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Abstract

Part one consists of seven chapters corresponding to seven lectures delivered. The first chapter gives general introduction to structural optimization, discusses typical objectives, design variables, constraints and equations of state. Chapter 2 applies the concept of local shell buckling to optimization of elastic shells under stability constraints. The remaining chapters are devoted to optimization with respect to plastic or creep buckling: trusses, columns, arches, plates and shells are optimized, in most cases with rheological properties of the material allowed for. The last chapter gives a short survey of recent results, obtained within the years 1984 – 1988.

Keywords

Optimal Design Design Variable Cylindrical Shell Structural Optimization Design Objective 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Prager, W.: Optimality criteria in structural design, Proc. Nat- Acad. Sci. USA 61 (1968), 3, 794 – 796.MathSciNetGoogle Scholar
  2. 2.
    Prager, W.: Conditions for structural optimality, Computers and Structures 2 (1972), 5, 833 – 840.Google Scholar
  3. 3.
    Prager, W. and J-E- Taylor: Problems of optimal structural design, Trans. ASME, J. Appl. Mech. 35 (1968), 1, 102 – 106.MATHGoogle Scholar
  4. 4.
    Berke, L. and V.B. Venkayyas Reviev of optimality criteria approaches in structural optimization, Proc. Struct. Optimiz. Symp, ASME, AMD 7 (1974), 23 – 34.Google Scholar
  5. 5.
    Save, H.A.: A general criterion for optimal structural design, J. Optimiz. Theory and Appl. 15 (1975), 1, 119 – 129.MATHMathSciNetGoogle Scholar
  6. 6.
    Fleury, C. and M. Geradin: Optimality criteria and mathematical programming in structural weight optimization, Comput. and Struct. 8 (1978), 7 – 17.MATHGoogle Scholar
  7. 7.
    Mróz, Z. and A. Mironov: Optimal design for global mechanical constraints, Arch. Mech. Stos. 32 (1980), 4, 505 – 516.MATHMathSciNetGoogle Scholar
  8. 8.
    Galileo Galilei Linceo: Discorsi e dimostrazioni maternatiche, Leiden 1638.Google Scholar
  9. 9.
    Gajewski, A. and M. Życzkowski: Optimal structural design under stability constraints, Kluwer — Nijhoff, Dordrecht 1988.MATHGoogle Scholar
  10. 10.
    Krzyś, W. and M. Życzkowski: Klasyfikaeja problemów kształtowania wytrzymałościowego, Czasopismo Techniczne 68 (1963), 2, 1 – 4.Google Scholar
  11. 11.
    Życzkowski, M.: Optimal structural design in rheology, J. Appl. Mech. 38 (1971), 1, 39 – 46.Google Scholar
  12. 12.
    Życzkowski, M. and A. Gajewski: Optimal structural design under stability constraints, Proc. IUTAM Symp. Collapse — the Buckling of Structures, London 1982, Cambridge Univ. Press 1983, 299 – 332.Google Scholar
  13. 13.
    Razani, R.: The behavior of the fully stressed design of structures and its relationship to minimum weight design, AIAA Journal 3 (1965), 12, 2262 – 2268.Google Scholar
  14. 14.
    Kicher, T.P.: Optimum design — minimum weight versus fully stressed, Proc. ASCE, J. Struct. Div. 92 (1966), 6, 265 – 279.Google Scholar
  15. 15.
    Reinschmidt, K., C.A. Cornell and J.F. Brotchie: Iterative design and structural optimization, Proc. ASCE, J. Struct. Div. 92 (1966), ST6, 281 – 318.Google Scholar
  16. 16.
    Malkov, V.P. and R.G. Strongin: Minimum weight design based on strength constraints (in Russian), Mietody Reshenya Zadach Uprugosti i Plastichnosti 4, Gorky 1971, 138 – 149.Google Scholar
  17. 17.
    Gallagher, R.H.: Fully stressed design, Optimum structural design: theory and applications, Wiley, New York 1973, 19 – 32.Google Scholar
  18. 18.
    Nemirovsky, Yu.V. and B.S. Reznikov: Beams and plates of uniform strength in creep conditions (in Russian), Mashinovedenye (1969), 2, 58 – 64.Google Scholar
  19. 19.
    Życzkowski, M. and W. Swisterski: Optimal structural design of flexible beams with respect to creep rupture time, Proc. IUTAM Symp. Structural Control, Waterloo 1979, North — Holland 1980, 795 – 810.Google Scholar
  20. 20.
    Drucker, D.C. and R.T. Shields Design for minimum weight, Proc. 9th Int. Congr. Appl. Mech., Brussels 1956, vol. 5 (1957), 212 – 222.Google Scholar
  21. 21.
    Drucker, D.C. and R.T. Shield: Bounds on minimum weight design, Quart. Appl. Math. 15 (1957), 269 – 281.MATHMathSciNetGoogle Scholar
  22. 22.
    Zavelani-Rossi, A.: Minimum — weight design for two -dimensional bodies, Meccanica 4 (1969), 4, 445 – 452.Google Scholar
  23. 23.
    Kordas, Z. and M. Życzkowski: Investigations of the shape of thick-walled non-circular cylinders showing full plasticization at the collapse, Bull. Acad. Pol., Ser. Sci. Techn. 18 (1970), 10, 839 – 847 (English extensive summary);Google Scholar
  24. 23a.
    Kordas, Z. and M. Życzkowski: Investigations of the shape of thick-walled non-circular cylinders showing full plasticization at the collapse, Rozpr. Inż. 18 (1970), 3, 371 – 390 (Polish full text).Google Scholar
  25. 24.
    Kordas, Z.: Problematyka określania ksztaltów ciał wykazujacych całkowite uplastycznienie w stadium zniszczenia, Zeszyty Naukowe Politechniki Krakowskiej, Podstawowe Nauki Techniczne 15 (1977).Google Scholar
  26. 25.
    Bochenek, B., Z. Kordas and M. Życzkowski: Optimal plastic design of a cross section under torsion with small bending, J. Struct. Mech. 11 (1983), 3, 383 – 400.Google Scholar
  27. 26.
    Skrzypek, J. and M. Życzkowski: Termination of processes of finite plastic deformations of incomplete toroidal shells, Solid Mech. Arch. 8 (1983), 1, 39 – 98.MATHGoogle Scholar
  28. 27.
    Szuwalski, K. and M. Życzkowski: On the phenomenon of decohesion in perfect plasticity, Int. J. Solid Struct. 9 (1973), 1, 85 – 98.Google Scholar
  29. 28.
    Wasiutyński, Z.: O kształtowaniu wytrzymałościowym, Akademia Nauk Technicznych, Warszawa 1939.Google Scholar
  30. 29.
    Prager, W.: Optimal structural design for given stiffness in stationary creep, Z. angew Math. Physik 19 (1968), 252 – 256.MATHGoogle Scholar
  31. 30.
    Niordson, F.: On the optimal design of a vibrating beam, Quart. Appl. Math. 23 (1965), 1, 47 – 53.MathSciNetGoogle Scholar
  32. 31.
    Olhoff, N.: A survey of the optimal design of vibrating structural elements. Shock and Vibration Digest 8 (1976), 8, 3 – 10; 9, 3 – 10.Google Scholar
  33. 32.
    Troitsky, V.A.: Optimization of elastic bars in the presence of free vibrations (in Russian), Izv. AN SSSR, Mekh. Tverd. Tela (1976), 3, 145 – 152.Google Scholar
  34. 33.
    Shanley, F.R.: Principles of structural design for minimum weight, J. Aero. Sci. 16 (1949), 3.Google Scholar
  35. 34.
    Shanley, F.R.: Weight — strength analysis of aircraft structures, McGraw-Hill, New York — Toronto — London 1952.Google Scholar
  36. 35.
    Spunt, L.: Optimum structural design, Prentice — Hall, Englewood Cliffs, N.J., 1971.Google Scholar
  37. 36.
    Neut, A., van der: The interaction of local buckling and column failure of thin-walled compression members, Proc. 12th Int. Congr. Appl. Mech. Stanford 1968, Springer 1969, 389 – 399.Google Scholar
  38. 37.
    Thompson, J.M.T.: Optimization as a generator of structural instability, Int. J. Mech. Sci. 14 (1972), 9, 627 – 629.Google Scholar
  39. 38.
    Thompson, J.M.T. and W.J. Supple: Erosion of optimum designs by compound branching phenomena, J. Mech. Phys. Solids 21 (1973), 3, 135 – 144.Google Scholar
  40. 39.
    Volmir, A.S.: Stability of elastic systems (in Russian), Fizmatgiz, Moskva 1963; Stability of deformable systems (in Russian), Nauka, Moskva 1967.Google Scholar
  41. 40.
    Życzkowski, M. and J. Kruzelecki: Optimal design of shells with respect to their stability, Proc. IUTAM Symp. Optimization in Structural Design, Warsaw 1973, Springer 1975, 229 – 247.Google Scholar
  42. 41.
    Prager, W.: Introduction to structural optimization, CISM Courses 212, Springer, Wien — New York 1974.MATHGoogle Scholar
  43. 42.
    Markiewicz, M.: Kształtowanie prostych ustrojów kratowych przy warunkach stateczności sprężysto — -plastycznej metodą wyznaczania konturu całkowitej niejednoznaczności, Rozpr. Inż. 28 (1980), 4, 569 – 584.MATHMathSciNetGoogle Scholar
  44. 43.
    Markiewicz, M. and M. Życzkowski: Contour of complete non-uniqueness as a method of structural optimization with stability constraints, J. Optimiz. Theory Appl. 35 (1981), 1, 23 – 30.MATHGoogle Scholar
  45. 44.
    Bürgermeister, G. and H. Steup: Stabilitätstheorie, Teil 1, Akademie — Verlag, Berlin 1957; Teil 2 (with H. Kretzschmar), Berlin 1963.Google Scholar
  46. 45.
    Wojdanowska, R. and M. Życzkowski: Optimal trusses transmitting a force to a given contour in creep conditions, Int. J. Mech. Sci. 26 (1984), 1, 21 – 28.MATHGoogle Scholar
  47. 46.
    Shtaerman, I.Ya.: Stability of shells (in Russian), Trudy Kievsk. Aviats. Instituta 1 (1936).Google Scholar
  48. 47.
    Rabotnov, Yu.N.: Local stability of shells (in Russian), Dokl. AN SSSR, Novaya Seria 52 (1946), 2, 111 – 112.MathSciNetGoogle Scholar
  49. 48.
    Shirshov, V.P.: Local stability of shells (in Russian), Trudy II Vsesoy. Konf. po Teorii Plastin i Obolochek, Lvov 1961, Kiev 1962, 314 – 317.Google Scholar
  50. 49.
    Axelrad, E.L: On local buckling of thin shells, Int. J. Non-Linear Mech. 20 (1985), 4, 249 – 259.MATHGoogle Scholar
  51. 50.
    Krużelecki, J.: Optimal design of a cylindrical shell under overall bending with axial force, Bull. Acad. Pol., Ser- Sci. Techn- 35 (1987) (English extensive summary); Rozpr. Inż. 33 (1985), 1/2, 135 – 149, (Polish full text).Google Scholar
  52. 51.
    Krużelecki, J.: Optimization of shells under combined loadings via the concept of uniform stability, Optimization of distributed parameter structures, Ed. by E.J. Haug and J. Cea, Nijhoff, Vol. II, 929 – 950 (1981).Google Scholar
  53. 52.
    Krużelecki, J. and M. Życzkowski: Optimal design of an elastic cylindrical shell under overal bending with torsion, Solid Mechanics Archives 9 (1984), 3, 269 – 306.Google Scholar
  54. 53.
    Krużelecki, J. and M. Życzkowski: Optimal structural design of shells — a survey, Solid Mechanics Archives 10 (1985), 2, 101 – 170.MATHGoogle Scholar
  55. 54.
    Pflüger, A.: Stabilitätsprobleme der Elastostatik, Springer, Berlin — Göttingen — Heidelberg 1950 (1964, 1975).MATHGoogle Scholar
  56. 55.
    Laasonen, P.: Nurjahdustuen edul1isimmasta poikipin-nanvalinnasta, Tekn- Aikakauslehti 38 (1948), 2, 49.Google Scholar
  57. 56.
    Krzyś, W.: Optimale Formen Bedrückter dünnwandiger Stützen im elastisch-plastischen Bereich, Wiss. Z. TU Dresden 17 (1968), 2, 407 – 410.Google Scholar
  58. 57.
    Krzyś, W.: Optimum design of thin — walled closed cross — section columns, Bull. Acad. Pol., Ser. Sci. Techn. 21 (1973), 8, 409 – 420.Google Scholar
  59. 58.
    Bleich, F.: Buckling strength of metal structures, McGraw-Hill, New York 1952.Google Scholar
  60. 59.
    Siegfried, W.: Failure from creep as influenced by the state of stress, J. Appl. Mech. 10 (1943), 4, 202 – 212.Google Scholar
  61. 60.
    Freudenthal, A.M.: Some time effects in structural analysis, Rep. 6th Int. Congr. Appl. Mech., Paris 1946.Google Scholar
  62. 61.
    Rzhanitsyn, A.R.: Deformation processes of structures consisting of viscoelastic elements, (in Russian), Dokl. AN SSSR 52 (1946), 25, 1.Google Scholar
  63. 62.
    Ross, A.D.: The effect of creep on instability and indeterminacy investigated by plastic models, Struct. Eng. 24 (1946), 413.Google Scholar
  64. 63.
    Wojdanowska, R.: Optimal design of weakly curved compressed bars with Maxwell type creep effects, Arch. Mech. Stos. 30 (1978), 6, 845 – 851.Google Scholar
  65. 64.
    Wojdanowska, R. and M. Życzkowski: On optimal imperfect columns subject to linear creep buckling, J. Appl. Mech. 47 (1980), 2, 438 – 439.Google Scholar
  66. 65.
    Kempner, J.: Creep bending and buckling of non-linearly viscoelastic columns, PIBAL Rep. No. 200, Brooklyn 1952; NACA TN 3137, Jan. 1954.Google Scholar
  67. 66.
    Hoff, N.J.: Buckling and stability, J. Roy. Aero. Sci. 58 (1954), 3 – 52.Google Scholar
  68. 67.
    Gerard, G.: A creep buckling hypothesis, J. Aero. Sci. 23 (1956), 9, 879 – 882.MATHMathSciNetGoogle Scholar
  69. 68.
    Rabotnov, Yu.N. (G.N.) and S.A. Shesterikovs Creep stability of columns and plates, Prikl. Mat. Mekh. 21 (1957), 3, 406 – 412 (Russian version);Google Scholar
  70. 68a.
    Rabotnov, Yu.N. (G.N.) and S.A. Shesterikovs Creep stability of columns and plates, Prikl. Mat. Mekh. J. Mech. Phys. Solids 6 (1957), 1, 27 – 34 (English version).MATHGoogle Scholar
  71. 69.
    Życzkowski, M. and R. Wojdanowska-Zając: Optimal structural design with respect to creep buckling, Proc. IUTAM Symp. Creep in Structures 2, Göteborg 1970, Springer 1972, 371 – 387.Google Scholar
  72. 70.
    Błachut, J. and M. Życzkowski: Bimodal optimal design of clamped-clamped columns under creep conditions, Int. J. Solids Struct. 20 (1984), 6, 571 – 577.MATHGoogle Scholar
  73. 71.
    Wróblewski, A.: Parametryczna optymalizacja prętów mimośrodowo ściskanych w nawiązaniu do teorii wyboczenia pełzającego Kempnera — Hoffa (in print).Google Scholar
  74. 72.
    Ṡwisterski, W., A. Wróblewski and M. Życzkowskis Geometrically non-linear eccentrically compressed columns of uniform creep strength vs. optimal columns, Int. J. Non-Linear Mech. 18 (1983), 4, 287 – 296.Google Scholar
  75. 73.
    Życzkowski, M. Recent results on optimal design in creep conditions, Euromech Coll. 164 on Optimization Methods in Structural Design, Siegen 1982, Bibliograph. Inst. Zürich 1983, 444 – 449.Google Scholar
  76. 74.
    Wróblewski, A. and M. Życzkowski: On multimodal optimization of circular arches against plane and spatial creep buckling, Structural Optimization 1 (1989), 2.Google Scholar
  77. 75.
    Kordas, Z.: Stability of the elastically clamped compressed bar in the general case of behaviour of the loading, Bull. Acad. Pol., Ser. Sci. Techn. 11 (1963), 419 – 428 (English extensive summary);Google Scholar
  78. 75a.
    Kordas, Z.: Stability of the elastically clamped compressed bar in the general case of behaviour of the loading, Rozpr. Inż. 11 (1963), 3, 435 – 448 (Polish full text).MATHGoogle Scholar
  79. 76.
    Bochenek, B. and A. Gajewski: Multimodal optimal design of a circular funicular arch with respect to in-plane and out-of-plane buckling, J. Struct. Mech. 14 (1986), 3, 257 – 274.Google Scholar
  80. 77.
    Wróblewski, A.: Optimal design of a circular plate with respect to creep buckling (in print).Google Scholar
  81. 78.
    Rysz, M. and M. Życzkowski: Optimal design of a cylindrical shell under overall bending and axial force with respect to creep stability. Structural Optimization 1 (1989), 1.Google Scholar
  82. 79.
    Haftka, R.T. and R.V. Grandhi: Structural shape optimization — a survey, 26th Struct. Dyn. and Mat. Conf., Part I, New York 1985, 617 – 628.Google Scholar
  83. 80.
    Levy, R. and O.E. Lev: Recent developments in structural optimization, Proc. ASCE, J. Struct. Engng. 113 (1987), 9, 1939 – 1962.Google Scholar
  84. 81.
    Życzkowski, M.: Optimal structural design under creep conditions, Mech. Teor. Stos. 24 (1986), 3, 243 – 258 (Polish version), Appl. Mech. Rev., 41 (1988), 12, 453 – 461 (English extended version).Google Scholar
  85. 82.
    Haftka, R.T. and M.P. Kamat: Elements of structural optimization, Nijhoff, Dordrecht 1985.MATHGoogle Scholar
  86. 83.
    Haug, E.J., K.K. Choi and V. Komkov: Design sensitivity analysis of structural systems, Academic Press, Orlando — San Diego — New York 1986.MATHGoogle Scholar
  87. 84.
    Save, M. and W. Prager: Structural optimization, Vol.1, Optimality criteria, Plenum Press, New York 1985.MATHGoogle Scholar
  88. 85.
    Banichuk, N.V.: Introduction to structural optimization (in Russian), Nauka, Moskva 1986.Google Scholar
  89. 86.
    Banichuk, N.V. and A.A. Barsuk: Application of spectral decomposition of eigenvalues in structural optimization under stability constraints (in Russian), Problemy Ustoych. i Pred. Nes. Sposobn. Konstruktsiy, Leningrad 1983, 17 – 24.Google Scholar
  90. 87.
    Bratus, A.S. and A.P. Seyranian: Bimodal solutions in optimization of eigenvalues (in Russian), Prikl. Mat. Mekh. 47 (1983), 4, 546 – 554.MathSciNetGoogle Scholar
  91. 88.
    Shin, Y.S., R.H. Plaut and R.T. Haftka: Simultaneous analysis and design for eigenvalue maximization, AIAA/ASME/ASCE/AHS 28th Struct., Struct. Dyn. and Mat. Conf., Monterey, 1987, New York 1987, 334 – 342.Google Scholar
  92. 89.
    Antman, S.S. and C.L. Adler: Design of material properties that yield a prescribed global buckling response, Trans. ASME, J. Appl. Mech. 54 (1987), 2, 263 – 266.MATHMathSciNetGoogle Scholar
  93. 90.
    Bushnell, D.: PANDA 2 — program for minimum weight design of stiffened, composite, locally buckled panels, Comp. and Struct. 25 (1987), 4, 469 – 605.MATHGoogle Scholar
  94. 91.
    Seyranian, A.P.: On a certain problem of Lagrange (in Russian), Izv. AN SSSR, Mekh. Tverd. Tela (1984), 2, 101 – 111.Google Scholar
  95. 92.
    Madsen, N.: Analytical determination of higher buckling modes for unimodal optimal columns, J. Struct. Mech. 11 (1984), 4, 545 – 560.MathSciNetGoogle Scholar
  96. 93.
    Olhoff, N.: Structural optimization by variational methods, Computer Aided Optimal Design, Proc. NATO Adv. Study Institute, Tróia 1986, Springer 1987, 87 – 164.Google Scholar
  97. 94.
    Efremov, A.Yu. and K.A. Matveev: Shape optimization of bars in stability problems (in Russian), Dinam. i Prochnost Aviats. Konstr., Novosibirsk 1986, 89 – 92.Google Scholar
  98. 95.
    Pfefferkorn, W.: Der dünnwandige Knickstab mit minimierter Masse, IfL — Mitteilungen 25 (1986), 3, 65 – 67.Google Scholar
  99. 96.
    Larichev, A.D.: Optimization of stability of thin-walled bars of open cross-section, (in Russian), Prikl. Probl. Prochn. Plastichn. (Gorky), 1986, No. 34, 97 – 103.Google Scholar
  100. 97.
    Mikulski, T. and C. Szymczak: Optymalne kształtowanie przekroju poprzecznego ściskanych pretów cienkościennych o przekroju otwartym, Zesz. Nauk. Polit. Gdańskiej 42 (1987), 73 – 92.Google Scholar
  101. 98.
    Hasegawa, A-, H. Abo, M. Mauroof and F. Nishino: A simplifiield analysis and optimality on the steel column behavior with local buckling, Proc. Jap. Soc. Eng. 1986, No. 374, 195 – 204.Google Scholar
  102. 99.
    Kartvelishvili, V.M.: On optimal solutions to a Prandtl’s problem (in Russian), Issled. po stroit. mekh. i nadezhn. konstr., Moskva 1986, 81 – 89.Google Scholar
  103. 100.
    Wang, C.M., V. Thevendran, K.L. Tea and S. Kitipornchai: Optimal design of tapered beams for maximum buckling strength, Eng. Struct. 8 (1986), 4, 276 – 284.Google Scholar
  104. 101.
    Vison, J.R.: Optimum design of composite honeycomb sandwich panels subjected to uniaxial compression, AIAA Journal 24 (1986), 10, 1690 – 1696.Google Scholar
  105. 102.
    Vinson, J.R.: Minimum weight web-core sandwich panels subjected to combined uniaxial compression and in-plane shear loads, AIAA/ASME/ASCE/AHS 28th Struct., Struct. Dyn. and Mat. Conf., Monterey 1987, New York 1987, 282 – 288.Google Scholar
  106. 103.
    Nakagiri, S. and H. Takabatake: Optimum design of FRP laminated plates under axial compression by use of the Hessian matrix, Proc. Int. Conf. Computer Mechanics ’86, Tokyo, Vol. 2, Tokyo 1986, X/71 – X/76.Google Scholar
  107. 104.
    Mróz, Z.: Sensitivity analysis and optimal design with account for varying shape and support conditions. Computer Aided Optimal Design, Proc. NATO Adv. Study Institute, Tróia 1986, Springer 1987, 407 – 438.Google Scholar
  108. 105.
    McGrattan, R.J.: Weight optimization of stiffened cylindrical panels, Trans. ASME, J. Pressure Vessel Techn. 109 (1987), 1, 1 – 9.Google Scholar
  109. 106.
    Błachut, J.: Optimal barrel — shaped shells under buckling constraints, AIAA Journal 25 (1987), 1, 186 – 188.Google Scholar

Copyright information

© Springer-Verlag Wien 1989

Authors and Affiliations

  • M. Zyczkowski
    • 1
  1. 1.Technical University of CracowCracowPoland

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