Skip to main content

Minimum-Weight Plate Design Via Prager’s Layout Theory (Prager Memorial Lecture)

  • Conference paper
Computer Aided Optimal Design: Structural and Mechanical Systems

Part of the book series: NATO ASI Series ((NATO ASI F,volume 27))

Abstract

During the last decade of his immensely creative life, Professor William Prager’s research was directed at two central objectives, the derivation of a comprehensive set of static-kinematic optimality criteria and the development of an optimal layout theory. As the late Professor Prager’s closest former associate, the first author will review briefly these fields in the first part of this memorial lecture.

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

Access this chapter

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. Prager, W., Shield, R.T.: A general theory of optimal plastic design. J. Appl. Mech. 34 (1967) 184–186.

    Article  MATH  Google Scholar 

  2. Rozvany, G.I.N.: Optimal design of flexural systems. Oxford: Pergamon Press (1976). Russian version: Moscow: Stroiizdat, (1980).

    Google Scholar 

  3. Rozvany, G.I.N.: Variational methods and optimality criteria, in Haug, E.J.; Cea, J. (eds.): Optimization of distributed parameter structures, Proc. NATO ASI, Iowa, 1980. Alphen aan Rhiijn: Sijthoff and Noordhoff (1981) 82–111.

    Google Scholar 

  4. Rozvany, G.I.N.: Variational methods and optimality criteria, in Haug, E.J.; Cea, J. (eds.): Optimization of distributed parameter structures, Proc. NATO ASI, Iowa, 1980. Alphen aan Rhiijn: Sijthoff and Noordhoff (1981) 82–111.

    Google Scholar 

  5. Rozvany, G.I.N.: Prager-Shield optimality criteria with bounded spatial gradients. J. Engrg. Mech. ASCE 110 (1984) 129–137.

    Article  Google Scholar 

  6. Olhoff, N.; Rozvany, G.I.N.: Optimal grillage layout for given natural frequency. J. Engrg. Mech. ASCE 108 (1982) 971–974.

    Google Scholar 

  7. Rozvany, G.I.N.; Ong, T.G.; Karihaloo, B.L.: A general theory of optimal elastic design for structures with segmentation. J. Appl. Mech, ASME, 53 (1986) 242–248.

    Article  MATH  Google Scholar 

  8. Rozvany, G.I.N.; Ong, T.G.; Yep, K.M.: Optimal elastic design with constrained taper: prescribed deflections. J. Engrg. Mech. ASCE, 112 (1986) 845–850.

    Article  Google Scholar 

  9. Prager, W.; Rozvany, G.I.N.: Optimization of structural geometry, in: Bednarek, A.R., Cesari, L. (eds.): Dynamical systems. New York: Academic Press (1977) 265–294.

    Google Scholar 

  10. Prager, W.; Rozvany, G.I.N.: Optimal layout of grillages. J. Struct. Mech. 5 (1977) 1–18 (also: 14th IUTAM Congress, Delft, (1976) paper No. 310).

    Google Scholar 

  11. Rozvany, G.I.N.: Optimality criteria for grids, shells and arches, in: Haug, E.J.; Cea, J. (eds.): Optimization of distributed parameter structures, Proc. NATO ASI, Iowa, 1980. Alphen aan Rhijn: Sijthoff and Noordhoff (1981) 112–151.

    Google Scholar 

  12. Rozvany, G.I.N.: A general theory of optimal structural layouts, Proc. Int. Symp. on Optimum Structural Design. Tucson, Arizona: University of Arizona (1981) 4.37–4.45. Extended version: Structural layout theory: the present state of knowledge. Chapter 7 in: Atrek, E.; Gallagher, R.H.; Ragsdell, K.M. and Zienkiewicz, O.C. (eds.): New directions in optimum structural design. Chichester, England: Wiley & Sons (1984) 167–196.

    Google Scholar 

  13. Rozvany, G.I.N.; Wang, C.M.: Extensions of Prager’s layout theory, in: Eschenauer, H.; Olhoff, N. (eds.): Optimization methods in structural design, Proc. Euromech. Colloquium, Siegen ( 1982 ). Mannheim: Wissenschaftsverlag (1983) 103–110.

    Google Scholar 

  14. Rozvany, G.I.N.; Ong, T.G.: Optimal design of plates, shells and shellgrids, in: Proc. IUTAM Symp. Inelastic Behaviour of Plates and Shells, Rio de Janeiro, Aug. 1985, Berlin: Springer Verlag (1986) 357–384.

    Google Scholar 

  15. Michell, A.G.M.: The limits of economy of material in frame structures. Phil Mag., 8 (1904) 589–597.

    Google Scholar 

  16. Kohn, R.V.; Strang, G.: Optimal design for torsional rigidity, in: Atluri, S.N.; Gallagher, R.H. and Zienkiewicz, O.C. (eds.): Hybrid and mixed finite element methods. Chichester, England: Wiley & Sons (1983) 281–288.

    Google Scholar 

  17. Cheng, K-T.; Olhoff, N.: An investigation concerning optimal design of solid elastic plates. Int. J. Solids Struct. 17 (1981) 305–323.

    Article  MathSciNet  MATH  Google Scholar 

  18. Rozvany, G.I.N.; Wang, C.M.: Constrained optimal layouts through Prager-Shield criteria. J. Engrg. Mech. ASCE 109 (1983) 648–653.

    Article  Google Scholar 

  19. Rozvany, G.I.N.; Wang, C.M.: Optimal layout theory: allowance for selfweight. J. Engrg. Mech. ASCE 110 (1984) 66–83.

    Article  Google Scholar 

  20. Rozvany, G.I.N.; Yep, K.M.; Sandler, R.: Optimal layout of long-span truss-grids, I–II, Int. J. Solids Struct. 22 (1986) 209–223, 225–238.

    Article  MATH  Google Scholar 

  21. Rozvany, G.I.N.; Ong, T.G.: A general theory of optimal layouts for elastic structures. J. Engrg. Mech. ASCE, 112 (1986) 851–857.

    Article  Google Scholar 

  22. Rozvany, G.I.N.; Hill, R.: A computer algorithm for deriving analytically and plotting optimal structural layout. Proc. NASA Symp.: Future trends in computerised structural analysis and design, Washington, (1978) 295–300. Oxford: Pergamon, 1978. Also Computers and Struct. 10 (1979) 295–300.

    Google Scholar 

  23. Hill, R.; Rozvany, G.I.N.: Prager’s layout theory: a non-numeric computer method for generating optimal structural configurations and weight-influence surfaces. Comp. Meth. Appl. Mech. Engrg. 49 (1985) 131–148.

    Article  MATH  Google Scholar 

  24. Rozvany, G.I.N.; Prager, W.: A new class of optimization problems: optimal archgrids. Comp. Meth. Appl. Mech. Engrg. 19 (1979) 127–150.

    Article  MathSciNet  MATH  Google Scholar 

  25. Rozvany, G.I.N.; Nakamura, H. Kuhnell, B.T.: Optimal archgrids: allowance for self-weight. Comp. Meth. Appl. Mech. Engrg. 24 (1980) 287–304.

    Article  MATH  Google Scholar 

  26. Rozvany, G.I.N.; Wang, C.M.; Dow, M.: Prager-structures: archgrids and cable networks of optimal layout. Comp. Meth. Appl. Mech. Engrg. 31 (1982) 91–114.

    Article  MathSciNet  MATH  Google Scholar 

  27. Rozvany, G.I.N.; Wang, C.M.: On plane Prager-structures I-II. Int. J. Mech. Sci. 25 (1983) 519–527, 529–541.

    Article  MATH  Google Scholar 

  28. Rozvany, G.I.N.; Olhoff, N.; Cheng, K.-T.; Taylor, J.: On the solid plate paradox in structural optimization. J. Struct. Mech. 10 (1982) 1–32.

    Article  MathSciNet  Google Scholar 

  29. Wang, C.-M.; Rozvany, G.I.N.; Olhoff, N.: Optimal plastic design of axisymmetric solid plates with a maximum thickness constraint. Computers Struct. 18 (1984) 653–665.

    Article  MATH  Google Scholar 

  30. Kozlowski, W.; Mroz, Z.: Optimal design of solid plates. Int. J. Solids Struct. 5 (1969) 781–794.

    Article  Google Scholar 

  31. Lurie, K.A.; Fedorov, A.V.; Cherkaev, A.V.: On the existence of solutions to some problems of optimal design for bars and plates. J. Optimiz. Theory Appl. 42 (1984) 247–281.

    Article  MathSciNet  MATH  Google Scholar 

  32. Lurie, K.A.; Fedorov, A.V.; Cherkaev, A.V.: Regularization of optimal design problems for bars and plates. I,II. J. Optimiz. Theory Appl. 37 (1982) 499–521, 523–543.

    Google Scholar 

  33. Rozvany, G.I.N.; Ong, T.G.; Olhoff, N.; Bendsoe, M.P.; Szeto, W.T.: Least-weight design of perforated elastic plates. DCAMM-report. No. 306, 1985. Extended version: Parts I and II, accepted. Int. J. Solids Struct.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rozvany, G.I.N., Ong, TG. (1987). Minimum-Weight Plate Design Via Prager’s Layout Theory (Prager Memorial Lecture). In: Mota Soares, C.A. (eds) Computer Aided Optimal Design: Structural and Mechanical Systems. NATO ASI Series, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83051-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83051-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83053-2

  • Online ISBN: 978-3-642-83051-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics