Structural shape and topology optimization based on level-set modelling and the element-propagating method

References

• Allaire , G. , Gournay , F. , Jouve , F. and Toader , A. M. 2005 . Structural optimization using topological and shape sensitivity via a level set method . Control and Cybernetics , 34 ( 1 ) : 59 – 81 .
   Web of Science ®Google Scholar
• Allaire , G. and Jouve , F. 2005 . A level-set method for vibration and multiple loads structural optimization . Computer Methods in Applied Mechanics and Engineering , 194 ( 30–33 ) : 3269 – 329 .
   Web of Science ®Google Scholar
• Allaire , G. , Jouve , F. and Toader , A. M. 2004 . Structural optimization using sensitivity analysis and a level set method . Journal of Computational Physics , 194 ( 1 ) : 363 – 393 .
   Web of Science ®Google Scholar
• Amstutz , S. and Andra , H. 2006 . A new algorithm for topology optimization using a level-set method . Journal of Computational Physics , 216 ( 2 ) : 573 – 588 .
   Web of Science ®Google Scholar
• Bendsoe , M. P. and Kikuchi , N. 1988 . Generating optimal topologies in structural design using a homogenization method . Computer Methods in Applied Mechanics and Engineering , 71 ( 2 ) : 197 – 224 .
   Web of Science ®Google Scholar
• Bendsoe , M. P. and Sigmund , O. 2003 . Topology optimization: Theory methods and applications , Berlin : Springer–Verlag .
   Google Scholar
• Bourdin , B. 2001 . Filters in topology optimization . International Journal for Numerical Methods in Engineering , 50 ( 9 ) : 2143 – 2158 .
   Web of Science ®Google Scholar
• Cea , J. , Garreau , S. , Guillaume , P. and Masmoudi , M. 2000 . The shape and topological optimizations connection . Computer Methods in Applied Mechanics and Engineering , 188 ( 4 ) : 713 – 726 .
   Web of Science ®Google Scholar
• Chen , J. , Shapiro , V. , Suresh , K. and Tsukanov , I. in press . Shape optimization with topological changes and parametric control . International Journal of Numerical Methods in Engineering ,
   Google Scholar
• Garreau , S. , Guillaume , P. and Masmoudi , M. 2001 . The topological asymptotic for PDE systems: The elasticity case . SIAM Journal on Control Optimization , 39 ( 6 ) : 1756 – 1778 .
   Web of Science ®Google Scholar
• Haug , E. J. , Choi , K. K. and Komkov , V. 1986 . Design sensitivity analysis of structural systems , Orlando : Academic Press .
   Google Scholar
• Liu , Z. , Korvink , J. G. and Huang , R. 2005 . Structure topology optimization: Fully coupled level set method via FEMLAB . Structural and Multidisciplinary Optimization , 29 ( 6 ) : 407 – 417 .
   Web of Science ®Google Scholar
• Luo , Z. , Wang , M. Y. , Wang , S. and Wei , P. in press . A level set-based parameterization method for structural shape and topology optimization . International Journal for Numerical Methods in Engineering ,
   Google Scholar
• Mei , Y. and Wang , X. 2004 . A level set method for structural topology optimization and its applications . Advances in Engineering Software , 35 ( 7 ) : 415 – 441 .
   Web of Science ®Google Scholar
• Nha , C. D. , Xie , Y. M. , Hira , A. and Steven , G. P. 1996 . Evolutionary structural optimization for problems with stiffness constraints . Finite Elements in Analysis and Design , 21 ( 4 ) : 239 – 251 .
   Google Scholar
• Novotny , A. A. , Feijoo , R. A. , Taroco , E. and Padra , C. 2003 . Topological sensitivity analysis . Computer Methods in Applied Mechanics and Engineering , 192 ( 9–10 ) : 803 – 829 .
   Google Scholar
• Osher , S. and Fedkiw , R. 2003 . Level set method and dynamic implicit surfaces , New York : Springer–Verlag .
   Google Scholar
• Osher , S. and Santosa , F. 2001 . Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum . Journal of Computational Physics , 171 ( 1 ) : 272 – 288 .
   Web of Science ®Google Scholar
• Osher , S. and Sethian , J. A. 1988 . Front propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations . Journal of Computational Physics , 79 ( 1 ) : 12 – 49 .
   Web of Science ®Google Scholar
• Pironneau , O. 1984 . Optimal design for elliptic systems , New York : Springer–Verlag .
   Google Scholar
• Rozvany , G. 2001 . Aims, scope, methods, history and unified terminology of computer aided topology optimization in structural mechanics . Structural and Multidisciplinary Optimization , 21 ( 2 ) : 90 – 108 .
   Web of Science ®Google Scholar
• Sethian , J. A. 1999 . Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision and materials science , Cambridge : Cambridge University Press .
   Google Scholar
• Sethian , J. A. and Wiegmann , A. 2000 . Structural boundary design via level set and immersed interface methods . Journal of Computational Physics , 163 ( 2 ) : 489 – 528 .
   Web of Science ®Google Scholar
• Shi , Y. and Karl , W. C. A fast level set method without solving PDEs . Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing . March 18–23 , Philadelphia, PA, USA. Vol. II , pp. 97 – 100 .
   Google Scholar
• Sigmund , O. 1997 . On the design of compliant mechanism using topology optimization . Mechanics of Structures and Machines , 25 ( 4 ) : 495 – 526 .
   Google Scholar
• Sigmund , O. 2001 . A 99 line topology optimization code written in Matlab . Structural and Multidisciplinary Optimization , 21 ( 2 ) : 120 – 127 .
   Web of Science ®Google Scholar
• Sigmund , O. and Petersson , J. 1998 . Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima . Structural Optimization , 16 ( 1 ) : 68 – 75 .
   Web of Science ®Google Scholar
• Sokolowski , J. and Zochowski , A. 1999 . On the topological derivative in shape optimization . SIAM Journal on Control Optimization , 37 ( 4 ) : 1251 – 1272 .
   Web of Science ®Google Scholar
• Sokolowski , J. and Zolesio , J. P. 1992 . Introduction to Shape Optimization: Shape Sensitivity Analysis , New York : Springer–Verlag .
   Google Scholar
• Steven , G. P. , Li , Q. and Querin , O. M. Some thoughts on the physics and mechanics of the evolutionary structural optimization process . 3rd ASMO UK/ISSMO Conference on Engineering Design Optimization . July 9–10 , Harrogate, North Yorkshire, UK. pp. 195 – 202 .
   Google Scholar
• Wang , M. Y. and Wang , S. 2005 . Bilateral filtering for structural topology optimization . International Journal for Numerical Methods in Engineering , 63 ( 13 ) : 1911 – 1938 .
   Web of Science ®Google Scholar
• Wang , M. Y. and Wang , X. 2004 . “Color” level sets: A multi–phase level set method for structural topology optimization with multiple materials . Computer Methods in Applied Mechanics and Engineering , 193 ( 6–8 ) : 469 – 496 .
   Web of Science ®Google Scholar
• Wang , M. Y. , Wang , X. and Guo , D. 2003 . A level set method for structural topology optimization . Computer Methods in Applied Mechanics and Engineering , 192 ( 1–2 ) : 227 – 246 .
   Web of Science ®Google Scholar
• Wang , S. and Wang , M. Y. 2006 . Radial basis function and level set method for structural topology optimization . International Journal for Numerical Methods in Engineering , 65 ( 12 ) : 2060 – 2090 .
   Web of Science ®Google Scholar
• Wang , X. , Wang , M. Y. and Guo , D. 2004 . Structural shape and topology optimization in a level-set-based framework of region representation . Structural and Multidisciplinary Optimization , 27 ( 1–2 ) : 1 – 19 .
   Web of Science ®Google Scholar
• Xia , Q. , Wang , M. Y. , Wang , S. and Chen , S. 2006 . Semi-Lagrange method for level-set-based structural topology and shape optimization . Structural and Multidisciplinary Optimization , 31 ( 6 ) : 419 – 429 .
   Web of Science ®Google Scholar
• Xie , Y. M. and Steven , G. P. 1997 . Evolutionary Structural Optimization , New York : Springer–Verlag .
   Google Scholar