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Novotny and de Souza Neto, E.A. and Feijóo, R.A.}, - journal = {Computer Methods in Applied Mechanics and Engineering}, - number = {5-8}, - pages = {727-739}, - title = {Sensitivity of the macroscopic thermal conductivity tensor to topological microstructural changes}, - volume = {198}, - year = {2009} -} - -@article{bb_Haber1996, - author = {Haber, R. and Jog, C. and Bendsoe, M.}, - day = {01}, - issn = {1615-1488}, - journal = {Structural Optimization}, - month = {Feb}, - number = {1}, - pages = {1-12}, - title = {A new approach to variable-topology shape design using a constraint on perimeter}, - volume = {11}, - year = {1996} -} - -@article{bb-Henrichsen2016, - author = {Henrichsen, Soren R and Weaver, Paul M and Lindgaard, Esben and Lund, Erik}, - journal = {International Journal for Numerical Methods in Engineering}, - number = {8}, - pages = {902-940}, - title = {Post-buckling optimization of composite structures using Koiter's method}, - volume = {108}, - year = {2016} -} - -@article{bb_Huang2010, - author = {Huang, X. and Xie, Y. M.}, - journal = {Structural Engineering and Mechanics}, - number = {5}, - pages = {581-595}, - title = {Evolutionary topology optimization of geometrically and materially nonlinear structures under prescribed design load}, - volume = {34}, - year = {2010} -} - -@book{bb_Huang2010book, - author = {Huang, X. and Xie, Y. M.}, - pages = {942–948}, - publisher = {Wiley}, - title = {Evolutionary Topology Optimization of Continuum Structures: Methods and Applications}, - year = {2010} -} - -@article{bb_Huang20102, - author = {Huang, Xiaodong and Xie, Yi Min}, - journal = {Structural and Multidisciplinary Optimization}, - pages = {671-683}, - title = {A further review of ESO type methods for topology optimization}, - volume = {41}, - year = {2010} -} - -@article{bb_Xie2010Evolutionary, - author = {X. Huang and Y. M. Xie}, - journal = {Structural and Multidisciplinary Optimization}, - number = {1-6}, - pages = {409-416}, - title = {Evolutionary topology optimization of continuum structures with an additional displacement constraint}, - volume = {40}, - year = {2010} -} - -@article{bb_Jog2001, - author = {Jog, C.}, - journal = {International Journal for Numerical Methods in Engineering}, - number = {July 1999}, - pages = {1607-1618}, - title = {A robust dual algorithm for topology design of structures in discrete variables}, - volume = {50}, - year = {2001} -} - -@article{bb_Jog2002, - author = {Jog, C. 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This paper presents a filter that incorporates the main characteristics of a generic AM process, and that can easily be included in conventional density-based topology optimization procedures. Use of this filter ensures that optimized designs comply with typical geometrical AM restrictions. Its performance is illustrated on compliance minimization problems, and a 2D Matlab implementation is provided.}, - author = {Langelaar, Matthijs}, - day = {01}, - doi = {10.1007/s00158-016-1522-2}, - issn = {1615-1488}, - journal = {Structural and Multidisciplinary Optimization}, - month = {Mar}, - number = {3}, - pages = {1--13}, - title = {An additive manufacturing filter for topology optimization of print-ready designs}, - url = {https://doi.org/10.1007/s00158-016-1522-2}, - volume = {55}, - year = {2016} -} - -@article{bb_Li2013A, - author = {Li, Ming and Gao, Shuming. and Zhang, Kai}, - journal = {Computer Methods in Applied Mechanics and Engineering}, - number = {2}, - pages = {89–103}, - title = {A goal-oriented error estimator for the analysis of simplified designs}, - volume = {255}, - year = {2013} -} - -@article{LIU2016Survey, - author = {Jikai Liu and Yongsheng Ma}, - journal = {Advances in Engineering Software}, - pages = {161-175}, - title = {A survey of manufacturing oriented topology optimization methods}, - volume = {100}, - year = {2016} -} - -@article{bb-Manktelow2013, - author = {Manktelow, Kevin L. and Leamy, Michael J. and Ruzzene, Massimo}, - journal = {Journal of the Mechanics and Physics of Solids}, - number = {12}, - pages = {2433--2453}, - title = {Topology design and optimization of nonlinear periodic materials}, - volume = {61}, - year = {2013} -} - -@article{bb_Mattheck1990A, - author = {Mattheck, C. and Burkhardt, S.}, - journal = {International Journal of Fatigue}, - number = {3}, - pages = {185-190}, - title = {A new method of structural shape optimization based on biological growth}, - volume = {12}, - year = {1990} -} - -@article{bb_Mei2007, - author = {Mei, Yu L. and Wang, Xiao Ming and Cheng, Gengdong}, - journal = {Applied Mathematics and Mechanics (English Edition)}, - number = {104060}, - pages = {707-719}, - title = {Binary discrete method of topology optimization}, - volume = {28}, - year = {2007} -} - -@inproceedings{bb-Niemann2012, - author = {Niemann, Steffen and Kolesnikov, Boris and Hühne, Christian and Querin, Osvaldo and Toropov, Vassili}, - booktitle = {Aircraft Structural Design Conference}, - title = {The Use of Topology Optimisation in the Conceptual Design of a Next Generation Lattice Composite Fuselage Structure}, - year = {2012} -} - -@inproceedings{bb-nithin2016, - author = {Sai Nithin Reddy K and Ian Ferguson and Mary Frecker and Timothy W. Simpson and Corey J. Dickman and Corey J. Dickman}, - booktitle = {ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference}, - title = {Topology optimization software for additive manufacturing: a review of current capabilities and a real-world example}, - year = {2016} -} - -@article{Oden2000Estimation, - author = {Oden, J. Tinsley and Vemaganti, Kumar S.}, - journal = {Journal of Computational Physics}, - number = {1}, - pages = {22-47}, - title = {Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials: I. 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N.}, - journal = {Structural and Multidisciplinary Optimization}, - number = {3}, - pages = {217-237}, - title = {A critical review of established methods of structural topology optimization}, - volume = {37}, - year = {2009} -} - -@article{bb-Ruan2012Global, - author = {Ning, Ruan and Gao, David Yang}, - journal = {Mathematics}, - title = {Global Optimal Solution to Discrete Value Selection Problem with Inequality Constraints}, - year = {2012} -} - -@book{Saad2003Iterative, - author = {Saad, Yousef}, - publisher = {SIAM}, - title = {Iterative Methods for Sparse Linear Systems, Second Edition}, - year = {2003} -} - -@article{bb_Sigmund1997, - author = {Ole Sigmund}, - journal = {Mechanics Based Design of Structures and Machines}, - number = {4}, - pages = {493-524}, - publisher = {Taylor & Francis}, - title = {On the Design of Compliant Mechanisms Using Topology Optimization}, - volume = {25}, - year = {1997} -} - -@article{bb_Sigmund1998, - author = {Sigmund, O. and Petersson, J.}, - doi = {10.1007/bf01214002}, - journal = {Structural Optimization}, - month = {aug}, - number = {1}, - pages = {68-75}, - publisher = {Springer Science and Business Media LLC}, - title = {Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima}, - url = {https://doi.org/10.1007%2Fbf01214002}, - volume = {16}, - year = {1998} -} - -@article{bb_Sigmund2012, - author = {Sigmund, Ole and Maute, Kurt}, - journal = {Structural and Multidisciplinary Optimization}, - number = {4}, - pages = {471-475}, - title = {Sensitivity filtering from a continuum mechanics perspective}, - volume = {46}, - year = {2012} -} - -@article{bb_Sokolowski99, - author = {Sokolowski, J. and Zochowski, A.}, - journal = {Structural Optimization}, - pages = {1251-1272}, - title = {On the topological derivative in shape optimization}, - volume = {37}, - year = {1999} -} - -@article{bb_Stolpe2003, - author = {Stolpe, M. and Svanberg, K.}, - journal = {International Journal for Numerical Methods in Engineering}, - number = {5}, - pages = {723-739}, - title = {Modelling topology optimization problems as linear mixed 0-1 programs}, - volume = {57}, - year = {2003} -} - -@article{bb_Stolpe2011, - author = {Stolpe, Mathias and Bendsoe, Martin P.}, - journal = {Structural and Multidisciplinary Optimization}, - number = {2}, - pages = {151-164}, - publisher = {Springer}, - title = {Global optima for the Zhou-Rozvany problem}, - volume = {43}, - year = {2011} -} - -@article{bb-Suresh2012, - author = {Suresh, Krishnan}, - journal = {Structural and Multidisciplinary Optimization}, - number = {1}, - pages = {49-61}, - title = {Efficient generation of large-scale pareto-optimal topologies}, - volume = {47}, - year = {2012} -} - -@article{bb_Suresh2010A, - author = {Suresh, Krishnan}, - journal = {Structural and Multidisciplinary Optimization}, - number = {5}, - pages = {665-679}, - title = {A 199-line Matlab code for Pareto-optimal tracing in topology optimization}, - volume = {42}, - year = {2010} -} - -@article{Svanberg1987Svanberg, - author = {Svanberg, Krister}, - doi = {10.1002/nme.1620240207}, - journal = {International Journal for Numerical Methods in Engineering}, - month = {feb}, - number = {2}, - pages = {359-373}, - publisher = {Wiley}, - title = {The method of moving asymptotes—a new method for structural optimization}, - url = {https://doi.org/10.1002%2Fnme.1620240207}, - volume = {24}, - year = {1987} -} - -@article{bb_Svanberg2006, - author = {K. 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Graph.}, - keywords = {energy minimization, flow visualization, image-based rendering, texture animation, texture synthesis}, - month = {July}, - number = {3}, - pages = {795--802}, - publisher = {ACM}, - title = {Texture Optimization for Example-based Synthesis}, - volume = {24}, - year = {2005} -} - -@article{Kopf:2007, - acmid = {1276380}, - address = {New York, NY, USA}, - author = {Kopf, Johannes and Fu, Chi-Wing and Cohen-Or, Daniel and Deussen, Oliver and Lischinski, Dani and Wong, Tien-Tsin}, - issn = {0730-0301}, - issue_date = {July 2007}, - journal = {ACM Trans. Graph.}, - keywords = {solid texture, texture synthesis}, - month = {July}, - number = {3}, - publisher = {ACM}, - title = {Solid Texture Synthesis from 2D Exemplars}, - volume = {26}, - year = {2007} -} - -@article{Chen:2010, - abstract = {The synthesis quality is one of the most important aspects in solid texture synthesis algorithms. In recent years several methods are proposed to generate high quality solid textures. However, these existing methods often suffer from the synthesis artifacts such as blurring, missing texture structures, introducing aberrant voxel colors, and so on. In this paper, we introduce a novel algorithm for synthesizing high quality solid textures from 2D exemplars. We first analyze the relevant factors for further improvements of the synthesis quality, and then adopt an optimization framework with the k-coherence search and the discrete solver for solid texture synthesis. The texture optimization approach is integrated with two new kinds of histogram matching methods, position and index histogram matching, which effectively cause the global statistics of the synthesized solid textures to match those of the exemplars. Experimental results show that our algorithm outperforms or at least is comparable to the previous solid texture synthesis algorithms in terms of the synthesis quality.}, - author = {Chen, Jiating -and Wang, Bin}, - day = {01}, - doi = {10.1007/s00371-009-0408-3}, - issn = {1432-2315}, - journal = {The Visual Computer}, - month = {Apr}, - number = {4}, - pages = {253--262}, - title = {High quality solid texture synthesis using position and index histogram matching}, - url = {https://doi.org/10.1007/s00371-009-0408-3}, - volume = {26}, - year = {2010} -} - -@article{Turner:2016, - author = {David M. Turner and Surya R. 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M.}, + journal = {Materials and Design}, + pages = {1023-1034}, + title = {Multi-scale design of composite materials and structures for maximum natural frequencies}, + volume = {51}, + year = {2013} +} + +@article{b20-Guo2014Stress, + author = {Guo, Xu and Zhang, Weisheng and Zhong, Wenliang}, + doi = {10.1016/j.cma.2013.10.003}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + number = {1}, + pages = {632-655}, + publisher = {Elsevier BV}, + title = {Stress-related topology optimization of continuum structures involving multi-phase materials}, + url = {https://doi.org/10.1016%2Fj.cma.2013.10.003}, + volume = {268}, + year = {2014} +} + +@article{Radman2014, + author = {Radman, A. and Huang, X. and Xie, Yimin}, + doi = {10.1016/j.commatsci.2014.04.064}, + journal = {Computational Materials Science}, + number = {91}, + pages = {266--273}, + publisher = {Elsevier BV}, + title = {Topological design of microstructures of multi-phase materials for maximum stiffness or thermal conductivity}, + url = {https://doi.org/10.1016%2Fj.commatsci.2014.04.064}, + volume = {91}, + year = {2014} +} + +@article{b22-Vogiatzis2016Topology, + title={Topology optimization of multi-material negative Poisson’s ratio metamaterials using a reconciled level set method}, + author={Vogiatzis, Panagiotis and Chen, Shikui and Wang, Xiao and Li, Tiantian and Wang, Lifeng}, + journal={Computer-Aided Design}, + volume={83}, + pages={15--32}, + year={2017}, + publisher={Elsevier} +} + +@article{b23-Asadpoure2017Topology, + title={Topology optimization of multiphase architected materials for energy dissipation}, + author={Asadpoure, Alireza and Tootkaboni, Mazdak and Valdevit, Lorenzo}, + journal={Computer Methods in Applied Mechanics and Engineering}, + volume={325}, + pages={314--329}, + year={2017}, + publisher={Elsevier} +} + +@article{bb_Xia2016Bi, + title={Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review}, + author={Xia, Liang and Xia, Qi and Huang, Xiaodong and Xie, Yi Min}, + journal={Archives of Computational Methods in Engineering}, + volume={25}, + number={2}, + pages={437--478}, + year={2018}, + publisher={Springer} +} + +@article{bb_Allaire2002A, + author = {Allaire, Gregoire and Jouve, Francois and Toader, Anca Maria}, + journal = {Comptes Rendus Mathematique}, + number = {12}, + pages = {1125-1130}, + title = {A level-set method for shape optimization}, + volume = {334}, + year = {2002} +} + +@article{bb-Ansola2007A, + author = {Ansola, Ruben and Vegueria,Estrella, A and Canales, Javier and Tarrago, Jose A.}, + journal = {Finite Elements in Analysis and Design}, + number = {1-2}, + pages = {53-62}, + title = {A simple evolutionary topology optimization procedure for compliant mechanism design}, + volume = {44}, + year = {2007} +} + +@article{bb-Arora1994, + author = {Arora, J. S. and Huang, M. W. and Hsieh, C. C.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {2-3}, + pages = {69-85}, + title = {Methods for optimization of nonlinear problems with discrete variables: A review}, + volume = {8}, + year = {1994} +} + +@article{bb_Beckers1999, + author = {Beckers, M.}, + journal = {Structural Optimization}, + number = {4}, + pages = {14-24}, + title = {Topology optimization using a dual method with discrete variales}, + volume = {17}, + year = {1999} +} + +@article{bb_Beckers2000, + author = {Beckers, Muriel}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {48}, + pages = {1761-1784}, + title = {Dual methods for discrete structural optimization problems}, + volume = {48}, + year = {2000} +} + +@article{Bends1995Optimization, + title={Optimization of structural topology, shape, and material}, + author={Bends{\o}e, Martin P}, + volume={414}, + year={1995}, + publisher={Springer} +} + +@article{bb-Benson2010, + author = {Benson, D.J. and Bazilevs, Y. and Hsu, M.C. and Hughes, T.J.R.}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + number = {5-8}, + pages = {276-289}, + title = {Isogeometric shell analysis: The Reissner–Mindlin shell}, + volume = {199}, + year = {2010} +} + +@article{bb_Browne2011, + title={A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints}, + author={Browne, PA and Budd, C and Gould, NIM and Kim, H Alicia and Scott, JA}, + journal={International Journal for Numerical Methods in Engineering}, + volume={92}, + number={12}, + pages={1026--1043}, + year={2012}, + publisher={Wiley Online Library} +} + +@article{bb_Bruns2002, + author = {Bruns, T. E. and Sigmund, O. and Tortorelli, D. A.}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {10}, + pages = {1215-1237}, + title = {Numerical methods for the topology optimization of structures that exhibit snap-through}, + volume = {55}, + year = {2002} +} + +@article{bb-Cai2014, + author = {Cai, Kun and Gao, David Yang and Qin, Qing H}, + journal = {Mathematics and mechanics of solids}, + number = {6}, + pages = {659-671}, + title = {Post-buckling solutions of hyper-elastic beam by canonical dual finite element method}, + volume = {19}, + year = {2014} +} + +@article{bb_Cai2015Stress, + author = {Cai, Shouyu and Zhang, Weihong}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + pages = {267-290}, + title = {Stress constrained topology optimization with free-form design domains}, + volume = {289}, + year = {2015} +} + +@article{bb-Cheng1981An, + author = {Cheng, Keng Tung and Olhoff, Niels}, + journal = {International Journal of Solids and Structures}, + number = {3}, + pages = {305-323}, + title = {An investigation concerning optimal design of solid elastic plates}, + volume = {17}, + year = {1981} +} + +@article{bb_Diaz1995, + author={Diaz, Alejandro and Sigmund, Ole}, + journal = {Structural Optimization}, + number = {1}, + pages = {40-45}, + publisher = {Springer}, + title = {Checkerboard patterns in layout optimization}, + volume = {10}, + year = {1995} +} + +@article{bb_VanDijk2013, + author = {van Dijk, N. P. and Maute, Kurt and Langelaar, M. and van Keulen, F.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {3}, + pages = {437-472}, + title = {Level-set methods for structural topology optimization: a review}, + volume = {48}, + year = {2013} +} + +@article{De2003Topological, + author = {De Faria, Jr and Novotny, Aa and Feijoo, Ra and Taroco, E and Padra, C}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + number = {7-8}, + pages = {803-829}, + title = {Topological sensitivity analysis}, + volume = {192}, + year = {2003} +} + +@article{bb-Gao2014Canonical, + author = {Gao, David Y and Ruan, Ning and Latorre, Vittorio}, + journal = {Mathematics and Mechanics of Solids}, + number = {3}, + title = {Canonical Duality-Triality Theory: Bridge Between Nonconvex Analysis/Mechanics and Global Optimization in Complex Systems}, + volume = {21}, + year = {2014} +} + +@article{bb_Giusti2009, + author = {Giusti, S.M. and A.A. Novotny and de Souza Neto, E.A. and Feij{\'o}o, R.A.}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + number = {5-8}, + pages = {727-739}, + title = {Sensitivity of the macroscopic thermal conductivity tensor to topological microstructural changes}, + volume = {198}, + year = {2009} +} + +@article{bb_Haber1996, + author = {Haber, R. and Jog, C. and Bendsoe, M.}, + day = {01}, + issn = {1615-1488}, + journal = {Structural Optimization}, + number = {1}, + pages = {1-12}, + title = {A new approach to variable-topology shape design using a constraint on perimeter}, + volume = {11}, + year = {1996} +} + +@article{bb-Henrichsen2016, + author = {Henrichsen, Soren R and Weaver, Paul M and Lindgaard, Esben and Lund, Erik}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {8}, + pages = {902-940}, + title = {Post-buckling optimization of composite structures using Koiter's method}, + volume = {108}, + year = {2016} +} + +@article{bb_Huang2010, + author = {Huang, X. and Xie, Y. M.}, + journal = {Structural Engineering and Mechanics}, + number = {5}, + pages = {581-595}, + title = {Evolutionary topology optimization of geometrically and materially nonlinear structures under prescribed design load}, + volume = {34}, + year = {2010} +} + +@book{bb_Huang2010book, + title={Evolutionary topology optimization of continuum structures: methods and applications}, + author={Huang, Xiaodong and Xie, Mike}, + year={2010}, + publisher={John Wiley and Sons} +} + +@article{bb_Huang20102, + author = {Huang, Xiaodong and Xie, Yi Min}, + journal = {Structural and Multidisciplinary Optimization}, + pages = {671-683}, + title = {A further review of {ESO} type methods for topology optimization}, + volume = {41}, + number = {5}, + publisher = {Springer}, + year = {2010} +} + +@article{bb_Xie2010Evolutionary, + author = {X. Huang and Y. M. Xie}, + journal = {Structural and Multidisciplinary Optimization}, + number = {1-6}, + pages = {409-416}, + title = {Evolutionary topology optimization of continuum structures with an additional displacement constraint}, + volume = {40}, + year = {2010} +} + +@article{bb_Jog2001, + author = {Jog, C.}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {July 1999}, + pages = {1607-1618}, + title = {A robust dual algorithm for topology design of structures in discrete variables}, + volume = {50}, + year = {2001} +} + +@article{bb_Jog2002, + author = {Jog, C. S.}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {7}, + pages = {1007-1019}, + title = {Topology design of structures using a dual algorithm and a constraint on the perimeter}, + volume = {54}, + year = {2002} +} + +@article{bb_kohn, + author = {Robert Kohn and G Strang}, + journal = {Communications on Pure and Applied Mathematics}, + pages = {113--137, 139--182, and 353--377}, + title = {Optimal design and relaxation of variational problems}, + volume = {39}, + year = {1986} +} + +@article{bb_Lang20161, + abstract = {Additive manufacturing (AM) offers exciting opportunities to manufacture parts of unprecedented complexity. Topology optimization is essential to fully exploit this capability. However, AM processes have specific limitations as well. When these are not considered during design optimization, modifications are generally needed in post-processing, which add costs and reduce the optimized performance. This paper presents a filter that incorporates the main characteristics of a generic AM process, and that can easily be included in conventional density-based topology optimization procedures. Use of this filter ensures that optimized designs comply with typical geometrical AM restrictions. Its performance is illustrated on compliance minimization problems, and a 2D Matlab implementation is provided.}, + author = {Langelaar, Matthijs}, + day = {01}, + doi = {10.1007/s00158-016-1522-2}, + issn = {1615-1488}, + journal = {Structural and Multidisciplinary Optimization}, + number = {3}, + pages = {1--13}, + title = {An additive manufacturing filter for topology optimization of print-ready designs}, + url = {https://doi.org/10.1007/s00158-016-1522-2}, + volume = {55}, + year = {2016} +} + +@article{bb_Li2013A, + author = {Li, Ming and Gao, Shuming. and Zhang, Kai}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + number = {2}, + pages = {89–103}, + title = {A goal-oriented error estimator for the analysis of simplified designs}, + volume = {255}, + year = {2013} +} + +@article{LIU2016Survey, + author = {Jikai Liu and Yongsheng Ma}, + journal = {Advances in Engineering Software}, + pages = {161-175}, + title = {A survey of manufacturing oriented topology optimization methods}, + volume = {100}, + year = {2016} +} + +@article{bb-Manktelow2013, + author = {Manktelow, Kevin L. and Leamy, Michael J. and Ruzzene, Massimo}, + journal = {Journal of the Mechanics and Physics of Solids}, + number = {12}, + pages = {2433--2453}, + title = {Topology design and optimization of nonlinear periodic materials}, + volume = {61}, + year = {2013} +} + +@article{bb_Mattheck1990A, + author = {Mattheck, C. and Burkhardt, S.}, + journal = {International Journal of Fatigue}, + number = {3}, + pages = {185-190}, + title = {A new method of structural shape optimization based on biological growth}, + volume = {12}, + year = {1990} +} + +@article{bb_Mei2007, + author = {Mei, Yu L. and Wang, Xiao Ming and Cheng, Gengdong}, + journal = {Applied Mathematics and Mechanics (English Edition)}, + number = {104060}, + pages = {707-719}, + title = {Binary discrete method of topology optimization}, + volume = {28}, + year = {2007} +} + +@article{niemann2013use, + title={The use of topology optimisation in the conceptual design of next generation lattice composite aircraft fuselage structures}, + author={Niemann, Steffen and Kolesnikov, Boris and Lohse-Busch, Heike and H{\"u}hne, Christian and Querin, Osvaldo M and Toropov, Vassili V and Liu, D}, + journal={The Aeronautical Journal}, + volume={117}, + number={1197}, + pages={1139--1154}, + year={2013}, + publisher={Cambridge University Press} +} + +@inproceedings{bb-nithin2016, + title={Topology optimization software for additive manufacturing: A review of current capabilities and a real-world example}, + author={Reddy K, Sai Nithin and Ferguson, Ian and Frecker, Mary and Simpson, Timothy W and Dickman, Corey J}, + booktitle={International Design Engineering Technical Conferences and Computers and Information in Engineering Conference}, + volume={50107}, + pages={V02AT03A029}, + year={2016}, + organization={American Society of Mechanical Engineers} +} + +@article{Oden2000Estimation, + author = {Oden, J. Tinsley and Vemaganti, Kumar S.}, + journal = {Journal of Computational Physics}, + number = {1}, + pages = {22-47}, + title = {Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials: I. Error estimates and adaptive algorithms}, + volume = {164}, + year = {2000} +} + +@article{Osher2004Level, + author = {Osher, Stanley and Fedkiw, Ronald}, + journal = {Applied Mechanics Reviews}, + number = {3}, + pages = {B15}, + title = {Level Set Methods and Dynamic Implicit Surfaces}, + volume = {57}, + year = {2003} +} + +@article{bb_Petersson1999, + author = {Petersson, J.}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + number = {1-2}, + pages = {123-140}, + title = {Some convergence results in perimeter-controlled topology optimization}, + volume = {171}, + year = {1999} +} + +@article{Qian2013Topology, + author = {Qian, Xiaoping}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + number = {3}, + pages = {15-35}, + title = {Topology optimization in B-spline space}, + volume = {265}, + year = {2013} +} + +@article{bb_Qian2017Undercut, + author = {Qian, Xiaoping}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {3}, + pages = {247--272}, + publisher = {Wiley Online Library}, + title = {Undercut and overhang angle control in topology optimization: A density gradient based integral approach}, + volume = {111}, + year = {2017} +} + +@article{bb_Rozvany2001, + author = {Rozvany, G.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {2}, + pages = {90-108}, + title = {Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics}, + volume = {21}, + year = {2001} +} + +@article{bb_Rozvany2009, + author = {Rozvany, George I. N.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {3}, + pages = {217-237}, + title = {A critical review of established methods of structural topology optimization}, + volume = {37}, + year = {2009} +} + +@article{bb-Ruan2012Global, + author = {Ning, Ruan and Gao, David Yang}, + journal = {Mathematics}, + title = {Global Optimal Solution to Discrete Value Selection Problem with Inequality Constraints}, + year = {2012} +} + +@book{Saad2003Iterative, + author = {Saad, Yousef}, + publisher = {SIAM}, + title = {Iterative Methods for Sparse Linear Systems, Second Edition}, + year = {2003} +} + +@article{bb_Sigmund1997, + author = {Ole Sigmund}, + journal = {Mechanics Based Design of Structures and Machines}, + number = {4}, + pages = {493-524}, + publisher = {Taylor and Francis}, + title = {On the Design of Compliant Mechanisms Using Topology Optimization}, + volume = {25}, + year = {1997} +} + +@article{bb_Sigmund1998, + author = {Sigmund, O. and Petersson, J.}, + doi = {10.1007/bf01214002}, + journal = {Structural Optimization}, + number = {1}, + pages = {68-75}, + publisher = {Springer Science and Business Media LLC}, + title = {Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima}, + url = {https://doi.org/10.1007%2Fbf01214002}, + volume = {16}, + year = {1998} +} + +@article{bb_Sigmund2012, + author = {Sigmund, Ole and Maute, Kurt}, + journal = {Structural and Multidisciplinary Optimization}, + number = {4}, + pages = {471-475}, + title = {Sensitivity filtering from a continuum mechanics perspective}, + volume = {46}, + year = {2012} +} + +@article{bb_Sokolowski99, + author = {Sokolowski, J. and Zochowski, A.}, + journal = {Structural Optimization}, + pages = {1251-1272}, + title = {On the topological derivative in shape optimization}, + number = {4}, + volume = {37}, + year = {1999} +} + +@article{bb_Stolpe2003, + author = {Stolpe, M. and Svanberg, K.}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {5}, + pages = {723-739}, + title = {Modelling topology optimization problems as linear mixed 0-1 programs}, + volume = {57}, + year = {2003} +} + +@article{bb_Stolpe2011, + author = {Stolpe, Mathias and Bendsoe, Martin P.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {2}, + pages = {151-164}, + publisher = {Springer}, + title = {Global optima for the Zhou-Rozvany problem}, + volume = {43}, + year = {2011} +} + +@article{bb-Suresh2012, + author = {Suresh, Krishnan}, + journal = {Structural and Multidisciplinary Optimization}, + number = {1}, + pages = {49-61}, + title = {Efficient generation of large-scale pareto-optimal topologies}, + volume = {47}, + year = {2012} +} + +@article{bb_Suresh2010A, + author = {Suresh, Krishnan}, + journal = {Structural and Multidisciplinary Optimization}, + number = {5}, + pages = {665-679}, + title = {A 199-line Matlab code for Pareto-optimal tracing in topology optimization}, + volume = {42}, + year = {2010} +} + +@article{bb_Svanberg2006, + author = {K. Svanberg and M. Werme}, + journal = {International Journal for Numerical Methods in Engineering}, + number = {12}, + pages = {1670-1699}, + title = {Topology optimization by a neighbourhood search method based on efficient sensitivity calculations}, + volume = {67}, + year = {2006} +} + +@article{bb_Svanberg2007, + author = {Svanberg, Krister and Werme, Mats}, + journal = {Structural and Multidisciplinary Optimization}, + number = {34}, + pages = {277-299}, + title = {Sequential integer programming methods for stress constrained topology optimization}, + volume = {34}, + year = {2007} +} + +@article{bb_Tovar2010, + author = {Tovar, A. and Khandelwal, Kapil}, + journal = {2nd International Conference on Engineering Optimization}, + pages = {1-10}, + title = {Uniqueness in linear and nonlinear topology optimization and approximate solutions}, + year = {2010} +} + +@article{XIA2014117, + title = {A reduced multiscale model for nonlinear structural topology optimization}, + journal = {Computer Methods in Applied Mechanics and Engineering}, + volume = {280}, + pages = {117-134}, + year = {2014}, + issn = {0045-7825}, + doi = {https://doi.org/10.1016/j.cma.2014.07.024}, + url = {https://www.sciencedirect.com/science/article/pii/S0045782514002564}, + author = {Liang Xia and Piotr Breitkopf} +} + +@article{bb_Young19993D, + author = {Young, V. and Querin, O. M. and Steven, G. P. and Xie, Y. M.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {2}, + pages = {183-192}, + title = {{3D} and multiple load case bi-directional evolutionary structural optimization ({BESO})}, + volume = {18}, + year = {1999} +} + +@article{bb_Zhao2017Self, + author = {Zhao, Dengyang and Li, Ming and Liu, Yusheng}, + journal = {arXiv.org}, + title = {Self-supporting Topology Optimization for Additive Manufacturing}, + year = {2017} +} + +@article{bb_Zhou20012, + author = {Zhou, M. and Shyy,, Y. K. and Thomas, H. L.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {1998}, + pages = {152-158}, + title = {Checkerboard and minimum member size control in topology optimization}, + volume = {21}, + year = {2001} +} + +@article{bb_Zhou2001, + author = {Zhou, M. and Rozvany, George I. N.}, + journal = {Structural and Multidisciplinary Optimization}, + number = {1}, + pages = {80-83}, + title = {On the validity of {ESO} type methods in topology optimization}, + volume = {21}, + year = {2001} +} + +@book{gao-book00, + author = {Gao, David Yang}, + pages = {477-478(2)}, + publisher = {Springer, Berlin}, + title = {Duality Principles in Nonconvex Systems}, + year = {2000} +} + +@article{gao-ruan-jogo10, + author = {Gao, David Yang and Ning, Ruan}, + journal = {Journal of Global Optimization}, + number = {3}, + pages = {463-484}, + title = {Solutions to quadratic minimization problems with box and integer constraints}, + volume = {47}, + year = {2010} +} + +@article{gao-jimo07, + author = {Gao, David Yang}, + journal = {Journal of Industrial and Management Optimization}, + number = {2}, + pages = {293-304}, + title = {Solutions and optimality criteria to box constrained nonconvex minimization problems}, + volume = {3}, + year = {2007} +} + +@article{gao-cs88, + author = {Gao, David Yang}, + journal = {Computers and Structures}, + number = {6}, + pages = {749-755}, + title = {Panpenalty finite element programming for plastic limit analysis}, + volume = {28}, + year = {1988} +} + +@article{gs-89, + author = {Gao, David Yang and Strang, Gilbert}, + journal = {Quarterly Applied Math}, + number = {3}, + pages = {487-504}, + title = {Geometric nonlinearity: Potential energy, complementary energy, and the gap function}, + volume = {47}, + year = {1989} +} + +@article{santos-gao, + author = {Santos, HAFA and Gao, David Yang}, + journal = {International Journal of Non-Linear Mechanics}, + number = {2}, + pages = {240-247}, + publisher = {Elsevier}, + title = {Canonical dual finite element method for solving post-buckling problems of a large deformation elastic beam}, + volume = {47}, + year = {2012} +} + +@article{gao-jem96, + author = {Gao, David Yang}, + journal = {Journal of engineering mathematics}, + number = {3}, + pages = {339-353}, + publisher = 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