensitivity of the CWROM are derived.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344; SC0019303

OSTI ID:: 1818413

Alternate ID(s):: OSTI ID: 1782360

Report Number(s):: LLNL-JRNL--815816; 1025147

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 381; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (56)

Local stability of trusses in the context of topology optimization Part I: Exact modelling Achtziger, W. Structural Optimization, Vol. 17, Issue 4 https://doi.org/10.1007/bf01206999	journal	December 1999
Resolving issues with member buckling in truss topology optimization using a mixed variable approach Mela, Kristo Structural and Multidisciplinary Optimization, Vol. 50, Issue 6 https://doi.org/10.1007/s00158-014-1095-x	journal	July 2014
Implementation and detailed assessment of a GNAT reduced-order model for subsurface flow simulation Jiang, Rui; Durlofsky, Louis J. Journal of Computational Physics, Vol. 379 https://doi.org/10.1016/j.jcp.2018.11.038	journal	February 2019
On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows Grimberg, Sebastian; Farhat, Charbel; Youkilis, Noah Journal of Computational Physics, Vol. 419 https://doi.org/10.1016/j.jcp.2020.109681	journal	October 2020
Analysis of a complex of statistical variables into principal components. Hotelling, H. Journal of Educational Psychology, Vol. 24, Issue 6 https://doi.org/10.1037/h0071325	journal	January 1933
Coupling of substructures for dynamic analyses. Craig, Roy R.; Bampton, Mervyn C. C. AIAA Journal, Vol. 6, Issue 7 https://doi.org/10.2514/3.4741	journal	July 1968
Accelerating design optimization using reduced order models Choi, Youngsoo; Oxberry, Geoffrey; White, Daniel arXiv https://doi.org/10.48550/arxiv.1909.11320	preprint	January 2019
The method of moving asymptotes—a new method for structural optimization Svanberg, Krister International Journal for Numerical Methods in Engineering, Vol. 24, Issue 2 https://doi.org/10.1002/nme.1620240207	journal	February 1987
Port reduction in parametrized component static condensation: approximation and a posteriori error estimation: PORT REDUCTION IN PARAMETRIZED COMPONENT STATIC CONDENSATION Eftang, Jens L.; Patera, Anthony T. International Journal for Numerical Methods in Engineering, Vol. 96, Issue 5 https://doi.org/10.1002/nme.4543	journal	July 2013
Optimal shape design as a material distribution problem Bendsøe, M. P. Structural Optimization, Vol. 1, Issue 4 https://doi.org/10.1007/BF01650949	journal	December 1989
Optimization methods for truss geometry and topology design Bendsøe, M. P.; Ben-Tal, A.; Zowe, J. Structural Optimization, Vol. 7, Issue 3 https://doi.org/10.1007/BF01742459	journal	April 1994
Topology optimization of trusses by growing ground structure method Hagishita, T.; Ohsaki, M. Structural and Multidisciplinary Optimization, Vol. 37, Issue 4 https://doi.org/10.1007/s00158-008-0237-4	journal	April 2008
Design optimization using hyper-reduced-order models Amsallem, David; Zahr, Matthew; Choi, Youngsoo Structural and Multidisciplinary Optimization, Vol. 51, Issue 4 https://doi.org/10.1007/s00158-014-1183-y	journal	November 2014
Truss optimization with discrete design variables: a critical review Stolpe, Mathias Structural and Multidisciplinary Optimization, Vol. 53, Issue 2 https://doi.org/10.1007/s00158-015-1333-x	journal	September 2015
Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures Wang, Chuang; Zhu, Ji Hong; Zhang, Wei Hong Structural and Multidisciplinary Optimization, Vol. 58, Issue 1 https://doi.org/10.1007/s00158-018-2009-0	journal	June 2018
Topology optimization for microstructural design under stress constraints Collet, Maxime; Noël, Lise; Bruggi, Matteo Structural and Multidisciplinary Optimization, Vol. 58, Issue 6 https://doi.org/10.1007/s00158-018-2045-9	journal	July 2018
Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design Watts, Seth; Arrighi, William; Kudo, Jun Structural and Multidisciplinary Optimization, Vol. 60, Issue 5 https://doi.org/10.1007/s00158-019-02297-5	journal	May 2019
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Wächter, Andreas; Biegler, Lorenz T. Mathematical Programming, Vol. 106, Issue 1 https://doi.org/10.1007/s10107-004-0559-y	journal	April 2005
Reduced-order modeling of blood flow for noninvasive functional evaluation of coronary artery disease Buoso, Stefano; Manzoni, Andrea; Alkadhi, Hatem Biomechanics and Modeling in Mechanobiology, Vol. 18, Issue 6 https://doi.org/10.1007/s10237-019-01182-w	journal	June 2019
Equivalent displacement based formulations for maximum strength truss topology design Achtziger, W.; Bendsøe, M.; Ben-Tal, A. IMPACT of Computing in Science and Engineering, Vol. 4, Issue 4 https://doi.org/10.1016/0899-8248(92)90005-S	journal	December 1992
Efficient estimation of cardiac conductivities via POD-DEIM model order reduction Yang, Huanhuan; Veneziani, Alessandro Applied Numerical Mathematics, Vol. 115 https://doi.org/10.1016/j.apnum.2017.01.006	journal	May 2017
Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries Iapichino, Laura; Quarteroni, Alfio; Rozza, Gianluigi Computers & Mathematics with Applications, Vol. 71, Issue 1 https://doi.org/10.1016/j.camwa.2015.12.001	journal	January 2016
A static condensation reduced basis element method: Complex problems Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. Computer Methods in Applied Mechanics and Engineering, Vol. 259 https://doi.org/10.1016/j.cma.2013.02.013	journal	June 2013
A new certification framework for the port reduced static condensation reduced basis element method Smetana, Kathrin Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.09.020	journal	January 2015
Multiscale isogeometric topology optimization for lattice materials Wang, Yingjun; Xu, Hang; Pasini, Damiano Computer Methods in Applied Mechanics and Engineering, Vol. 316 https://doi.org/10.1016/j.cma.2016.08.015	journal	April 2017
A component-based hybrid reduced basis/finite element method for solid mechanics with local nonlinearities Ballani, J.; Huynh, D. B. P.; Knezevic, D. J. Computer Methods in Applied Mechanics and Engineering, Vol. 329 https://doi.org/10.1016/j.cma.2017.09.014	journal	February 2018
An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations Dal Santo, N.; Deparis, S.; Manzoni, A. Computer Methods in Applied Mechanics and Engineering, Vol. 344 https://doi.org/10.1016/j.cma.2018.06.035	journal	February 2019
Multiscale topology optimization using neural network surrogate models White, Daniel A.; Arrighi, William J.; Kudo, Jun Computer Methods in Applied Mechanics and Engineering, Vol. 346 https://doi.org/10.1016/j.cma.2018.09.007	journal	April 2019
Topology optimization of hierarchical lattice structures with substructuring Wu, Zijun; Xia, Liang; Wang, Shuting Computer Methods in Applied Mechanics and Engineering, Vol. 345 https://doi.org/10.1016/j.cma.2018.11.003	journal	March 2019
Concurrent two-scale topological design of multiple unit cells and structure using combined velocity field level set and density model Wang, Yaguang; Kang, Zhan Computer Methods in Applied Mechanics and Engineering, Vol. 347 https://doi.org/10.1016/j.cma.2018.12.018	journal	April 2019
Efficient topology optimization of multicomponent structure using substructuring-based model order reduction method Koh, Hyeong Seok; Kim, Jun Hwan; Yoon, Gil Ho Computers & Structures, Vol. 228 https://doi.org/10.1016/j.compstruc.2019.106146	journal	February 2020
Localized Model Reduction in Porous Media Flow∗1The authors would like to thanks the US DoD - Army Research Once and Foundation CMG for supporting this project. Ghasemi, Mohamadreza; Gildin, Eduardo IFAC-PapersOnLine, Vol. 48, Issue 6 https://doi.org/10.1016/j.ifacol.2015.08.038	journal	January 2015
Topology optimization for concurrent design of layer-wise graded lattice materials and structures Zhang, Huikai; Wang, Yaguang; Kang, Zhan International Journal of Engineering Science, Vol. 138 https://doi.org/10.1016/j.ijengsci.2019.01.006	journal	May 2019
POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model Ştefănescu, R.; Navon, I. M. Journal of Computational Physics, Vol. 237 https://doi.org/10.1016/j.jcp.2012.11.035	journal	March 2013
Conservative model reduction for finite-volume models Carlberg, Kevin; Choi, Youngsoo; Sargsyan, Syuzanna Journal of Computational Physics, Vol. 371 https://doi.org/10.1016/j.jcp.2018.05.019	journal	October 2018
Gradient-based constrained optimization using a database of linear reduced-order models Choi, Youngsoo; Boncoraglio, Gabriele; Anderson, Spenser Journal of Computational Physics, Vol. 423 https://doi.org/10.1016/j.jcp.2020.109787	journal	December 2020
POD-DEIM reduction of computational EMG models Mordhorst, M.; Strecker, T.; Wirtz, D. Journal of Computational Science, Vol. 19 https://doi.org/10.1016/j.jocs.2017.01.009	journal	March 2017
Reduced order modeling based shape optimization of surface acoustic wave driven microfluidic biochips Antil, Harbir; Heinkenschloss, Matthias; Hoppe, Ronald H. W. Mathematics and Computers in Simulation, Vol. 82, Issue 10 https://doi.org/10.1016/j.matcom.2010.10.027	journal	June 2012
Design of manufacturable 3D extremal elastic microstructure Andreassen, Erik; Lazarov, Boyan S.; Sigmund, Ole Mechanics of Materials, Vol. 69, Issue 1 https://doi.org/10.1016/j.mechmat.2013.09.018	journal	February 2014
Sequential Quadratic Programming Boggs, Paul T.; Tolle, Jon W. Acta Numerica, Vol. 4 https://doi.org/10.1017/S0962492900002518	journal	January 1995
A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation Phuong Huynh, Dinh Bao; Knezevic, David J.; Patera, Anthony T. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 47, Issue 1 https://doi.org/10.1051/m2an/2012022	journal	November 2012
Topology Optimization of Periodic Structures With Substructuring Fu, Junjian; Xia, Liang; Gao, Liang Journal of Mechanical Design, Vol. 141, Issue 7 https://doi.org/10.1115/1.4042616	journal	March 2019
Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures Smetana, Kathrin; Patera, Anthony T. SIAM Journal on Scientific Computing, Vol. 38, Issue 5 https://doi.org/10.1137/15M1009603	journal	January 2016
ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications Buhr, Andreas; Engwer, Christian; Ohlberger, Mario SIAM Journal on Scientific Computing, Vol. 39, Issue 4 https://doi.org/10.1137/15M1054213	journal	January 2017
Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction Choi, Youngsoo; Carlberg, Kevin SIAM Journal on Scientific Computing, Vol. 41, Issue 1 https://doi.org/10.1137/17M1120531	journal	January 2019
SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction Choi, Youngsoo; Coombs, Deshawn; Anderson, Robert SIAM Journal on Scientific Computing, Vol. 42, Issue 2 https://doi.org/10.1137/19M1242963	journal	January 2020
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics Kunisch, K.; Volkwein, S. SIAM Journal on Numerical Analysis, Vol. 40, Issue 2 https://doi.org/10.1137/S0036142900382612	journal	January 2002
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization Gill, Philip E.; Murray, Walter; Saunders, Michael A. SIAM Review, Vol. 47, Issue 1 https://doi.org/10.1137/S0036144504446096	journal	January 2005
Primal-Dual Interior Methods for Nonconvex Nonlinear Programming Forsgren, Anders; Gill, Philip E. SIAM Journal on Optimization, Vol. 8, Issue 4 https://doi.org/10.1137/S1052623496305560	journal	November 1998
A Static Condensation Reduced Basis Element Approximation: Application to Three-Dimensional Acoustic Muffler Analysis Huynh, D. B. P. International Journal of Computational Methods, Vol. 11, Issue 03 https://doi.org/10.1142/S021987621343010X	journal	June 2014
POD-DEIM Based Model Order Reduction for the Spherical Shallow Water Equations with Turkel-Zwas Finite Difference Discretization Zhao, Pengfei; Liu, Cai; Feng, Xuan Journal of Applied Mathematics, Vol. 2014 https://doi.org/10.1155/2014/292489	journal	January 2014
Component-based reduced basis for parametrized symmetric eigenproblems Vallaghé, Sylvain; Huynh, Phuong; Knezevic, David J. Advanced Modeling and Simulation in Engineering Sciences, Vol. 2, Issue 1 https://doi.org/10.1186/s40323-015-0021-0	journal	May 2015
Fast Multiscale Reservoir Simulations With POD-DEIM Model Reduction Yang, Yanfang; Ghasemi, Mohammadreza; Gildin, Eduardo SPE Journal, Vol. 21, Issue 06 https://doi.org/10.2118/173271-PA	journal	June 2016
Uber Die Beste Annaherung Von Funktionen Einer Gegebenen Funktionenklasse Kolmogoroff, A. The Annals of Mathematics, Vol. 37, Issue 1 https://doi.org/10.2307/1968691	journal	January 1936
Dynamic analysis of structural systems using component modes Hurty, Walter C. AIAA Journal, Vol. 3, Issue 4 https://doi.org/10.2514/3.2947	journal	April 1965
Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing Chen, Wenjiong; Zheng, Xiaonan; Liu, Shutian Materials, Vol. 11, Issue 11 https://doi.org/10.3390/ma11112073	journal	October 2018

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Related Subjects

97 MATHEMATICS AND COMPUTING
Topology optimization
component-wise reduced order model
design optimization
domain decomposition
lattice-type structure design
static condensation

Component-wise reduced order model lattice-type structure design

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References (56)

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