Skip to main content
SpringerLink
Log in

Dynamic programming and the optimum design of rotating disks

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The minimum-weight design of elastic rotating disks under various design criteria has been studied using ideas of dynamic programming and invariant imbedding. It is shown that the criterion of minimum potential energy furnishes a remarkably simple solution in terms of a linear partial differential equation subject to initial conditions. The treatment of more general design constraints leads to the development of a number of stable, two-sweep iterative procedures. A series of numerical examples incorporating various design constraints is presented to show the accuracy and feasibility of the method. The sensitivity of the radial stresses to small changes in the thickness of the disk is noticed. On the other hand, the high stability of the volume with respect to the design criteria is stressed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chern, J. M., andPrager, W.,Optimal Design of Rotating Disk for Given Radial Displacement of Edge, Journal of Optimization Theory and Applications, Vol. 6, No. 2, 1970.

  2. Wasiutynski, Z., andBrandt, A.,The Present State of Knowledge in the Field of Optimum Design of Structures, Applied Mechanics Review, Vol. 16, No. 5, 1963.

  3. Sheu, C. Y., andPrager, W.,Recent Developments in Optimal Structural Design, Applied Mechanics Review, Vol. 2, No. 10, 1968.

  4. Distefano, J. N.,Dynamic Programming and a Max-Min Problem in the Theory of Structures, Journal of the Franklin Institute (to appear).

  5. Timoshenko, S.,Theory of Elasticity, McGraw-Hill Book Company, 1934.

  6. Distefano, J. N.,Dynamic Programming and Invariant Imbedding in Structural Mechanics, Lecture Notes in Operations Research and Mathematical Systems, No. 52, Edited by R. Bellman and E. Denman, Springer-Verlag, Berlin, 1972.

    Google Scholar 

  7. Bellman, R., Glicksberg, I., andGross, O.,Some Aspects of the Mathematical Theory of Control Processes, The RAND Corporation, Report No. R-313, 1958.

Download references

Author information

Authors and Affiliations

  1. University of California at Berkeley, Berkeley, California

    N. Distefano (Professor of Civil Engineering)

Authors
  1. N. Distefano
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by W. Prager

This work was partially supported by a University of California grant. The author wishes to thank Mr. R. Todeschini, who carried out the numerical computations.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Distefano, N. Dynamic programming and the optimum design of rotating disks. J Optim Theory Appl 10, 109–128 (1972). https://doi.org/10.1007/BF00934975

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00934975

Keywords

Search

Navigation