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:
Blaise Bourdin, Antonin Chambolle
ESAIM: COCV, 9 (2003) 19-48
Published online: 2003-09-15
This article has been cited by the following article(s):
Phase‐Field Relaxation of Topology Optimization with Local Stress Constraints
Martin Burger and Roman Stainko
SIAM Journal on Control and Optimization 45 (4) 1447 (2006)
DOI: 10.1137/05062723X
See this article
Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation
Rouhollah Tavakoli and Seyyed Mohammad Mohseni
Structural and Multidisciplinary Optimization 49 (4) 621 (2014)
DOI: 10.1007/s00158-013-0999-1
See this article
Soft Image Segmentation Based on the Mixture of Gaussians and the Phase-Transition Theory
Celia A. Z. Barcelos, Yunmei Chen and Fuhua Chen
Applied Mathematics 05 (18) 2888 (2014)
DOI: 10.4236/am.2014.518275
See this article
Design of diaphragm structure for piezoresistive pressure sensor using topology optimization
Benliang Zhu, Xianmin Zhang, Yanzhen Zhang and Sergej Fatikow
Structural and Multidisciplinary Optimization 55 (1) 317 (2017)
DOI: 10.1007/s00158-016-1470-x
See this article
A New Framework of Multiphase Segmentation and Its Application to Partial Volume Segmentation
Fuhua Chen, Yunmei Chen and Hemant D. Tagare
Applied Computational Intelligence and Soft Computing 2011 1 (2011)
DOI: 10.1155/2011/786369
See this article
Variational Analysis and Aerospace Engineering
Grégoire Allaire, François Jouve and Georgios Michailidis
Springer Optimization and Its Applications, Variational Analysis and Aerospace Engineering 116 1 (2016)
DOI: 10.1007/978-3-319-45680-5_1
See this article
Incorporating topological derivatives into level set methods
Martin Burger, Benjamin Hackl and Wolfgang Ring
Journal of Computational Physics 194 (1) 344 (2004)
DOI: 10.1016/j.jcp.2003.09.033
See this article
ISOCOMP: Unified geometric and material composition for optimal topology design
Hung-Yun Lin, Mahidhar Rayasam and Ganesh Subbarayan
Structural and Multidisciplinary Optimization 51 (3) 687 (2015)
DOI: 10.1007/s00158-014-1164-1
See this article
Isogeometric topology optimization using trimmed spline surfaces
Yu-Deok Seo, Hyun-Jung Kim and Sung-Kie Youn
Computer Methods in Applied Mechanics and Engineering 199 (49-52) 3270 (2010)
DOI: 10.1016/j.cma.2010.06.033
See this article
A closer look at consistent operator splitting and its extensions for topology optimization
Cameron Talischi and Glaucio H. Paulino
Computer Methods in Applied Mechanics and Engineering 283 573 (2015)
DOI: 10.1016/j.cma.2014.07.005
See this article
Efficient topology optimization using GPU computing with multilevel granularity
Jesús Martínez-Frutos, Pedro J. Martínez-Castejón and David Herrero-Pérez
Advances in Engineering Software 106 47 (2017)
DOI: 10.1016/j.advengsoft.2017.01.009
See this article
A new boundary search scheme for topology optimization of continuum structures with design-dependent loads
Hui Zhang, Xiong Zhang and Shutian Liu
Structural and Multidisciplinary Optimization 37 (2) 121 (2008)
DOI: 10.1007/s00158-007-0221-4
See this article
Topology optimization using the lattice Boltzmann method incorporating level set boundary expressions
Kentaro Yaji, Takayuki Yamada, Masato Yoshino, et al.
Journal of Computational Physics 274 158 (2014)
DOI: 10.1016/j.jcp.2014.06.004
See this article
Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids
Harald Garcke, Claudia Hecht, Michael Hinze and Christian Kahle
SIAM Journal on Scientific Computing 37 (4) A1846 (2015)
DOI: 10.1137/140969269
See this article
Boundary effects in a phase-field approach to topology optimization
Mathias Wallin and Matti Ristinmaa
Computer Methods in Applied Mechanics and Engineering 278 145 (2014)
DOI: 10.1016/j.cma.2014.05.012
See this article
Motion planning and open loop control design for linear distributed parameter systems with lumped controls
J. Rudolph and F. Woittennek
International Journal of Control 81 (3) 457 (2008)
DOI: 10.1080/00207170701561435
See this article
PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes
Cameron Talischi, Glaucio H. Paulino, Anderson Pereira and Ivan F. M. Menezes
Structural and Multidisciplinary Optimization 45 (3) 329 (2012)
DOI: 10.1007/s00158-011-0696-x
See this article
Topology optimization for submerged buoyant structures
R. Picelli, R. van Dijk, W.M. Vicente, et al.
Engineering Optimization 49 (1) 1 (2017)
DOI: 10.1080/0305215X.2016.1164147
See this article
Structural Optimization Based on the Phase Field Method and Sensitivity Analysis
Akihiro TAKEZAWA, Shinji NISHIWAKI and Mitsuru KITAMURA
Transactions of the Japan Society of Mechanical Engineers Series A 76 (761) 1 (2010)
DOI: 10.1299/kikaia.76.1
See this article
Relating phase field and sharp interface approaches to structural topology optimization
Luise Blank, Harald Garcke, M. Hassan Farshbaf-Shaker and Vanessa Styles
ESAIM: Control, Optimisation and Calculus of Variations 20 (4) 1025 (2014)
DOI: 10.1051/cocv/2014006
See this article
Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems
R. Picelli, W.M. Vicente and R. Pavanello
Engineering Optimization 47 (10) 1324 (2015)
DOI: 10.1080/0305215X.2014.963069
See this article
Volume preserving nonlinear density filter based on heaviside functions
Shengli Xu, Yuanwu Cai and Gengdong Cheng
Structural and Multidisciplinary Optimization 41 (4) 495 (2010)
DOI: 10.1007/s00158-009-0452-7
See this article
Binary Level-Set Shape Optimization Model and Algorithm for Volumetric Modulated Arc Therapy in Radiotherapy Treatment
Li-Tien Cheng, Bin Dong, Chunhua Men, Xun Jia and Steve Jiang
SIAM Journal on Scientific Computing 35 (6) B1321 (2013)
DOI: 10.1137/120890430
See this article
Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints
Luise Blank, Harald Garcke, Lavinia Sarbu and Vanessa Styles
Numerical Methods for Partial Differential Equations 29 (3) 999 (2013)
DOI: 10.1002/num.21742
See this article
Shape and topology optimization based on the phase field method and sensitivity analysis
Akihiro Takezawa, Shinji Nishiwaki and Mitsuru Kitamura
Journal of Computational Physics 229 (7) 2697 (2010)
DOI: 10.1016/j.jcp.2009.12.017
See this article
Topology optimization for thermal conductors considering design-dependent effects, including heat conduction and convection
A. Iga, S. Nishiwaki, K. Izui and M. Yoshimura
International Journal of Heat and Mass Transfer 52 (11-12) 2721 (2009)
DOI: 10.1016/j.ijheatmasstransfer.2008.12.013
See this article
Shape and Topology Optimization in Stokes Flow with a Phase Field Approach
Harald Garcke and Claudia Hecht
Applied Mathematics & Optimization 73 (1) 23 (2016)
DOI: 10.1007/s00245-015-9291-7
See this article
Optimal topologies derived from a phase-field method
Mathias Wallin, Matti Ristinmaa and Henrik Askfelt
Structural and Multidisciplinary Optimization 45 (2) 171 (2012)
DOI: 10.1007/s00158-011-0688-x
See this article
Topology optimization using a mixed formulation: An alternative way to solve pressure load problems
O. Sigmund and P.M. Clausen
Computer Methods in Applied Mechanics and Engineering 196 (13-16) 1874 (2007)
DOI: 10.1016/j.cma.2006.09.021
See this article
Topology optimization with design-dependent pressure loading
Bin Zheng, Ching-jui Chang and Hae Chang Gea
Structural and Multidisciplinary Optimization 38 (6) 535 (2009)
DOI: 10.1007/s00158-008-0317-5
See this article
Topology optimization of reflector antennas based on integrated thermal-structural-electromagnetic analysis
Naigang Hu, Hong Bao, Baoyan Duan, et al.
Structural and Multidisciplinary Optimization 55 (2) 715 (2017)
DOI: 10.1007/s00158-016-1581-4
See this article
A variational binary level-set method for elliptic shape optimization problems
Shengfeng Zhu, Xiaoxia Dai and Chunxiao Liu
International Journal of Computer Mathematics 88 (14) 3026 (2011)
DOI: 10.1080/00207160.2011.565873
See this article
Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method
Rouhollah Tavakoli
Computer Methods in Applied Mechanics and Engineering 276 534 (2014)
DOI: 10.1016/j.cma.2014.04.005
See this article
A critical comparative assessment of differential equation-driven methods for structural topology optimization
Arun L. Gain and Glaucio H. Paulino
Structural and Multidisciplinary Optimization 48 (4) 685 (2013)
DOI: 10.1007/s00158-013-0935-4
See this article
An operator splitting algorithm for Tikhonov-regularized topology optimization
Cameron Talischi and Glaucio H. Paulino
Computer Methods in Applied Mechanics and Engineering 253 599 (2013)
DOI: 10.1016/j.cma.2012.05.024
See this article
Volume preserving projection filters and continuation methods in topology optimization
Lei Li and Kapil Khandelwal
Engineering Structures 85 144 (2015)
DOI: 10.1016/j.engstruct.2014.10.052
See this article
Howard's algorithm in a phase-field topology optimization approach
Mathias Wallin and Matti Ristinmaa
International Journal for Numerical Methods in Engineering 94 (1) 43 (2013)
DOI: 10.1002/nme.4434
See this article
Explicit feature control in structural topology optimization via level set method
Xu Guo, Weisheng Zhang and Wenliang Zhong
Computer Methods in Applied Mechanics and Engineering 272 354 (2014)
DOI: 10.1016/j.cma.2014.01.010
See this article
Numerical Estimation of Piecewise Constant Robin Coefficient
Bangti Jin and Jun Zou
SIAM Journal on Control and Optimization 48 (3) 1977 (2009)
DOI: 10.1137/070710846
See this article
An evolutionary topology optimization approach with variationally controlled growth
Dustin R. Jantos, Philipp Junker and Klaus Hackl
Computer Methods in Applied Mechanics and Engineering 310 780 (2016)
DOI: 10.1016/j.cma.2016.07.022
See this article
An alternative truly-mixed formulation to solve pressure load problems in topology optimization
Matteo Bruggi and Carlo Cinquini
Computer Methods in Applied Mechanics and Engineering 198 (17-20) 1500 (2009)
DOI: 10.1016/j.cma.2008.12.009
See this article
Undercut and overhang angle control in topology optimization: A density gradient based integral approach
Xiaoping Qian
International Journal for Numerical Methods in Engineering 111 (3) 247 (2017)
DOI: 10.1002/nme.5461
See this article
A numerical convergence study regarding homogenization assumptions in phase field modeling
B. Kiefer, T. Furlan and J. Mosler
International Journal for Numerical Methods in Engineering (2017)
DOI: 10.1002/nme.5547
See this article
Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition
Shiwei Zhou and Michael Yu Wang
Structural and Multidisciplinary Optimization 33 (2) 89 (2006)
DOI: 10.1007/s00158-006-0035-9
See this article
Structural optimization using sensitivity analysis and a level-set method
Grégoire Allaire, François Jouve and Anca-Maria Toader
Journal of Computational Physics 194 (1) 363 (2004)
DOI: 10.1016/j.jcp.2003.09.032
See this article
Two-scale dynamic optimal design of composite structures in the time domain using equivalent static loads
B. Xu, X. Huang and Y.M. Xie
Composite Structures 142 335 (2016)
DOI: 10.1016/j.compstruct.2016.01.090
See this article
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Joshua D. Deaton and Ramana V. Grandhi
Structural and Multidisciplinary Optimization 49 (1) 1 (2014)
DOI: 10.1007/s00158-013-0956-z
See this article
Phase field method to optimize dielectric devices for electromagnetic wave propagation
Akihiro Takezawa and Mitsuru Kitamura
Journal of Computational Physics 257 216 (2014)
DOI: 10.1016/j.jcp.2013.09.051
See this article
A binary level set model and some applications to Mumford-Shah image segmentation
J. Lie, M. Lysaker and Xue-Cheng Tai
IEEE Transactions on Image Processing 15 (5) 1171 (2006)
DOI: 10.1109/TIP.2005.863956
See this article
Optimal design of multiphase composites under elastodynamic loading
Rouhollah Tavakoli
Computer Methods in Applied Mechanics and Engineering 300 265 (2016)
DOI: 10.1016/j.cma.2015.11.026
See this article
Topology optimization of 3D structures with design-dependent loads
Hui Zhang, Shu-Tian Liu and Xiong Zhang
Acta Mechanica Sinica 26 (5) 767 (2010)
DOI: 10.1007/s10409-010-0370-3
See this article
Topology Optimization in Aircraft and Aerospace Structures Design
Ji-Hong Zhu, Wei-Hong Zhang and Liang Xia
Archives of Computational Methods in Engineering 23 (4) 595 (2016)
DOI: 10.1007/s11831-015-9151-2
See this article
Level-set methods for structural topology optimization: a review
N. P. van Dijk, K. Maute, M. Langelaar and F. van Keulen
Structural and Multidisciplinary Optimization 48 (3) 437 (2013)
DOI: 10.1007/s00158-013-0912-y
See this article
Sharp Interface Limit for a Phase Field Model in Structural Optimization
Luise Blank, Harald Garcke, Claudia Hecht and Christoph Rupprecht
SIAM Journal on Control and Optimization 54 (3) 1558 (2016)
DOI: 10.1137/140989066
See this article
Methods for Reliable Topology Changes for Perimeter-Regularized Geometric Inverse Problems
Benjamin Hackl
SIAM Journal on Numerical Analysis 45 (5) 2201 (2007)
DOI: 10.1137/060652208
See this article
Stress-constrained topology optimization with design-dependent loading
Edmund Lee, Kai A. James and Joaquim R. R. A. Martins
Structural and Multidisciplinary Optimization 46 (5) 647 (2012)
DOI: 10.1007/s00158-012-0780-x
See this article
Topology and shape optimization methods using evolutionary algorithms: a review
David J. Munk, Gareth A. Vio and Grant P. Steven
Structural and Multidisciplinary Optimization 52 (3) 613 (2015)
DOI: 10.1007/s00158-015-1261-9
See this article
Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum
Shengfeng Zhu, Chunxiao Liu and Qingbiao Wu
Computer Methods in Applied Mechanics and Engineering 199 (45-48) 2970 (2010)
DOI: 10.1016/j.cma.2010.06.007
See this article
Optimal Fine-Scale Structures in Compliance Minimization for a Shear Load
Robert V. Kohn and Benedikt Wirth
Communications on Pure and Applied Mathematics 69 (8) 1572 (2016)
DOI: 10.1002/cpa.21589
See this article
Optimal fine-scale structures in compliance minimization for a uniaxial load
R. V. Kohn and B. Wirth
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470 (2170) 20140432 (2014)
DOI: 10.1098/rspa.2014.0432
See this article
PolyTop++: an efficient alternative for serial and parallel topology optimization on CPUs & GPUs
Leonardo S. Duarte, Waldemar Celes, Anderson Pereira, Ivan F. M. Menezes and Glaucio H. Paulino
Structural and Multidisciplinary Optimization 52 (5) 845 (2015)
DOI: 10.1007/s00158-015-1252-x
See this article
Structural topology optimization with design-dependent pressure loads
Cunfu Wang, Min Zhao and Tong Ge
Structural and Multidisciplinary Optimization 53 (5) 1005 (2016)
DOI: 10.1007/s00158-015-1376-z
See this article
On piecewise constant level-set (PCLS) methods for the identification of discontinuous parameters in ill-posed problems
A De Cezaro, A Leitão and X-C Tai
Inverse Problems 29 (1) 015003 (2013)
DOI: 10.1088/0266-5611/29/1/015003
See this article
Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review
Liang Xia, Qi Xia, Xiaodong Huang and Yi Min Xie
Archives of Computational Methods in Engineering (2016)
DOI: 10.1007/s11831-016-9203-2
See this article
Large strain phase-field-based multi-material topology optimization
Mathias Wallin, Niklas Ivarsson and Matti Ristinmaa
International Journal for Numerical Methods in Engineering 104 (9) 887 (2015)
DOI: 10.1002/nme.4962
See this article
An Extension of the Projected Gradient Method to a Banach Space Setting with Application in Structural Topology Optimization
Luise Blank and Christoph Rupprecht
SIAM Journal on Control and Optimization 55 (3) 1481 (2017)
DOI: 10.1137/16M1092301
See this article
Phase-field based topology optimization with polygonal elements: a finite volume approach for the evolution equation
Arun L. Gain and Glaucio H. Paulino
Structural and Multidisciplinary Optimization 46 (3) 327 (2012)
DOI: 10.1007/s00158-012-0781-9
See this article
Topology optimization of a coupled thermal-fluid system under a tangential thermal gradient constraint
Xiaoping Qian and Ercan M. Dede
Structural and Multidisciplinary Optimization 54 (3) 531 (2016)
DOI: 10.1007/s00158-016-1421-6
See this article
Phase-field topology optimization model that removes the curvature effects
Tomohiro TAKAKI and Junji KATO
Mechanical Engineering Journal 4 (2) 16-00462 (2017)
DOI: 10.1299/mej.16-00462
See this article
New Trends in Shape Optimization
Harald Garcke and Claudia Hecht
International Series of Numerical Mathematics, New Trends in Shape Optimization 166 103 (2015)
DOI: 10.1007/978-3-319-17563-8_5
See this article
Topology optimization using a reaction–diffusion equation
Jae Seok Choi, Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki and Jeonghoon Yoo
Computer Methods in Applied Mechanics and Engineering 200 (29-32) 2407 (2011)
DOI: 10.1016/j.cma.2011.04.013
See this article
Finite strain topology optimization based on phase-field regularization
Mathias Wallin and Matti Ristinmaa
Structural and Multidisciplinary Optimization 51 (2) 305 (2015)
DOI: 10.1007/s00158-014-1141-8
See this article
Structural Optimization Based on the Phase Field Method : Validation of Perimeter Constraint Effect and Extension to Compliant Mechanism Design Problem and Eigen-Frequency Maximization Problem
Akihiro TAKEZAWA, Shinji NISHIWAKI and Mitsuru KITAMURA
Transactions of the Japan Society of Mechanical Engineers Series A 75 (760) 1784 (2009)
DOI: 10.1299/kikaia.75.1784
See this article
Design and testing for shape control of piezoelectric structures using topology optimization
Quantian Luo and Liyong Tong
Engineering Structures 97 90 (2015)
DOI: 10.1016/j.engstruct.2015.04.006
See this article
Morphology-based black and white filters for topology optimization
Ole Sigmund
Structural and Multidisciplinary Optimization 33 (4-5) 401 (2007)
DOI: 10.1007/s00158-006-0087-x
See this article
Multiscale Structural Topology Optimization
Multiscale Structural Topology Optimization 145 (2016)
DOI: 10.1016/B978-1-78548-100-0.50011-2
See this article
Structural topology optimization with design-dependent pressure loads
Edmund Lee and Joaquim R.R.A. Martins
Computer Methods in Applied Mechanics and Engineering 233-236 40 (2012)
DOI: 10.1016/j.cma.2012.04.007
See this article
Efficient variational constitutive updates for Allen–Cahn-type phase field theory coupled to continuum mechanics
Alexander Bartels and Jörn Mosler
Computer Methods in Applied Mechanics and Engineering 317 55 (2017)
DOI: 10.1016/j.cma.2016.11.024
See this article
Shape optimization with a level set based mesh evolution method
G. Allaire, C. Dapogny and P. Frey
Computer Methods in Applied Mechanics and Engineering 282 22 (2014)
DOI: 10.1016/j.cma.2014.08.028
See this article
Isogeometric Analysis for Topology Optimization with a Phase Field Model
Luca Dedè, Micheal J. Borden and Thomas J. R. Hughes
Archives of Computational Methods in Engineering 19 (3) 427 (2012)
DOI: 10.1007/s11831-012-9075-z
See this article
Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method
Hongling Ye, Ning Chen, Yunkang Sui and Jun Tie
Mathematical Problems in Engineering 2015 1 (2015)
DOI: 10.1155/2015/491084
See this article
Topology optimization of energy absorbing structures with maximum damage constraint
Lei Li, Guodong Zhang and Kapil Khandelwal
International Journal for Numerical Methods in Engineering (2017)
DOI: 10.1002/nme.5531
See this article
Topology optimization of slightly compressible fluids
A. Evgrafov
ZAMM 86 (1) 46 (2006)
DOI: 10.1002/zamm.200410223
See this article
Length scale and manufacturability in density-based topology optimization
Boyan S. Lazarov, Fengwen Wang and Ole Sigmund
Archive of Applied Mechanics 86 (1-2) 189 (2016)
DOI: 10.1007/s00419-015-1106-4
See this article
Topology optimization approaches
Ole Sigmund and Kurt Maute
Structural and Multidisciplinary Optimization 48 (6) 1031 (2013)
DOI: 10.1007/s00158-013-0978-6
See this article
A volumetric geometry and topology parameterisation for fluids-based optimisation
J. Hall, T.C.S. Rendall, C.B. Allen and D.J. Poole
Computers & Fluids 148 137 (2017)
DOI: 10.1016/j.compfluid.2017.02.005
See this article