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Original Articles

New Type of Optimal Topologies by Iterative Method

Pages 149-171 | Received 01 Aug 2004, Accepted 01 Dec 2004, Published online: 07 Feb 2007

REFERENCES

  • Adelman , H. M. , Narayanaswami , R. ( 1976 ). Resizing procedure for structure under combined mechanical and thermal loading . AIAA Journal 14 : 1484 – 1486 .
  • Barta , J. ( 1957 ). On the minimum weight of certain redundant structures . Acta Technica Academiae Scientiarum Hungarieae 18 : 67 – 76 .
  • Bendsoe , M. P. , Kikuchi , N. ( 1988 ). Generating optimal topologies in structural design using a homogenization method . Computer Methods in Applied Mechanical Engineering Structural Optimization 71 : 197 – 224 . [CROSSREF]
  • Bendsoe , M. P. (1989). Optimal shape design as a material distribution problem. Structural Optimization 1:193–202. [CROSSREF] [CSA]
  • Bendsoe , M. P. , Mota Soares , C. A. ( 1992 ). Topology design of structures . In: Proc. NATO ARW. Sesimbra, Portugal, Dordrecht : Kluwer .
  • Bendsoe , M. P. , Sigmund , O. ( 1999 ). Material interpolation schemes in topology optimization . Archive of Applied Mechanics 69 : 635 – 654 .
  • Bendsoe , M. P. , Sigmund , O. ( 2003 ). Topology Optimization Theory, Methods and Applications . Berlin : Springer .
  • Berke , L. ( 1970 ). An efficient approach to the minimum weight design of deflection limited design . AFFDL-TM-70-4-FDTR, Wright-Patterson AFB .
  • Berke , L. , Khot , N. S. ( 1974 ). Use of optimality criteria methods for large scale system . Agard Lecture Series 70 : 1 – 29 .
  • Chan , H. S. Y. ( 1963 ). Optimal Michell frameworks for three parallel forces . Report No. 167, College of Aeronautics , Cranfield , UK .
  • Chan , H. S. Y. ( 1964 ). Tabulation of some layouts and virtual displacement fields in the theory of michell optimal structures . Note No. 161, College of Aeronautics , Cranfield , UK .
  • Cheng , K. T. , Olhoff , N. ( 1981 ). An investigation concerning optimal design of solid elastic plates . International Journal of Solids and Structure 17 : 305 – 323 . [CROSSREF] [CSA]
  • Cilley , F. H. ( 1900 ). The exact design of statically determinate frameworks and exposition of its possibility but futility . ASME Transactions 43 : 353 – 407 .
  • Díaz , A. R. , Sigmund , O. ( 1995 ). Checkerboard patterns in layout optimization . Structural Optimization 10 : 40 – 45 . [CROSSREF] [CSA]
  • Fleury , C. , Sander , G. ( 1977 ). Relations between optimality criteria and mathematical programming in structural optimization. In: Proceedings of the USC Symposium on Applied Computer Methods in Engineering . Los Angeles , CA , Vol. 1 , pp. 507 – 520 .
  • Fleury , C. , Geradin , M. ( 1978 ). Optimality criteria and mathematical programming in structural weight optimization . Computer and Structures 8 : 7 – 17 . [CROSSREF]
  • Fleury , C. ( 1979 ). Structural weight optimization by dual methods of convex programming . Journal for Numerical Methods in Engineering 14 : 1761 – 1783 .
  • Fleury , C. , Schmit , L. A. ( 1980 ). Primal and dual methods in structural optimization . Journal of Structural Division ASCE 106 ( ST5 ): 1117 – 1133 .
  • Fleury , C. , Braibant , V. ( 1986 ). Structural optimization a new dual method using mixed variables . Journal of Numerical Methods in Engineering 23 : 409 – 428 .
  • Gallagher , R. H. (1973). Fully stressed design. In: Gallagher , R. H. Zienkiewicz , O. C. , eds. Optimum Structural Design Theory and Applications . London : Wiley, pp. 19–32.
  • Gáspár , Zs. , Lógó , J. , Rozvany , G. I. N. ( 2002 ). On design-dependent constraints and singular topologies . Structural and Multidisciplinary Optimization 24 ( 4 ): 338 – 342 . [CROSSREF]
  • Gellatly , R. A. , Gallagher , R. H. ( 1966 ). A procedure for automated minimum weight structural design, Part I, theoretical basis . Aeronautical Quarterly XVII : 216 – 230 .
  • Gellatly , R. A. , Berke , L. ( 1971 ). Optimal structural design. AFFDL-TM-70-165 .
  • Gellatly , R. A. , Berke , L. ( 1973 ). Optimality criterion based algorithms . In: Gallagher , R. H. , Zienkiewicz , O. C. , eds. Optimum Structural Design Theory and Applications . London : Wiley , pp. 33 – 49 .
  • Hegenier , G. A. , Prager , W. ( 1969 ). On Michell truss . International Journal of Mechanical Sciences 11 : 209 – 215 . [CROSSREF]
  • Jog , C. S. , Haber , R. B. ( 1996 ). Stability of finite elements models for distributed-parameter optimization and topology design . Computer Methods in Applied Mechanics and Engineering 130 : 203 – 226 . [CROSSREF] [CSA]
  • Kiusalaas , J. ( 1972 ). Minimum weight design of structures via optimality criteria . NASA-TN-D7115 .
  • Kaliszky , S. , Lógó , J. ( 1991 ). Optimal design of dynamically loaded reinforced concrete frames under displacement and rotation constraints . Structural Optimization 3 : 121 – 131 . [CROSSREF]
  • Khot , N. S. , Berke , L. , Venkayya , V. B. ( 1979 ). Comparison of optimality criteria algorithms for minimum weight design of structures . AIAA Journal 17 : 182 – 190 .
  • Lansing , W. , Dwyer , W. , Emerton , R. , Ranalli , E. ( 1971 ). Application of fully stressed design procedure to wing and empennage structures . Journal of Aircraft 8 : 683 – 688 .
  • Lewinski , T. , Zhou , M. , Rozvany , G. I. N. ( 1994 ). Extended exact least-weight truss layouts–Part II Cantilever with horizontal axis of symmetry . Journal of Mechanical Science 36 : 399 – 419 . [CROSSREF]
  • Lógó , J. , Ghaemi , M. ( 2002 July 15–19 ). Topology optimization by SIMP method . In: Galantay , A. , Szeidl , Gy. , eds. Proceedings of the 9th International Conference on Numerical Methods and Computational Mechanics . Miskolc , Hungary , pp. 165 – 166 .
  • Maute , K. , Swartz , S. , Ramm , E. ( 1998 ). Adaptive topology optimization of elastoplastic structures . Structural Optimization 15 : 81 – 91 . [CROSSREF]
  • Melchers , R. E. ( 2005 ). On extending the range of Michell-like optimal topologies structures . Structural and Multidisc. Optimization 29 : 85 – 92 . [CROSSREF]
  • Michell , A. G. M. ( 1904 ). The limits of economy of material in frames structures . Philosophical Magazine 8 : 589 – 597 .
  • Nagtegal , J. C. (1973). A new approach to optimal design of elastic structures. Computer Methods in Applied Mechanics and Engineering 2:255–264. [CROSSREF] [CSA]
  • Poulsen , T. A. ( 2002 ). A simple scheme to prevent checkerboard patterns and one node connected hinges in topology optimization . Structural and Multidisciplinary Optimization 24 : 396 – 399 . [CROSSREF]
  • Prager , W. , Shield , R. T. ( 1968 ). Optimal design of multi-purpose structures . Internarional Journal of Solids and Structures 4 ( 4 ): 469 – 475 . [CROSSREF]
  • Prager , W. , Taylor , J. E. ( 1968 ). Problems of optimal structural design . Journal of Applied Mechanics, ASME 35 : 122 – 106 .
  • Prager , W. ( 1970 ). Optimization of structural design . Journal of Optimization Theory and Application 6 ( 1 ): 1 – 21 . [CROSSREF]
  • Prager , W. ( 1972 ). Condition for optimality . Computers and Structures 2 : 833 – 840 . [CROSSREF]
  • Prager , W. , Rozvany , G. I. N. ( 1977 ). Optimal layout of grillages . Journal of Structural Mechanics 5 : 1 – 18 .
  • Rossow , M. P. , Taylor , J. E. ( 1973 ). A finite element method for the optimal design of variable thickness sheets . AIAA Journal 11 : 1566 – 1569 .
  • Rozvany , G. I. N. ( 1989 ). Structural Design via Optimality Criteria Dordrect : Kluwer Academic Publisher .
  • Rozvany , G. I. N. , Bendsoe , M. P. , Kirsh , U. ( 1995 ). Layout optimization of structures . Applied Mechanical Reviews 48 ( 2 ): 41 – 118 .
  • Rozvany , G. I. N. ( 1996 ). Some shortcomings in Michell's truss theory . Structural Optimization 12 : 244 – 250 . [CROSSREF]
  • Rozvany , G. I. N. ( 1997 ). Partial relaxation of the orthogonality requirement for classical michell structures . Structural Optimization 13 : 271 – 274 . [CROSSREF]
  • Rozvany , G. I. N. ( 1997 ). Optimization in Structural Mechanics . CISM Cources and Lectures Notes 374 . Vienna : Springer Verlag .
  • Rozvany , G. I. N. , Gollub , W. , Zhou , M. ( 1997 ). Exact Michell trusses for various combinations of line supports. Part II . Structural and Optimization 14 : 138 – 149 . [CROSSREF]
  • Rozvany , G. I. N. ( 1997 ). Aims, scope, basic concepts and methods of topology optimization , In: Rozvany , G. I. N. , ed. Topology Optimization in Structural Mechanics . Vienna : Springer , pp. 1 – 56 .
  • Rozvany , G. I. N. ( 2001 ). Stress ratio and compliance based methods in topology optimization—a critical review . Structural and Multidisciplinary Optimization 21 : 109 – 119 . [CROSSREF]
  • Rozvany , G. I. N. , Lógó , J. , Querin , O. M. (2004 August 15–21). New classes of analytically derived optimal topologies and their numerical confirmation. In XXI International Congress of Theoretical and Applied Mechanics Gutkowski , W. , Kowalewski , T. A. , eds. ICTAM04 Abstracts Book and CD-ROM Proceedings. IPPT PAN Warsaw, Poland.
  • Schmit , L. A. ( 1960 ). Structural design by systematic synthesis . ASCE Journal of Structural Engineering . In: Proceedings of the 2nd ASCE Conference on Electronic Computation . ASCE : Pittsburg , pp. 105 – 122 .
  • Schmit , L. A. , Farshi , B. ( 1974 ). Some approximation concepts for structural synthesis . AIAA Journal 12 : 692 – 699 .
  • Schmit , L. A. , Fleury , C. ( 1980a ). Structural synthesis by combining approximation concepts and dual method . AIAA Journal 18 : 1252 – 1254 .
  • Schmit , L. A. , Fleury , C. ( 1980b ). Discrete-continuous variable structural synthesis using dual method . AIAA Journal 18 : 1515 – 1524 .
  • Sheu , C. Y. , Prager , W. ( 1968a ). Recent development in optimal structural design . Applied Mechanical Revises 21 ( 10 ) 985 – 992 .
  • Sheu , C. Y. , Prager , W. ( 1968b ). Minimum weight design with piecewise constance specific stiffness . Journal of Optimization Theory and Application 2 ( 3 ) 179 – 186 . [CROSSREF]
  • Sigmund , O. , Petersson , J. ( 1998 ). Numerical instabilities in topology optimization—a survey on procedures dealing with checkerboards, mesh-dependencies and local minima . Structural Optimization 16 : 68 – 75 . [CROSSREF]
  • Taig , I. C. , Kerr , R. I. ( 1973 ). Optimization of aircraft structures with multiple stiffness requirements . AGARD-CP-12316 .
  • Taylor , J. E. ( 1967 ). Strongest column an energy approach . Journal of Applied Mechanics 89 ( 2 ) 486 – 487 .
  • Venkayya , V. B. , Khot , N. S. , Reddy , V. S. ( 1968 ). Optimization of structures based on the study of strain energy distribution . AFFDL-TR-68-150 .
  • Venkayya , V. B. , Khot , N. S. , Reddy , V. S. ( 1969 ). Energy distribution in an optimum structural design . AFFDL-TR-68-156 .
  • Venkayya , V. B. ( 1971 ). Design of optimum structures . Computers and Structures 1 : 265 – 309 . [CROSSREF]
  • Zhou , M. , Rozvany , G. I. N. ( 1991 ). The COC algorithm, Part II Topological, geometrical and generalized shape optimization . Computer Methods in Applied Mechanical Engineering 89 : 309 – 336 . [CROSSREF]
  • Zhou , M. , Rozvany , G. I. N. ( 1992/1993 ). DCOC An optimality criterion method for large systems. Part I theory. Part II algorithm . Structural Optimization 5 : 12 – 25 . [CROSSREF]
  • Zhou , M. , Shyy , Y. K. , Thomas , H. L. ( 2001 ). Checkerboard and minimum member size control in topology optimization . Structure and Multidisciplinary Optimization 21 : 152 – 158 . [CROSSREF]
  • #Communicated by S. Kaliszky.

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