Shape and topology optimization of the robust compliance via the level set method
ESAIM: COCV, 14 1 (2008) 43-70
Published online: 2007-09-21
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Minimum stress optimal design with the level set method
Grégoire Allaire and François JouveEngineering Analysis with Boundary Elements 32 (11) 909 (2008)
DOI: 10.1016/j.enganabound.2007.05.007
See this article
Geometric Partial Differential Equations - Part II
Grégoire Allaire, Charles Dapogny and François JouveHandbook of Numerical Analysis, Geometric Partial Differential Equations - Part II 22 1 (2021)
DOI: 10.1016/bs.hna.2020.10.004
See this article
Robust Topology Optimization of Structures Under Loading Uncertainty
Junpeng Zhao and Chunjie WangAIAA Journal 52 (2) 398 (2014)
DOI: 10.2514/1.J052544
See this article
Optimal Design through the Sub-Relaxation Method
Pablo PedregalSEMA SIMAI Springer Series, Optimal Design through the Sub-Relaxation Method 11 1 (2016)
DOI: 10.1007/978-3-319-41159-0_1
See this article
Robust shape optimization of continuous structures via the level set method
Jesús Martínez-Frutos, David Herrero-Pérez, Mathieu Kessler and Francisco PeriagoComputer Methods in Applied Mechanics and Engineering 305 271 (2016)
DOI: 10.1016/j.cma.2016.03.003
See this article
Trends in PDE Constrained Optimization
Sergio Conti, Benedict Geihe, Martin Rumpf and Rüdiger SchultzInternational Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 193 (2014)
DOI: 10.1007/978-3-319-05083-6_13
See this article
A critical analysis of expected-compliance model in volume-constrained robust topology optimization with normally distributed loading directions, using a minimax-compliance approach alternatively
A. Csébfalvi and J. LógóAdvances in Engineering Software 120 107 (2018)
DOI: 10.1016/j.advengsoft.2018.02.003
See this article
Minmax topology optimization
Kevin Brittain, Mariana Silva and Daniel A. TortorelliStructural and Multidisciplinary Optimization 45 (5) 657 (2012)
DOI: 10.1007/s00158-011-0715-y
See this article
Topology optimization under uncertainty via non-intrusive polynomial chaos expansion
Vahid Keshavarzzadeh, Felipe Fernandez and Daniel A. TortorelliComputer Methods in Applied Mechanics and Engineering 318 120 (2017)
DOI: 10.1016/j.cma.2017.01.019
See this article
Integrated method for performance analysis of reliability-based topologically optimized components
Arshad Javed, Joshua Amrith Raj and BK RoutProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233 (19-20) 7019 (2019)
DOI: 10.1177/0954406219865757
See this article
Investigation on parametric sensitivity of topologically optimized structures
Arshad Javed and BK RoutProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226 (11) 2791 (2012)
DOI: 10.1177/0954406212437513
See this article
Tolerance range section of topologically optimized structure using combined array design of experiments approach
Arshad Javed and BK RoutProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227 (9) 2023 (2013)
DOI: 10.1177/0954406212468652
See this article
Evolutionary topology optimization of continuum structures under uncertainty using sensitivity analysis and smooth boundary representation
Jesús Martínez-Frutos and David Herrero-PérezComputers & Structures 205 15 (2018)
DOI: 10.1016/j.compstruc.2018.05.003
See this article
A linearized approach to worst-case design in parametric and geometric shape optimization
Grégoire Allaire and Charles DapognyMathematical Models and Methods in Applied Sciences 24 (11) 2199 (2014)
DOI: 10.1142/S0218202514500195
See this article
An optimization algorithm for automatic structural design
Nicola Ferro, Stefano Micheletti and Simona PerottoComputer Methods in Applied Mechanics and Engineering 372 113335 (2020)
DOI: 10.1016/j.cma.2020.113335
See this article
Robust topology optimization accounting for spatially varying manufacturing errors
M. Schevenels, B.S. Lazarov and O. SigmundComputer Methods in Applied Mechanics and Engineering 200 (49-52) 3613 (2011)
DOI: 10.1016/j.cma.2011.08.006
See this article
Optimal distribution of the internal null control for the one-dimensional heat equation
Arnaud Münch and Francisco PeriagoJournal of Differential Equations 250 (1) 95 (2011)
DOI: 10.1016/j.jde.2010.10.020
See this article
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Joshua D. Deaton and Ramana V. GrandhiStructural and Multidisciplinary Optimization 49 (1) 1 (2014)
DOI: 10.1007/s00158-013-0956-z
See this article
Robust topology optimization of truss structures with random loading and material properties: A multiobjective perspective
James N. Richardson, Rajan Filomeno Coelho and Sigrid AdriaenssensComputers & Structures 154 41 (2015)
DOI: 10.1016/j.compstruc.2015.03.011
See this article
Robust topology optimization of frame structures under geometric or material properties uncertainties
Navid Changizi and Mehdi JalalpourStructural and Multidisciplinary Optimization 56 (4) 791 (2017)
DOI: 10.1007/s00158-017-1686-4
See this article
Worst-case topology optimization of self-weight loaded structures using semi-definite programming
Erik Holmberg, Carl-Johan Thore and Anders KlarbringStructural and Multidisciplinary Optimization 52 (5) 915 (2015)
DOI: 10.1007/s00158-015-1285-1
See this article
Phase field method to optimize dielectric devices for electromagnetic wave propagation
Akihiro Takezawa and Mitsuru KitamuraJournal of Computational Physics 257 216 (2014)
DOI: 10.1016/j.jcp.2013.09.051
See this article
Optimality Conditions for Shape and Topology Optimization Subject to a Cone Constraint
Samuel Amstutz and Marc Ciligot–TravainSIAM Journal on Control and Optimization 48 (6) 4056 (2010)
DOI: 10.1137/080722874
See this article
Level-set methods for structural topology optimization: a review
N. P. van Dijk, K. Maute, M. Langelaar and F. van KeulenStructural and Multidisciplinary Optimization 48 (3) 437 (2013)
DOI: 10.1007/s00158-013-0912-y
See this article
Risk averse elastic shape optimization with parametrized fine scale geometry
Benedict Geihe, Martin Lenz, Martin Rumpf and Rüdiger SchultzMathematical Programming 141 (1-2) 383 (2013)
DOI: 10.1007/s10107-012-0531-1
See this article
Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties
Qinghai Zhao, Xiaokai Chen, Zheng-Dong Ma and Yi LinMathematical Problems in Engineering 2015 1 (2015)
DOI: 10.1155/2015/580980
See this article
A general framework for robust topology optimization under load-uncertainty including stress constraints
Carl-Johan Thore, Erik Holmberg and Anders KlarbringComputer Methods in Applied Mechanics and Engineering 319 1 (2017)
DOI: 10.1016/j.cma.2017.02.015
See this article
A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regime
Marc Dambrine and Antoine LaurainStructural and Multidisciplinary Optimization 54 (2) 215 (2016)
DOI: 10.1007/s00158-015-1384-z
See this article
Relaxation of an optimal design problem in fracture mechanic: the anti-plane case
Arnaud Münch and Pablo PedregalESAIM: Control, Optimisation and Calculus of Variations 16 (3) 719 (2010)
DOI: 10.1051/cocv/2009019
See this article
Robust structural topology optimization considering boundary uncertainties
Xu Guo, Weisheng Zhang and Li ZhangComputer Methods in Applied Mechanics and Engineering 253 356 (2013)
DOI: 10.1016/j.cma.2012.09.005
See this article
Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices
Junpeng Zhao and Chunjie WangComputer Methods in Applied Mechanics and Engineering 273 204 (2014)
DOI: 10.1016/j.cma.2014.01.018
See this article
Topology optimization with geometric uncertainties by perturbation techniques
B. S. Lazarov, M. Schevenels and O. SigmundInternational Journal for Numerical Methods in Engineering 90 (11) 1321 (2012)
DOI: 10.1002/nme.3361
See this article
Topology optimization of structures with interval random parameters
Ning Chen, Dejie Yu, Baizhan Xia and Zhengdong MaComputer Methods in Applied Mechanics and Engineering 307 300 (2016)
DOI: 10.1016/j.cma.2016.03.036
See this article
Robust shape optimization method for a linear elastic structure with unknown loadings
Masatoshi SHIMODA, Tomohiro NAGANO, Kohei SHINTANI and Satoshi ITOTransactions of the JSME (in Japanese) 81 (832) 15-00353 (2015)
DOI: 10.1299/transjsme.15-00353
See this article
Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system
Akihiro Takezawa, Satoru Nii, Mitsuru Kitamura and Nozomu KogisoComputer Methods in Applied Mechanics and Engineering 200 (25-28) 2268 (2011)
DOI: 10.1016/j.cma.2011.03.008
See this article
Shape Optimization for Stokes flows: a finite element convergence analysis
Ivan Fumagalli, Nicola Parolini and Marco VeraniESAIM: Mathematical Modelling and Numerical Analysis 49 (4) 921 (2015)
DOI: 10.1051/m2an/2014060
See this article
A unified stochastic framework for robust topology optimization of continuum and truss-like structures
J.N. Richardson, R. Filomeno Coelho and S. AdriaenssensEngineering Optimization 48 (2) 334 (2016)
DOI: 10.1080/0305215X.2015.1011152
See this article
Risk Averse Shape Optimization
Sergio Conti, Harald Held, Martin Pach, Martin Rumpf and Rüdiger SchultzSIAM Journal on Control and Optimization 49 (3) 927 (2011)
DOI: 10.1137/090754315
See this article
Isogeometric Analysis for Topology Optimization with a Phase Field Model
Luca Dedè, Micheal J. Borden and Thomas J. R. HughesArchives of Computational Methods in Engineering 19 (3) 427 (2012)
DOI: 10.1007/s11831-012-9075-z
See this article
Connecting architecture and engineering through structural topology optimization
Lauren L. Beghini, Alessandro Beghini, Neil Katz, William F. Baker and Glaucio H. PaulinoEngineering Structures 59 716 (2014)
DOI: 10.1016/j.engstruct.2013.10.032
See this article
An Explicit Formula for Computing the Sensitivity of the Effective Conductivity of Heterogeneous Composite Materials to Local Inclusion Transport Properties and Geometry
B. NøetingerMultiscale Modeling & Simulation 11 (3) 907 (2013)
DOI: 10.1137/120884961
See this article
Variational Analysis and Aerospace Engineering
Grégoire Allaire, François Jouve and Georgios MichailidisSpringer Optimization and Its Applications, Variational Analysis and Aerospace Engineering 116 1 (2016)
DOI: 10.1007/978-3-319-45680-5_1
See this article
A NOTE ON FORMULATIONS OF ROBUST COMPLIANCE OPTIMIZATION UNDER UNCERTAIN LOADS
Yoshihiro KANNOJournal of Structural and Construction Engineering (Transactions of AIJ) 80 (710) 601 (2015)
DOI: 10.3130/aijs.80.601
See this article
Combined shape and topology optimization of 3D structures
Asger Nyman Christiansen, J. Andreas Bærentzen, Morten Nobel-Jørgensen, Niels Aage and Ole SigmundComputers & Graphics 46 25 (2015)
DOI: 10.1016/j.cag.2014.09.021
See this article
A semidefinite programming approach to robust truss topology optimization under uncertainty in locations of nodes
Daiki Hashimoto and Yoshihiro KannoStructural and Multidisciplinary Optimization 51 (2) 439 (2015)
DOI: 10.1007/s00158-014-1146-3
See this article
Robust optimal shape design for an elliptic PDE with uncertainty in its input data
Jesús Martínez-Frutos, Mathieu Kessler and Francisco PeriagoESAIM: Control, Optimisation and Calculus of Variations 21 (4) 901 (2015)
DOI: 10.1051/cocv/2014049
See this article
Topology optimization applied to 2D elasticity problems considering the geometrical nonlinearity
Walliston S. Fernandes, Valério S. Almeida, Francisco A. Neves and Marcelo GrecoEngineering Structures 100 116 (2015)
DOI: 10.1016/j.engstruct.2015.05.042
See this article
Application of the smooth evolutionary structural optimization method combined with a multi-criteria decision procedure
Walliston S. Fernandes, Marcelo Greco and Valério S. AlmeidaEngineering Structures 143 40 (2017)
DOI: 10.1016/j.engstruct.2017.04.001
See this article
Microstructural topology optimization for minimizing the sound pressure level of structural–acoustic coupled systems with multi-scale random parameters
Shengwen Yin, Ning Chen, Dejie Yu and Zhengdong MaEngineering Optimization 51 (7) 1185 (2019)
DOI: 10.1080/0305215X.2018.1517259
See this article
Introducing Loading Uncertainty in Topology Optimization
Peter D. Dunning, H. Alicia Kim and Glen MullineuxAIAA Journal 49 (4) 760 (2011)
DOI: 10.2514/1.J050670
See this article
Non-parametric shape optimization method for robust design of solid, shell, and frame structures considering loading uncertainty
Masatoshi Shimoda, Tomohiro Nagano and Jin-Xing ShiStructural and Multidisciplinary Optimization (2018)
DOI: 10.1007/s00158-018-2144-7
See this article
POD-assisted strategies for structural topology optimization
Nicola Ferro, Stefano Micheletti and Simona PerottoComputers & Mathematics with Applications 77 (10) 2804 (2019)
DOI: 10.1016/j.camwa.2019.01.010
See this article
A discrete level-set topology optimization code written in Matlab
Vivien J. ChallisStructural and Multidisciplinary Optimization 41 (3) 453 (2010)
DOI: 10.1007/s00158-009-0430-0
See this article
Parametric topology optimization with multiresolution finite element models
Vahid Keshavarzzadeh, Robert M. Kirby and Akil NarayanInternational Journal for Numerical Methods in Engineering 119 (7) 567 (2019)
DOI: 10.1002/nme.6063
See this article
Constrained Optimization and Optimal Control for Partial Differential Equations
Pradeep Atwal, Sergio Conti, Benedict Geihe, et al.Constrained Optimization and Optimal Control for Partial Differential Equations 215 (2012)
DOI: 10.1007/978-3-0348-0133-1_12
See this article
Shape optimization with a level set based mesh evolution method
G. Allaire, C. Dapogny and P. FreyComputer Methods in Applied Mechanics and Engineering 282 22 (2014)
DOI: 10.1016/j.cma.2014.08.028
See this article
Risk-averse structural topology optimization under random fields using stochastic expansion methods
Jesús Martínez-Frutos, David Herrero-Pérez, Mathieu Kessler and Francisco PeriagoComputer Methods in Applied Mechanics and Engineering 330 180 (2018)
DOI: 10.1016/j.cma.2017.10.026
See this article
Large-scale stochastic topology optimization using adaptive mesh refinement and coarsening through a two-level parallelization scheme
Joan Baiges, Jesús Martínez-Frutos, David Herrero-Pérez, Fermin Otero and Alex FerrerComputer Methods in Applied Mechanics and Engineering 343 186 (2019)
DOI: 10.1016/j.cma.2018.08.028
See this article
Robust compliance topology optimization using the first-order second-moment method
Benedikt Kriegesmann and Julian K. LüdekerStructural and Multidisciplinary Optimization 60 (1) 269 (2019)
DOI: 10.1007/s00158-019-02216-8
See this article
Set-in-stone
Christian Schumacher, Jonas Zehnder and Moritz BächerACM Transactions on Graphics 37 (6) 1 (2019)
DOI: 10.1145/3272127.3275085
See this article
Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach
Yoshihiro KannoComputational Optimization and Applications 71 (2) 403 (2018)
DOI: 10.1007/s10589-018-0013-3
See this article
Tolerance range selection of topologically optimized structures with the effects of uncertainties of manufacturing process
Arshad Javed and BK RoutProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228 (18) 3441 (2014)
DOI: 10.1177/0954406214528484
See this article