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Optimal design of rotating disk for given radial displacement of edge

Abstract

Minimum-weight design of axially-symmetric, rotating, elastic disks is usually discussed in terms of uniform strength. In this paper, an alternative constraint is used: under the combined influence of centrifugal forces and a uniform radial traction along the circular edge, the radial displacement at this edge is to have a prescribed value. A necessary and sufficient optimality condition is derived, and its use in the determination of optimal disk profiles is illustrated by examples. It is shown that the resulting disks are far from satisfying the condition of uniform strength although their weights are only very slightly smaller than those of the corresponding disks of uniform strength.

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References

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    Den Hartog, J. P.,Advanced Strength of Materials, McGraw-Hill Book Company, New York, 1952.

  2. 2.

    Ranta, M. A.,On the Optimum Shape of a Rotating Disk of Any Isotropic Material, International Journal of Solids and Structures, Vol. 5, 1969.

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    Shield, R. T., andPrager, W.,Optimal Structural Design for Given Deflection, Journal of Applied Mathematics and Physics (to appear).

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Additional information

This research was sponsored by the Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract No. F33615-C-1826.

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Chern, J.M., Prager, W. Optimal design of rotating disk for given radial displacement of edge. J Optim Theory Appl 6, 161–170 (1970). https://doi.org/10.1007/BF00927049

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Keywords

  • Optimality Condition
  • Optimal Design
  • Centrifugal Force
  • Radial Displacement
  • Combine Influence