Level-set topology optimization with PDE generated conformal meshes

Schmidt, Mathias R.; Barrera, Jorge L.; Mittal, Ketan; Swartz, Kenneth E.; Tortorelli, Daniel A.

doi:10.1007/s00158-024-03870-3

Title: Level-set topology optimization with PDE generated conformal meshes

Journal Article · 24 October 2024 · Structural and Multidisciplinary Optimization

DOI: https://doi.org/10.1007/s00158-024-03870-3 · OSTI ID:2478207

^[1]; Barrera, Jorge L. ^[1]; Mittal, Ketan ^[1]; Swartz, Kenneth E. ^[1]; Tortorelli, Daniel A. ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

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

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2478207

Report Number(s):: LLNL--JRNL-858905; 1089187

Journal Information:: Structural and Multidisciplinary Optimization, Journal Name: Structural and Multidisciplinary Optimization Journal Issue: 10 Vol. 67; ISSN 1615-147X

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (48)

The Partition of Unity Method BabuŠKa, I.; Melenk, J. M. International Journal for Numerical Methods in Engineering, Vol. 40, Issue 4 https://doi.org/10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N	journal	February 1997
Elastic crack growth in finite elements with minimal remeshing Belytschko, T.; Black, T. International Journal for Numerical Methods in Engineering, Vol. 45, Issue 5 https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S	journal	June 1999
Filters in topology optimization Bourdin, Blaise International Journal for Numerical Methods in Engineering, Vol. 50, Issue 9 https://doi.org/10.1002/nme.116	journal	January 2001
A fictitious energy approach for shape optimization Scherer, M.; Denzer, R.; Steinmann, P. International Journal for Numerical Methods in Engineering, Vol. 82, Issue 3 https://doi.org/10.1002/nme.2764	journal	October 2009
Filters in topology optimization based on Helmholtz-type differential equations Lazarov, B. S.; Sigmund, O. International Journal for Numerical Methods in Engineering, Vol. 86, Issue 6 https://doi.org/10.1002/nme.3072	journal	December 2010
Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes: UNIVERSAL MESHES Rangarajan, Ramsharan; Lew, Adrián J. International Journal for Numerical Methods in Engineering, Vol. 98, Issue 4 https://doi.org/10.1002/nme.4624	journal	March 2014
Level Set Methods: An Overview and Some Recent Results Osher, Stanley; Fedkiw, Ronald P. Journal of Computational Physics, Vol. 169, Issue 2 https://doi.org/10.1006/jcph.2000.6636	journal	May 2001
Bubble method for topology and shape optimization of structures Eschenauer, H. A.; Kobelev, V. V.; Schumacher, A. Structural Optimization, Vol. 8, Issue 1 https://doi.org/10.1007/BF01742933	journal	August 1994
Level-set methods for structural topology optimization: a review van Dijk, N. P.; Maute, K.; Langelaar, M. Structural and Multidisciplinary Optimization, Vol. 48, Issue 3 https://doi.org/10.1007/s00158-013-0912-y	journal	March 2013
A survey of structural and multidisciplinary continuum topology optimization: post 2000 Deaton, Joshua D.; Grandhi, Ramana V. Structural and Multidisciplinary Optimization, Vol. 49, Issue 1 https://doi.org/10.1007/s00158-013-0956-z	journal	July 2013
Topology optimization approaches: A comparative review Sigmund, Ole; Maute, Kurt Structural and Multidisciplinary Optimization, Vol. 48, Issue 6 https://doi.org/10.1007/s00158-013-0978-6	journal	August 2013
A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model Zhang, Weisheng; Yuan, Jie; Zhang, Jian Structural and Multidisciplinary Optimization, Vol. 53, Issue 6 https://doi.org/10.1007/s00158-015-1372-3	journal	December 2015
A geometry projection method for the topology optimization of plate structures Zhang, Shanglong; Norato, Julián A.; Gain, Arun L. Structural and Multidisciplinary Optimization, Vol. 54, Issue 5 https://doi.org/10.1007/s00158-016-1466-6	journal	May 2016
Combined shape and topology optimization for minimization of maximal von Mises stress Lian, Haojie; Christiansen, Asger N.; Tortorelli, Daniel A. Structural and Multidisciplinary Optimization, Vol. 55, Issue 5 https://doi.org/10.1007/s00158-017-1656-x	journal	January 2017
Hole seeding in level set topology optimization via density fields Barrera, Jorge L.; Geiss, Markus J.; Maute, Kurt Structural and Multidisciplinary Optimization, Vol. 61, Issue 4 https://doi.org/10.1007/s00158-019-02480-8	journal	February 2020
Adaptive level set topology optimization using hierarchical B-splines Noël, L.; Schmidt, M.; Messe, C. Structural and Multidisciplinary Optimization, Vol. 62, Issue 4 https://doi.org/10.1007/s00158-020-02584-6	journal	July 2020
A review on feature-mapping methods for structural optimization Wein, Fabian; Dunning, Peter D.; Norato, Julián A. Structural and Multidisciplinary Optimization, Vol. 62, Issue 4 https://doi.org/10.1007/s00158-020-02649-6	journal	August 2020
Minimum feature size control in level set topology optimization via density fields Barrera, Jorge L.; Geiss, Markus J.; Maute, Kurt Structural and Multidisciplinary Optimization, Vol. 65, Issue 3 https://doi.org/10.1007/s00158-021-03096-7	journal	February 2022
Yet another parameter-free shape optimization method Swartz, Kenneth E.; Mittal, Ketan; Schmidt, Mathias Structural and Multidisciplinary Optimization, Vol. 66, Issue 12 https://doi.org/10.1007/s00158-023-03684-9	journal	November 2023
Finite cell method: h- and p-extension for embedded domain problems in solid mechanics Parvizian, Jamshid; Düster, Alexander; Rank, Ernst Computational Mechanics, Vol. 41, Issue 1 https://doi.org/10.1007/s00466-007-0173-y	journal	April 2007
Density and level set-XFEM schemes for topology optimization of 3-D structures Villanueva, Carlos H.; Maute, Kurt Computational Mechanics, Vol. 54, Issue 1 https://doi.org/10.1007/s00466-014-1027-z	journal	April 2014
XIGA: An eXtended IsoGeometric analysis approach for multi-material problems Noël, L.; Schmidt, M.; Doble, K. Computational Mechanics, Vol. 70, Issue 6 https://doi.org/10.1007/s00466-022-02200-y	journal	July 2022
Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines Schmidt, Mathias; Noël, Lise; Doble, Keenan Computational Mechanics, Vol. 71, Issue 6 https://doi.org/10.1007/s00466-023-02306-x	journal	March 2023
Shape Optimization of an Imperfect Interface: Steady-State Heat Diffusion Allaire, Grégoire; Bogosel, Beniamin; Godoy, Matías Journal of Optimization Theory and Applications, Vol. 191, Issue 1 https://doi.org/10.1007/s10957-021-01928-6	journal	September 2021
A regularization scheme for explicit level-set XFEM topology optimization Geiss, Markus J.; Barrera, Jorge L.; Boddeti, Narasimha Frontiers of Mechanical Engineering, Vol. 14, Issue 2 https://doi.org/10.1007/s11465-019-0533-2	journal	January 2019
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models Schillinger, Dominik; Ruess, Martin Archives of Computational Methods in Engineering, Vol. 22, Issue 3 https://doi.org/10.1007/s11831-014-9115-y	journal	May 2014
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations Osher, Stanley; Sethian, James A. Journal of Computational Physics, Vol. 79, Issue 1 https://doi.org/10.1016/0021-9991(88)90002-2	journal	November 1988
Generating optimal topologies in structural design using a homogenization method Bendsøe, Martin Philip; Kikuchi, Noboru Computer Methods in Applied Mechanics and Engineering, Vol. 71, Issue 2 https://doi.org/10.1016/0045-7825(88)90086-2	journal	November 1988
Topology optimization of non-linear elastic structures and compliant mechanisms Bruns, Tyler E.; Tortorelli, Daniel A. Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 26-27 https://doi.org/10.1016/S0045-7825(00)00278-4	journal	March 2001
A level set method for structural topology optimization Wang, Michael Yu; Wang, Xiaoming; Guo, Dongming Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 1-2 https://doi.org/10.1016/S0045-7825(02)00559-5	journal	January 2003
Generalized finite element methods for three-dimensional structural mechanics problems Duarte, C. A.; Babuška, I.; Oden, J. T. Computers & Structures, Vol. 77, Issue 2 https://doi.org/10.1016/S0045-7949(99)00211-4	journal	June 2000
High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries Barrera, Jorge-Luis; Kolev, Tzanio; Mittal, Ketan Computer-Aided Design, Vol. 158 https://doi.org/10.1016/j.cad.2023.103499	journal	May 2023
Combined shape and topology optimization of 3D structures Christiansen, Asger Nyman; Bærentzen, J. Andreas; Nobel-Jørgensen, Morten Computers & Graphics, Vol. 46 https://doi.org/10.1016/j.cag.2014.09.021	journal	February 2015
p-Laplace diffusion for distance function estimation, optimal transport approximation, and image enhancement Fayolle, Pierre-Alain; Belyaev, Alexander G. Computer Aided Geometric Design, Vol. 67 https://doi.org/10.1016/j.cagd.2018.09.003	journal	December 2018
MFEM: A modular finite element methods library Anderson, Robert; Andrej, Julian; Barker, Andrew Computers & Mathematics with Applications, Vol. 81 https://doi.org/10.1016/j.camwa.2020.06.009	journal	January 2021
The finite cell method for three-dimensional problems of solid mechanics Düster, A.; Parvizian, J.; Yang, Z. Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 45-48 https://doi.org/10.1016/j.cma.2008.02.036	journal	August 2008
Shape optimization with a level set based mesh evolution method Allaire, G.; Dapogny, C.; Frey, P. Computer Methods in Applied Mechanics and Engineering, Vol. 282 https://doi.org/10.1016/j.cma.2014.08.028	journal	December 2014
Condition number analysis and preconditioning of the finite cell method de Prenter, F.; Verhoosel, C. V.; van Zwieten, G. J. Computer Methods in Applied Mechanics and Engineering, Vol. 316 https://doi.org/10.1016/j.cma.2016.07.006	journal	April 2017
CutFEM topology optimization of 3D laminar incompressible flow problems Villanueva, Carlos H.; Maute, Kurt Computer Methods in Applied Mechanics and Engineering, Vol. 320 https://doi.org/10.1016/j.cma.2017.03.007	journal	June 2017
A reaction diffusion-based level set method using body-fitted mesh for structural topology optimization Zhuang, Zicheng; Xie, Yi Min; Zhou, Shiwei Computer Methods in Applied Mechanics and Engineering, Vol. 381 https://doi.org/10.1016/j.cma.2021.113829	journal	August 2021
Structural optimization using sensitivity analysis and a level-set method Allaire, Grégoire; Jouve, François; Toader, Anca-Maria Journal of Computational Physics, Vol. 194, Issue 1 https://doi.org/10.1016/j.jcp.2003.09.032	journal	February 2004
The immersed boundary method Peskin, Charles S. Acta Numerica, Vol. 11 https://doi.org/10.1017/S0962492902000077	journal	January 2002
A review of extended/generalized finite element methods for material modeling Belytschko, Ted; Gracie, Robert; Ventura, Giulio Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 4 https://doi.org/10.1088/0965-0393/17/4/043001	journal	April 2009
Topology optimization of continuum structures: A review* Eschenauer, Hans A.; Olhoff, Niels Applied Mechanics Reviews, Vol. 54, Issue 4 https://doi.org/10.1115/1.1388075	journal	July 2001
The Target-Matrix Optimization Paradigm for High-Order Meshes Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio SIAM Journal on Scientific Computing, Vol. 41, Issue 1 https://doi.org/10.1137/18M1167206	journal	January 2019
A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations Svanberg, Krister SIAM Journal on Optimization, Vol. 12, Issue 2 https://doi.org/10.1137/S1052623499362822	journal	January 2002
Topology-adaptive interface tracking using the deformable simplicial complex Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas ACM Transactions on Graphics, Vol. 31, Issue 3 https://doi.org/10.1145/2167076.2167082	journal	May 2012
Immersed Boundary Methods Mittal, Rajat; Iaccarino, Gianluca Annual Review of Fluid Mechanics, Vol. 37, Issue 1 https://doi.org/10.1146/annurev.fluid.37.061903.175743	journal	January 2005

Similar Records

Adaptive immersed isogeometric level-set topology optimization

Journal Article · 2024 · Structural and Multidisciplinary Optimization · OSTI ID:2522862

Schmidt, Mathias R.; Noël, Lise; Wunsch, Nils; +3 more

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

Journal Article · 2018 · Numerical Linear Algebra with Applications · OSTI ID:1438783

Osborn, Sarah; Zulian, Patrick; Benson, Thomas; +3 more

Parallel Computation of the Topology of Level Sets

Journal Article · 2004 · Algorithmica · OSTI ID:15015923

Pascucci, V; Cole-McLaughlin, K

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING
Body fitted mesh
Conformal mesh
Level-set method
Mathematics and Computing
Engineering
Mesh morphing
Topology optimization

Title: Level-set topology optimization with PDE generated conformal meshes

Citation Formats

References (48)

Similar Records

Related Subjects