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Optimum design of structures through variational principles

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Optimization and Stability Problems in Continuum Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 21))

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References

  1. Michell, A. G. M. The Limits of Economy in Frame-Structures. Phil. Mag. 8, 589–597 (1904).

    Google Scholar 

  2. Drucker, D. C., and Shield, R. T. Design for Minimum Weight. Proc. 9th International Congress of Applied Mechanics, Brussels 1956, pp. 212–222.

    Google Scholar 

  3. Drucker, D. C., and Shield, R. T. Bounds on Minimum Weight Design. Q. Appl. Math. 15, 269–281 (1957).

    Google Scholar 

  4. Shield, R. T. On the Optimum Design of Shells. J. Appl. Mech. 27, 316–322 (1960).

    Google Scholar 

  5. Prager, W., and Taylor, J. E. Problems of Optimal Structural Design. J. Appl. Mech. 35, 102–106 (1968).

    Google Scholar 

  6. Shield, R. T., and Prager, W. Optimal Structural Design for Given Deflection. J. Appl. Math. Phys. (ZAMP) 21, 513–523 (1970).

    Article  Google Scholar 

  7. Shield, R. T. Optimum Design Methods for Structures. Plasticity, Proc. 2nd Symp. Naval Struct. Mechanics, Providence 1960, pp. 580–591.

    Google Scholar 

  8. Wasiutyński, Z., and Brandt, A. The Present State of Knowledge in the Field of Optimum Design of Structures. Appl. Mech. Rev. 16, 341–350 (1963).

    Google Scholar 

  9. Sheu, C. Y., and Prager, W. Recent Developments in Optimal Structural Design. Appl. Mech. Rev. 21, 985–992 (1968).

    Google Scholar 

  10. Prager, W. Optimization of Structural Design. J. Optimization Theory and Applic. 6, 1–21 (1970).

    Article  Google Scholar 

  11. Anderson, C. A., and Shield, R. T. On the Validity of the Plastic Theory of Structures for Collapse under Highly Localized Loading. J. Appl. Mech. 33, 629–636 (1966).

    Google Scholar 

  12. Drucker, D. C., Prager, W., and Greenberg, H. J. Extended Limit Design Theorems for Continuous Media. Q. Appl. Math. 9, 381–389 (1952).

    Google Scholar 

  13. Prager, W. General Theory of Limit Design. Proc. 8th International Congress of Applied Mechanics, Istanbul 1952.

    Google Scholar 

  14. Mróz, Z. The Load Carrying Capacity and Minimum Weight Design of Annular Plates. Rozpr. Inäzyn. (Engin. Trans., Warsaw) 114, 605–625 (1958).

    Google Scholar 

  15. Onat, E. T., Schumann, W., and Shield, R. T. Design of Circular Plates for Minimum Weight. J. Appl. Math. Phys. (ZAMP) 8, 485–499 (1957).

    Article  Google Scholar 

  16. Prager, W., and Shield, R. T. Minimum Weight Design of Circular Plates under Arbitrary Loading. J. Appl. Math. Phys. (ZAMP) 10, 421–426 (1959).

    Google Scholar 

  17. Shield, R. T. Plate Design for Minimum Weight. Q. Appl. Math. 18, 131–144 (1960).

    Google Scholar 

  18. Shield, R. T. Optimum Design Methods for Multiple Loading. J. Appl. Math. Phys. (ZAMP) 14, 38–45 (1963).

    Article  Google Scholar 

  19. Save, M. A., and Shield, R. T. Minimum-Weight Design of Sandwich Shells Subjected to Fixed and Moving Loads. Proc. 11th International Congress of Applied Mechanics, Munich 1964, pp. 341–349.

    Google Scholar 

  20. Save, M. A. Some Aspects of Minimum-Weight Design. Engineering Plasticity, Cambridge Univ. Press 1968, pp. 611–626.

    Google Scholar 

  21. Prager, W., and Shield, R. T., Optimal Design of Multi-Purpose Structures. Int. J. Solids Structures 4, 469–475 (1968).

    Article  Google Scholar 

  22. Hemp, W. S. Studies in the Theory of Michell Structures. Proc. 11th International Congress of Applied Mechanics, Munich 1964, pp. 621–628.

    Google Scholar 

  23. Hegemeir, G. A., and Prager, W. On Michell Trusses. Int. J. Mech. Sci. 11, 209–215 (1969).

    Article  Google Scholar 

  24. Prager, W. On a Problem of Optimal Design. Non-homogeneity in Elasticity and Plasticity, Pergamon Press 1959, pp. 125–132.

    Google Scholar 

  25. Hu, T. C., and Shield, R. T. Minimum-Volume Design of Discs. J. Appl. Math. Phys. (ZAMP) 12, 414–433 (1961).

    Article  Google Scholar 

  26. Cox, H. L. The Design of Structures of Least Weight, Pergamon Press 1965.

    Google Scholar 

  27. Cox, H. L. The Theory of Design. Aeronautical Research Council Report 19791, Great Britain (1958).

    Google Scholar 

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P. K. C. Wang

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© 1973 Springer Verlag

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Shield, R.T. (1973). Optimum design of structures through variational principles. In: Wang, P.K.C. (eds) Optimization and Stability Problems in Continuum Mechanics. Lecture Notes in Physics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06214-9_2

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  • DOI: https://doi.org/10.1007/3-540-06214-9_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06214-1

  • Online ISBN: 978-3-540-38495-3

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