Skip to main content
SpringerLink
Log in

Part III

  • Chapter
Structural Optimization under Stability and Vibration Constraints

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 308))

  • 149 Accesses

Abstract

Part III deals with problems of elastic optimal design of conservative mechanical systems with respect to fundamental and higher order eigenvalues. The structural eigenvalues are used as objective functions or applied as behavioural constraints. They identify, e.g., natural frequencies of axial or torsional vibrations of rods and bars, transverse vibrations of beams, critical whirling speeds of rotating shafts, or structural buckling loads. A unified variational formulation for optimal design of one-dimensional continuum systems with respect to simple fundamental eigenvalue is presented first, and this serves as a framework for a thorough discussion of extended problems involving optimization with respect to bi- or multimodal fundamental eigenvalues, and higher order eigenvalues.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Wasiutynski, Z. & Brandt, A.: Appl. Mech. Rev. 16, 344–350 (1963).

    Google Scholar 

  2. Sheu, C.Y. & Prager, W.: Appl. Mech. Rev. 21, 985–992 (1968).

    Google Scholar 

  3. Prager, W.: AGARD-Rept. No. 589 (1971).

    Google Scholar 

  4. Niordson, F.I. & Pedersen, P.: Proc. 13th Int. Cong. Th. Appl. Mech. Moscow, 264–278, Springer-Verlag (1973).

    Google Scholar 

  5. Rozvany, G.I.N. & Mröz, Z.: Appl. Mech. Rev. 10, 1461–1470 (1977).

    Google Scholar 

  6. Venkayya, V.B.: Int. J. Num. Meth. in Engrg. 13, 203–228 (1978).

    Google Scholar 

  7. Schmit, L.A.: AIAA J. 19, 1249–1263 (1981).

    Google Scholar 

  8. Lev, O.E.: American Society of Civil Engineers, New York (1981).

    Google Scholar 

  9. Haug, E.J.: In Ref. [23], 3–74 (1981).

    Google Scholar 

  10. Vanderplaats, G.N.: AIAA J. 20, 992–1000 (1982).

    MATH  MathSciNet  Google Scholar 

  11. Ashley, H.: J. Aircraft 19, 5–28 (1982).

    Google Scholar 

  12. Olhoff, N. & Taylor, J.E.: J. Appl. Mech. 50, 1139–1151 (1983)

    MATH  MathSciNet  Google Scholar 

  13. Levy, R. & Lev, O.E.: Proc. ASCE, J. Struct. Engrg. 113 1939–62 (1987).

    Google Scholar 

  14. Hemp, W.S.: Optimum Structures, Clarendon, Oxford (1973).

    Google Scholar 

  15. Gallagher, R.H. & Zienkiewicz, O.C.: Optimum Structural Design, John Wiley, New York (1973).

    MATH  Google Scholar 

  16. Prager, W.: Introduction to Structural Optimization, Springer-Verlag (1974).

    MATH  Google Scholar 

  17. Distefano, N.: Non-Linear Processes in Engineering, Academic Press, New York (1974).

    Google Scholar 

  18. Sawczuk, A. & Mroz, Z. (Eds.): Optimization in Structural Design, Springer-Verlag, Berlin (1975).

    Google Scholar 

  19. Rozvany, G.I.N.: Optimal Design of Flexural Systems, Pergamon, Oxford (1976). Russian version: Strojizdat, Moscow (1980).

    Google Scholar 

  20. Reitman, M.I. & Shapiro, G.B.: Methods of Optimal Design of Deformable Bodies (in Russian), Nauka, Moscow (1976).

    Google Scholar 

  21. Haug, E.J. & Arora, J.S.: Applied Optimal Design, John Wiley, New York (1979).

    Google Scholar 

  22. Grinev, W.B. & Filippov, A.P.: Optimization of Beams Governed by Eigenvalue Problems (in Russian), Naukova Dumka, Kiev (1979).

    Google Scholar 

  23. Haug, E.J. & Cea, J. (Eds.): Optimization of Distributed Parameter Structures, Sijthoff & Nordhoff, Netherlands (1981).

    MATH  Google Scholar 

  24. Kirsch, U.: Optimum Structural Design, McGraw-Hill, New York (1981).

    Google Scholar 

  25. Carmichael, D.G.: Structural Modelling and Optimization, Ellis Horwood Ltd., Chichester (1981).

    MATH  Google Scholar 

  26. Troitskij, W.A. & Petuchov, L.W.: Optimal Design of Elastic Bodies (in Russian), Nauka, Moscow (1982).

    Google Scholar 

  27. Lepik, Ü.: Optimal Design of Inelastic Structures Under Dynamic Loading (in Russian; Extended summary in English), Walgus, Tallinn (1982).

    Google Scholar 

  28. Morris, A.J. (Ed.): Foundations of Structural Optimization: A Unified Approach, Wiley, New York (1982).

    Google Scholar 

  29. Eschenauer, H. & Olhoff, N. (Eds.): Optimization Methods in Structural Design, Bibliographisches Institut, Mannheim, FRG (1983).

    MATH  Google Scholar 

  30. Haug, E.J., Choi, K.K. & Komkov, V.: Design Sensitivity Analysis of Structural Systems, Academic Press, New York (1983).

    Google Scholar 

  31. Banichuk, N.V.: Problems and Methods of Optimal Structural Design, Plenum Press, New York (1983).

    Google Scholar 

  32. Brandt, A.M.: Criteria and Methods of Structural Optimization, Nijhoff Publishers, The Hague (1984).

    Google Scholar 

  33. Atrek, E., Gallagher, R.H., Ragsdele, K.M. & Zienkiewicz, O.C. (Eds.): New Directions in Optimum Structural Design, Wiley, New York (1984).

    MATH  Google Scholar 

  34. Vanderplaats, G.A.: Numerical Optimization Techniques for Engineering Design, McGraw-Hill, New York (1984).

    MATH  Google Scholar 

  35. Haftka, R.T. & Kamat, M.P.: Elements of Structural Optimization, Nijhoff Publishers, The Hague (1985).

    MATH  Google Scholar 

  36. Soares, C.A.M. (Ed.): Computer Aided Optimal Design: Structural and Mechanical Systems, Springer-Verlag, Berlin (1987).

    MATH  Google Scholar 

  37. Gajewski, A. & Zyczkowski, M.: Optimal Structural Design under Stability Constraints, Kluwer Academic Publishers, Dordrecht, Netherlands (1988).

    MATH  Google Scholar 

  38. Rozvany, G.I.N.: Structural Design via Optimality Criteria, Kluwer Academic Publishers, Dordrecht, Netherlands (1989).

    MATH  Google Scholar 

  39. Lurie, K.A.: Applied Optimal Control of Distributed Systems, Plenum Press, New York (to appear).

    Google Scholar 

  40. Lagrange, J.L.: Miscellanea Taurinensia V, 123 (1770–1773).

    Google Scholar 

  41. Clausen, T.: Mélanges Mathématiques et Astronomiques I, 279–294 (1849–1853).

    Google Scholar 

  42. Keller, J.B.: Arch. Rat. Mech. Anal. 5 275–285 (1960).

    Google Scholar 

  43. Niordson, F.I.: Quart. Appl. Math. 23, 47–53 (1965).

    MathSciNet  Google Scholar 

  44. Ashley, H. & Mcintosh, S.C. Jr.: Proc. 12th Int. Cong. Th. Appl. Mech. (Ed. M. Hetényi & W.G. Vincenti), 100–113, Stanford, Springer-Verlag (1969).

    Google Scholar 

  45. Pierson, B.L.: Int. J. Num. Meth. Engrg. 4 491–499 (1972).

    Google Scholar 

  46. Reitman, M.I. & Shapiro, G.S.: All-Union Symp. “On the Problems of Optimization in Mech. of Solid Deformable Bodies”, Vilnius, USSR, June (1974).

    Google Scholar 

  47. Rao, S.S.: Shock Vib. Dig. 7, 61–70 (1975).

    Google Scholar 

  48. Olhoff, N.: Shock Vib. Dig. 8, No. 8, 3–10 (Part I: Theory), 8, No. 9 3–10 (Part II: Applications (1976).

    Google Scholar 

  49. Olhoff, N.: Proc. 15th Int. Cong. Th. Appl. Mech., Toronto, Canada, 133–149, North-Holland (1980).

    Google Scholar 

  50. Keller, J.B. & Niordson, F.I.: J.Math. Mech. 16, 433–446 (1966).

    MATH  MathSciNet  Google Scholar 

  51. Taylor, J.E.: AIAA J. 6, 1379–1381 (1968).

    Google Scholar 

  52. Masur, E.F.: J. Engrg. Mech. Div., ASCE, 96, 621–640 (1970).

    Google Scholar 

  53. Prager, W & Taylor, J.E.: J. Appl. Mech. 35, 102–106 (1968).

    MATH  Google Scholar 

  54. Brach, R.M.: J. Opt. Th. & Appl. 11, 662–667 (1973).

    MATH  MathSciNet  Google Scholar 

  55. Taylor, J.E.: AIAA J. 5, 1911–1913 (1967).

    Google Scholar 

  56. Vavrick, D.J. & Warner, W.H.: J. Struct. Mech. 6, 233–246 (1978).

    Google Scholar 

  57. Seyranian, A.P.: Int. J. Solids Struct. 15, 749–759 (1979).

    MATH  Google Scholar 

  58. Olhoff, N. & Niordson, F.I.: ZAMM 59, T16–T26 (1979).

    MathSciNet  Google Scholar 

  59. Karihaloo, B.L. & Niordson, F.I.: J. Opt. Th. & Appl. 11, 638–654 (1973).

    MATH  MathSciNet  Google Scholar 

  60. Olhoff, N.: J. Struct. Mech. 4, 87–122 (1976).

    Google Scholar 

  61. Turner, M.J.: AIAA J. 5, 406–412 (1967).

    MATH  Google Scholar 

  62. Olhoff, N. & Taylor, J.E.: J. Opt. Th. & Appl. 27, 571–582 (1979).

    MATH  MathSciNet  Google Scholar 

  63. Taylor, J.E. & Liu, C.Y.: AIAA J. 6, 1497–1502 (1968).

    MATH  Google Scholar 

  64. Tadjbakhsh, I. & Keller, J.B.: J. Appl. Mech. 29, 159–164 (1962).

    MATH  MathSciNet  Google Scholar 

  65. Masur, E.F.: J. Opt. Th. & Appl. 15, 69–84 (1975).

    MathSciNet  Google Scholar 

  66. Popelar, C.H.: J. Struct. Mech. 5, 45–66 (1977).

    Google Scholar 

  67. Olhoff, N. & Rasmussen, S.H.: Int. J. Solids Struct. 13, 605–614 (1977).

    MATH  Google Scholar 

  68. Brach, R.M.: Int. J. Solids Struct. 4, 667–674 (1968).

    MATH  Google Scholar 

  69. Karihaloo, B.L. & Niordson, F.I.: Arch, of Mech. 24, 1029–1037 (1972).

    Google Scholar 

  70. Huang, N.C. & Sheu, C.Y.: Appl. Mech 35, 285–288 (1968).

    Google Scholar 

  71. Frauenthal, J.C.: J. Struct. Mech. 1, 79–89 (1972).

    Google Scholar 

  72. Adali, S.: Int. J. Solids Struct. 15, 935–949 (1979).

    MATH  MathSciNet  Google Scholar 

  73. Simitses, G.J., Kamat, M.P. & Smith, C.V. Jr.: AIAA J. 11, 1231–1232 (1973).

    Google Scholar 

  74. Rasmussen, S.H.: J. Struct. Mech. 4, 307–320 (1976).

    Google Scholar 

  75. Olhoff, N. & Taylor, J.E.: J. Struct. Mech. 6, 367–382 (1978).

    Google Scholar 

  76. Taylor, J.E.: J. Appl. Mech. 34, 486–487 (1967).

    Google Scholar 

  77. Banichuk, N.V. & Karihaloo, B.L.: Int. J. Solids Struct. 13, 725–733 (1977).

    MATH  Google Scholar 

  78. Banichuk, N.V.: MTT (Mechanics of Solids), 9, 150–154 (1974).

    Google Scholar 

  79. Mröz, Z. & Rozvany, G.I.N.: J. Struct. Mech. 5, 279–290 (1977).

    Google Scholar 

  80. Szelag, D. & Mröz, Z.: ZAMM 58, 501–510 (1978).

    MATH  Google Scholar 

  81. Masur, E.F.: In Ref. [18], 441–453 (1975)

    Google Scholar 

  82. Bendsøe, M.P., Olhoff, N. & Taylor, J.E.: J. Struct. Mech. 11 523–544 (1983–84).

    Google Scholar 

  83. Taylor, J.E. & Bendsoe, M.P.: Int. J. Solids Struct. 20, 301–314 (1984).

    MATH  MathSciNet  Google Scholar 

  84. Masur, E.F. & Mröz, Z.: Proc. IUTAM Symp. on Variational Methods in the Mech. of Solids (Ed. S. Nemat-Nasser), Northwestern Univ., USA, Pergamon Press (1980).

    Google Scholar 

  85. Masur, E.F.: Int. J. Solids Struct. 20, 211–231 (1984).

    MATH  MathSciNet  Google Scholar 

  86. Bratus, A.S. & Seyranian, A.P.: Prikl. Mat. Mekh. 47, 451–457 (1983).

    MathSciNet  Google Scholar 

  87. Bratus, A.S. & Seyranian, A.P.: Prikl. Mat. Mekh. 48, 466–474 (1984).

    MathSciNet  Google Scholar 

  88. Seyranian, A.P.: Doklady Acad. Nauk USSR 271, 337–40 (1983). English translation: Sov. Phys. Dokl. 28, 550–51 (1983).

    Google Scholar 

  89. Seyranian, A.P.: MTT (Mechanics of Solids) 19, 101–111 (1984).

    Google Scholar 

  90. Prager, S. & Prager, W.: Int. J. Mech. Sci. 21, 249–251 (1979).

    Google Scholar 

  91. Gajewski, A.: Int. J. Mech. Sci. 23, 11–16 (1981).

    MATH  Google Scholar 

  92. Blachut, J. & Gajewski, A.: Int. J. Solids Struct. 17, 653–667 (1981).

    MATH  Google Scholar 

  93. Blachut, J. & Gajewski, A.: Optimal Control Appl. Methods 2, 383–402 (1981).

    MATH  Google Scholar 

  94. Olhoff, N. & Plaut, R.H.: Int. J. Solids Struct. 19, 553–570 (1983).

    MATH  Google Scholar 

  95. Rezaie-Keyvan, N. & Masur, E.F.: J. Struct. Mech 13, 181–200 (1985).

    Google Scholar 

  96. Blachut, J.: Int. J. Mech. Sci. 26, 305–310 (1984).

    MATH  Google Scholar 

  97. Bochenek, B. & Gajewski, A.: J. Struct. Mech. 14, 257–274 (1986).

    Google Scholar 

  98. Gajewski, A.: Int. J. Mech. Sci. 27, 45–53 (1985).

    MATH  Google Scholar 

  99. Bochenek, B.: Int. J. Solids Struct. 23, 599–605 (1987).

    MATH  Google Scholar 

  100. Plaut, R.H., Johnson, L.W. & Olhoff, N.: J. Appl. Mech. 53, 130–134 (1986).

    MATH  Google Scholar 

  101. Seyranian, A.P. & Sharanyuk, A.V.: MTT (Mechanics of Solids) 21, 34–38 (1987).

    Google Scholar 

  102. Olhoff, N.: J. Struct. Mech. 5, 107–134 (1977).

    Google Scholar 

  103. Kamat, M.P. & Simitses, G.J.: Int. J. Solids Struct. 9, 415–429 (1973).

    MATH  Google Scholar 

  104. Vepa, K.: Quart. Appl. Mech. 31, 329–341 (1973/74).

    MATH  MathSciNet  Google Scholar 

  105. Seyranian, A.P.: MTT (Mechanics of Solids), 11, 147–152 (1976).

    Google Scholar 

  106. Masur, E.F.: In Ref. [18], 99–102 (1975)

    Google Scholar 

  107. Olhoff, N. & Parbery, R.: Int. J. Solids Struct. 20, 63–75 (1984).

    MATH  Google Scholar 

  108. Bendsoe, M.P. & Olhoff, N.: Optimal Control Appl. & Meth. 6, 191–200 (1985).

    MathSciNet  Google Scholar 

  109. Troitskii, V.A.: MTT (Mechanics of Solids), 11, 145–152 (1976).

    MathSciNet  Google Scholar 

  110. Mroz, Z. & Rozvany, G.I.N.: J. Opt. Th. & Appl. 15, 85–101 (1975).

    MATH  MathSciNet  Google Scholar 

  111. Rozvany, G.I.N.: J. Struct. Mech. 3, 359–402 (1974/75).

    Google Scholar 

  112. Pierson, B.L.: J. Struct. Mech. 5, 147–178 (1977).

    Google Scholar 

  113. Pedersen, P.: J. Struct. Mech. 10, 243–271 (1981/83).

    Google Scholar 

  114. Kibsgaard, S.: Structural Optimization 1 (1989) (to appear).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Aalborg, Aalborg, Denmark

    N. Olhoff

Authors
  1. N. Olhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technical University of Cracow, Poland

    M. Zyczkowski

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Wien

About this chapter

Cite this chapter

Olhoff, N. (1989). Part III. In: Zyczkowski, M. (eds) Structural Optimization under Stability and Vibration Constraints. International Centre for Mechanical Sciences, vol 308. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2969-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2969-2_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82173-2

  • Online ISBN: 978-3-7091-2969-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation