Aims, Problems and Methods of Structural Optimization

  • G. I. N. Rozvany
Part of the International Centre for Mechanical Sciences book series (CISM, volume 325)

Abstract

The main aim of this course is to discuss
  • optimality criteria (OC) methods, and

  • shape and layout optimization

in structural design.

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References — Chapters 1–10

  1. Bendsoe, M.P. 1989: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193–202.CrossRefGoogle Scholar
  2. Berke, L.; Khot, N.S. 1987: Structural optimization using optimality criteria. In: Mota Soares, C.A. (Ed.) Computer aided optimal design: structural and mechanical systems, pp. 271–312. Springer-Verlag, Berlin.CrossRefGoogle Scholar
  3. Berke, L.; Khot, N.S. 1988: Performance characteristics of optimality criteria methods. In: Rozvany, G.I.N.; Karihaloo, B.L. (Eds.) Structural optimization (Proc. IUTAM Symposium, Melbourne, 1988 ), pp. 39–46. Kluwer, Dordrecht.Google Scholar
  4. Cheng, K.-T.; Olhoff, N. 1981: An investigation concerning optimal design of solid elastic plates. Int. J. Solids Struct. 17, 305–323.CrossRefMATHMathSciNetGoogle Scholar
  5. Foulkes, J. 1954: The minimum-weight design of structural frames. Proc. Royal Soc. 223, No. 1155, 482–494.CrossRefMathSciNetGoogle Scholar
  6. Hemp, W.S. 1973: Optimum Structures. Clarendon, Oxford.Google Scholar
  7. Hegemier, G.A.; Prager, W. 1969: On Michell trusses. Int. J. Mech. Sci. 11, 209–215.CrossRefMATHGoogle Scholar
  8. Heyman, J. 1959: On the absolute minimum weight design of framed structures. Quart. J. Mech. Appl. Math. 12, 3, 314–324.CrossRefMATHMathSciNetGoogle Scholar
  9. Hill, R.H.; Rozvany, G.I.N. 1977: Optimal beam layouts: the free edge paradox. J. Appl. Mech. 44, 696–700.CrossRefGoogle Scholar
  10. Hill, R.H.; Rozvany, G.I.N. 1985: Prager’s layout theory: a nonnumeric computer method for generating optimal structural configurations and weight-influence surfaces. Comp. Meth. Appl. Mech. Engrg. 49, 1, 131–148.CrossRefMATHGoogle Scholar
  11. Kirsch, U. 1989: On the relationship between structural topologies and geometries. Struct. Optim. 2, 39–45.CrossRefGoogle Scholar
  12. Kirsch, U.; Rozvany, G.I.N. 1992: Design considerations in the optimization of structural topologies. In: Rozvany, G.I.N. (Ed.) Proc. NATO/DFG ASI, Optimization of large structural systems (held 23 September - 4 October 1991, Berchtesgaden). Kluwer, Dordrecht.Google Scholar
  13. Kohn, R.V.; Strang, G. 1986: Optimal design and relaxation of variational problems, I, II and III. Comm. Pure Appl. Math. 39, 113–137.CrossRefMATHMathSciNetGoogle Scholar
  14. Kozlowski, W.; Mr6z, Z. 1969: Optimal design of solid plates. Int. J. Solids Struct. 5, 8, 781–794.CrossRefGoogle Scholar
  15. Lagache, J.-M. 1981: Developments in Michell theory. In: Atrek, E.; Gallagher, R.H. (Eds.) Proc. Int. Symp. on Optimum Structural Design (held in Tucson, Oct. 1981), pp. 4.9–4. 16. University of Arizona, Tucson.Google Scholar
  16. Lurie, K.A.; Cherkaev, A.V. 1983: Optimal structural design and relaxed controls. Opt. Control Appl. Meth. 4, 4, 387–392.CrossRefMATHGoogle Scholar
  17. Lurie, K.A.; Cherkaev, A.V. 1984: G-Closure of a set of anisotropically conducting media in the two-dimensional case. J. Optimiz. Theory Appl. 42, 2, 283–304.CrossRefMATHMathSciNetGoogle Scholar
  18. Lurie, K.A.; Cherkaev, A.V. 1984: Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportions. Proc. Roy. Soc. Edinburgh 99 A, 71–87.Google Scholar
  19. Lurie, K.A.; Cherkaev, A.V. 1984: G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates. J. Opt. Theory Appl. 42, 2, 305–316.CrossRefMATHMathSciNetGoogle Scholar
  20. Lurie, K.A.; Cherkaev, A.V.; Fedorov, A.V. 1982: Regularization of optimal design problems for bars and plates. J. Optimiz. Theory Appl. 37, 4, 499–522, 523–543.Google Scholar
  21. Lurie, K.A.; Fedorov, A.V.; Cherkaev, A.V. 1984: On the existence of solutions for some problems of optimal design for bars and plates. J. Optimiz. Therory Appl. 42, 2, 247–281.CrossRefMATHMathSciNetGoogle Scholar
  22. Marcal, P.V.; Prager, W. 1964: A method of optimal plastic design. J. de Mécan. 3, 4, 509–530.Google Scholar
  23. Masur, E.F. 1970: Optimum stiffness and strength of elastic structures. J. Eng. Mech. ASCE 96, EM6, 1093–1106.Google Scholar
  24. Masur, E.F. 1975: Optimality in the presence of discreteness and discontinuity. In: Sawczuk, A.; Mr6z, Z. (Eds.) Optimization in structural design (Proc. IUTAM Symp. held in Warsaw, Aug. 1973), pp. 441–453, Springer-Verlag, Berlin.Google Scholar
  25. Maxwell, J.C. 1872: On reciprocal figures, frames and diagrams of force. Trans. Roy. Soc. Edinburgh 26, 1. Also in: Scientific Papers 2 ENiven, W.D. (Ed.), 1890] University Press, Cambridge, 174–177.Google Scholar
  26. Michell, A.G.M. 1904: The limits of economy of material in frame-structures. Phil. Mag. 8, 47, 589–597.CrossRefMATHGoogle Scholar
  27. Morley, C.T. 1966: The minimum reinforcement of concrete slabs. Int. J. Mech. Sci. 8, 305–319.CrossRefGoogle Scholar
  28. Mr6z, Z. 1963: Limit analysis of plastic structures subject to boundary variations. Arch. Mech. Stott. 15, 1, 63–76.Google Scholar
  29. Murat, F.; Tartar, L. 1985: Calcul des variations et homogénéisation. In: Les méthodes de l’homogénéisation: théorie et applications en physique. Coll. del la Dir. des Etudes et recherches de Elec. de France, Eyrolles, Paris, pp. 319–370.Google Scholar
  30. Nagetegaal, J.C.; Prager, W. 1973: Optimal layout of a truss for alternative loads. Int. J. Mech. Sci 15, 7, 583–592.CrossRefGoogle Scholar
  31. Olhoff, N.; Rozvany, G.I.N. 1982: Optimal grillage layout for given Natural frequency. J. Engrg. Mech. ASCE 108, EM5, 971–975.Google Scholar
  32. Ong. T.G. 1987: Structural optimization via static-kinematic optimality criteria. Ph. D Thesis, Monash Univ., Melbourne, Australia.Google Scholar
  33. Ong T.G.; Rozvany, G.I.N.; Szeto, W.T. 1988: Least weight design for perforated elastic plates for given compliance: non-zero Poisson’s ratio. Comp. Meth. Appl. Mech. Engrg. 66, 301–322.CrossRefMATHGoogle Scholar
  34. Prager, W. 1974: Introduction to structural optimization. (Course held Int. Centre for Mech. Sci. Udine. CSIM 212 ) Springer-Verlag, Vienna.Google Scholar
  35. Prager, W.; Rozvany, G.I.N. 1977: Optimization of structural geometry. In: Bednarek, A.R.; Cesari, L. (Eds.) Dynamical systems. Academic Press, New York.Google Scholar
  36. Prager, W,: Shield, R.T. 1967: A general theory of optimal plastic design. J. Appl. Mech. 34, 1, 184–186.Google Scholar
  37. Prager, W.; Taylor, J. 1968: Problems of optimal structural design. J. Appl. Mech. 35, 102–106.MATHGoogle Scholar
  38. Prager, W.; Rozvany, G.I.N. 1977: Optimal layout of grillages. J. Struct. Mech. 5, 1, 1–18.CrossRefGoogle Scholar
  39. Rozvany, G.I.N. 1974: Analytical treatment of some extended problems in structural optimization, Part II. J. Struct. Mech. 3, 4, 387–402.CrossRefGoogle Scholar
  40. Rozvany, G.I.N. 1976: Optimal design of flexural systems. Pergamon Press, Oxford. Russian translation: Stroiizdat, Moscow, 1980.Google Scholar
  41. Rozvany, G.I.N. 1977: New trends in structural optimization. Proc. 6th Australian Conf. Mech. Struct. Mater. (held in Christchurch, New Zealand ), Univ. Canterbury, pp. 391–398.Google Scholar
  42. Rozvany, G.I.N. 1979: Optimal beam layouts: allowance for cost of shear. Comp. Meth. Appl. Mech. Engrg. 19, 1, 49–58.CrossRefMathSciNetGoogle Scholar
  43. Rozvany, G.I.N. 1981: Variational methods and optimality criteria. In: Haug, E.J.; Cea, J. (Eds.) Optimization of distributed parameter structures (Proc. NATO ASI held in Iowa City), pp. 82–111. Sijthof and Noordhof, Alphen aan der Rijn, The Netherlands.Google Scholar
  44. Rozvany, G.I.N. 1981: Optimal criteria for grids, shells and arches. In: Haug, E.J.; Cea, J. (Eds.) Optimization of distributed parameter structures (Proc. NATO ASI held in Iowa City), pp. 112–151. Sijthof and Noordhof, Alphen aan der Rijn, The Netherlands.Google Scholar
  45. Rozvany, G.I.N. 1984: Structural layout theory: the present state of knowledge. In: Atrek, E.; Gallagher, R.H.; Ragsdell, K.M.; Zienkiewicz, O.C. (Eds.) New directions in optimum structural design, pp. 167–195. Wiley dt Sons, Chichester, England.Google Scholar
  46. Rozvany, G.I.N. 1989: Structural design via optimality criteria (the Prager approach to structural optimization). Kluwer, Dordrecht.CrossRefMATHGoogle Scholar
  47. Rozvany, G.I.N.; Booz, W.; Ong, T.G. 1987: Optimal layout theory: multiconstraint elastic design. In: Teo, K.L.; Paul, H.; Chew, C.L.; Wang, C.M. 1987: Proc. Int. Conf. on Optimization: Techniques and Applications (held in Singapore, April 1987), pp. 138–151. Nat. Univ. Singapore.Google Scholar
  48. Rozvany, G.I.N.; Gollub, W. 1990: Michell layouts for various combinations of line supports, Part I. Int. J. Mech. Sei. 32, 1021–1043.CrossRefMATHGoogle Scholar
  49. Rozvany, G.I.N.; Gollub, W.; Zhou, M. 1989: Optimal design of large discretized systems by iterative otimality criteria methods. In: Topping, B.H.V. (Ed.) Proc. NATO ASI, Optimization and decision support systems in civil engineering (held 25 June - 7 July 1989, Edinburgh). Kluwer, Dordrecht.Google Scholar
  50. Rozvany, G.I.N.; Gollub, W.; Zhou, M. 1989: Layout optimization in structural design. In: Topping, B.H.V. (Ed.) Proc. NATO ASI, Optimization and decision support systems in civil engineering (held 25 June - 7 July 1989, Edinburgh). Kluwer, Dordrecht.Google Scholar
  51. Rozvany, G.I.N.; Gollub, W.; Zhou, M. 1992: Michell layouts for various combinations of line supports, Part II (to be submitted to Int. J. Mech. Sci.).Google Scholar
  52. Rozvany, G.I.N.; Hill, R.H. 1976: General theory of optimal force transmission by flexure. Advances in Appl. Mech. 16, 184–308.Google Scholar
  53. Rozvany, G.I.N.; Hill, R.H. 1978: Optimal plastic design: superposition principles and bounds on the minimum cost. Comp. Meth. Appl. Mech. Engrg. 13, 2, 151–173.CrossRefMATHGoogle Scholar
  54. Rozvany, G.I.N.; Hill, R.H. 1978: A computer algorithm for deriving analytically and plotting optimal structural layout. In: Noor, A.K.; McComb, H.G. (Eds.) Trends in computerized analysis and synthesis (Proc. NASA/ASCE Symp. held in Washington D.C., Oct. 1978), pp. 295–300. Wiley, New York. Aslo: Comp. and Struct. 10, 1, 295–300.Google Scholar
  55. Rozvany, G.I.N.; Nakamura, H.; Kuhnell, B.T. 1980: Optimal archgrids: allowance for self-weight. Comp. Meth. Appl. Mech. Engrg. 24, 3, 287–304.CrossRefMATHGoogle Scholar
  56. Rozvany, G.I.N.; Olhoff, N.; Cheng, K.-T.; Taylor, J.E. 1982: On the solid plate paradox in structural optimization. DCAMM Report 212 June 1981 and J. Struct. Mech. 10, 1, 1–32.CrossRefMathSciNetGoogle Scholar
  57. Rozvany, G.I.N.; Ong, T.G. 1986: A general theory of optimal layouts for elastic structures. J. Engrg. Mech. Div. ASCE 112, 8, 851–857.CrossRefGoogle Scholar
  58. Rozvany, G.I.N.; Ong, T.G. 1986: Optimal plastic design of plates, shells and shellgrids. In: Bevilacqua, L.; Feijôo, R.; Valid, R. (Eds.) Inelastic behaviour of plates and shells (Proc. IUTAM Symp. held in Rio de Janeiro, August 1985 ), p. 357–384, Springer-Verlag, Berlin.Google Scholar
  59. Rozvany, G.I.N.; Ong, T.G. 1986: Update to “Analytical methods in structural optimization”. In: Steele, C.R.; Springer, G.S. (Eds.) Applied Mechanics Update, pp. 289–302, ASME, New York.Google Scholar
  60. Rozvany, G.I.N.; Ong, T.G. 1987: Minimum-weight plate design via Prager’s layout theory (Prager Memorial Lecture). In: Mota Soares (Ed.) Computer aided optimal design: structural and mechanical systems (Proc. NATO ASI held in Troia, Portugal, 1986 ), pp. 165–179, Springer-Verlag, Berlin.Google Scholar
  61. Rozvany, G.I.N.; Ong, T.G.; Olhoff, N.; Bendse, M.P.; Szeto, W.T.; Sandler, R.: Least-weight design of perforated elastic plates I and II. Int. J. Solids Struct. 23, 4, 521–536, 537–550.Google Scholar
  62. Rozvany, G.I.N.; Ong, T.G.; Sandler, R.; Szeto, W.T.; Olhoff, N.; Bendwie, M.P. 1987: Least-weight design of perforated elastic plates I. Int. J. of Solids Struct. 23, 4, 521–536.CrossRefMATHGoogle Scholar
  63. Rozvany, G.I.N.; Ong, T.G.; Sandler, R.; Szeto, W.T.; Olhoff, N.; Bendsoe, M.P. 1987: Least-weight design of perforated elastic plates II. Int. J. of Solids Struct. 23, 4, 537–550.CrossRefMATHGoogle Scholar
  64. Rozvany, G.I.N; Prager, W. 1976: Optimal design of partially discretized grillages. J. Mech. Phys. Solids 24, 2 /3, 125–136.CrossRefGoogle Scholar
  65. Rozvany, G.I.N.; Prager, W. 1979: A new class of structural optimization problems: optimal archgrids. Comp. Meth. Appl. Mech. Engrg. 19, 1, 127–150.CrossRefMATHMathSciNetGoogle Scholar
  66. Rozvany, G.I.N.; Rotthaus, M.; Spengemann, F.; Gollub, W.; Zhou, M. 1990: The Masur paradox. Mech. Struct. Mach. 18, 21–42.CrossRefGoogle Scholar
  67. Rozvany, G.I.N.; Wang, C.M. 1983: Constrained optimal layouts through Prager-Shield criteria. J. Engrg. Mech. Div. ASCE 109, 2, 648–653.CrossRefGoogle Scholar
  68. Rozvany, G.I.N.; Wang, C.M. 1983: On plane Prager-structures (I). Int. J. Mech. Sci. 25, 7, 519–527.CrossRefMATHGoogle Scholar
  69. Rozvany, G.I.N.; Wang, C.M. 1984: Optimal layout theory: allowance for selfweight. J. Engrg. Mech. Div. ASCE 110, EM1, 66–83.Google Scholar
  70. Rozvany, G.I.N.; Wang, C.M.; Dow, M. 1982: Prager structures: archgrids and cable networks of optimal layout. Comp. Meth. Appl. Mech. Engrg. 31, 1, 91–113.CrossRefMATHMathSciNetGoogle Scholar
  71. Rozvany, G.I.N.; Yep, K.M.; Sandler, R. 1984: Optimal design of long-span truss-grids. In: Nooshin, H. (Ed.) Proc. 3rd Int. Conf. on Space Structures (held at the University of Surrey, Guildford, Sept. 1984 ), pp. 689–694, Elsevier Appl. Sci. Publ., London.Google Scholar
  72. Rozvany, G.I.N.; Yep, K.M.; Sandler, R. 1986: Optimal layout of long-span truss-grids I. Int. J. of Solids Struct. 22, 2, 209–223.CrossRefMATHGoogle Scholar
  73. Rozvany, G.I.N.; Zhou, M.; Gollub, W. 1990: Continuum-type optimality criteria methods for large finite element systems with a displacement constraint. Part II. Struct. Optim. 2, 77–104.CrossRefGoogle Scholar
  74. Rozvany, G.I.N.; Zhou, M.; Gollub, W. 1991: Layout optimization in structural design. In: B.H.V. Topping (Ed.) Proc. NATO ASI, Optimization and decision support systems in civil engineering (held 25 June - 7 July 1989, Edinburgh). Kluwer, Dordrecht.Google Scholar
  75. Rozvany, G.I.N.; Zhou, M. 1991: A new direction in cross-section and layout optimization: the COC algorithm. In: Hernandez, S.; Brebbia, C.A. (Eds.) Proc. OPTI 91, Optimization of structural systems and industrial applications. Comp. Mech. Publ., Southampton.Google Scholar
  76. Rozvany, G.I.N.; Zhou, M. 1992: Continuum-based optimality criteria (COC) methods. In: Rozvany, G.I.N. (Ed.) Proc. NATO/DFG ASI, Optimization of large structural systems (held 23 September - 4 October 1991, Berchtesgaden). Kluwer, Dordrecht.Google Scholar
  77. Save, M. 1972: A unified formulation of the theory of optimal design with convex cost function. J. Struct. Mech. 1, 2, 267–276.CrossRefGoogle Scholar
  78. Shield, R.T. 1960: Plate design for minimum weight. Quart. Appl. Math. 18, 2, 131–144.MathSciNetGoogle Scholar
  79. Strang, G.; Kohn, R.V. 1986: Optimal design in elasticity and plasticity. Int. J. Num. Math. Eng. 22, 183–188.CrossRefMATHMathSciNetGoogle Scholar
  80. Spillers, W.R.; Lev. O. 1971: Design for two loading conditions. Int. J. Solids Struct. 7, 1261–1267.CrossRefMATHGoogle Scholar
  81. Wang, C.M. 1987: Optimization of multispan plane Prager-structures with variable support locations. J. Eng. Struct. 9, 157–161.CrossRefGoogle Scholar
  82. Wang, C.M.; Rozvany, G.I.N. 1983: On plane Prager-structures (II) — Non-parallel external loads and allowance for selfweight. Int. J. Mech. Sei. 25, 7, 529–541.Google Scholar
  83. Wang, C.M.; Rozvany, G.I.N.; Olhoff, N. 1984: Optimal plastic design of axesymmetric solid plates with a maximum thickness constraint. Comp. and Struct. 18, 4, 653–665.CrossRefMATHGoogle Scholar
  84. Zhou; M. 1990: Iterative continuum-type optimality criteria methods in structural optimization. Res. Report, Essen University.Google Scholar

Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • G. I. N. Rozvany
    • 1
  1. 1.Essen UniversityEssenGermany

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