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Michell cantilevers constructed within trapezoidal domains—Part III: force fields

Abstract

This paper complements the analysis of geometric properties of the Hencky nets within the Michell cantilevers constructed in the trapezoidal domains by providing the analytical formulae for the force fields. The force field analysis introduces a new division of the cantilever domain and enables an alternative method for computing the optimal weights.

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References

  1. Chan HSY (1967) Half-plane slip-line fields and Michell structures. Q J Mech Appl Math 20:453–469

  2. Graczykowski C, Lewiński T (2006a) Michell cantilevers constructed within trapezoidal domains—Part I: geometry of Hencky nets. Struct Multidisc Optim (in press)

  3. Graczykowski C, Lewiński T (2006b) Michell cantilevers constructed within trapezoidal domains—Part II: virtual displacement fields. Struct Multidisc Optim (in press)

  4. Hemp WS (1973) Optimum structures. Clarendon, Oxford

  5. Lewiński T, Zhou M, Rozvany GIN (1994a) Extended exact solutions for least-weight truss layouts. Part I: cantilever with a horizontal axis of symmetry. Int J Mech Sci 36:375–398

  6. Lewiński T, Zhou M, Rozvany GIN (1994b) Extended exact solutions for least-weight truss layouts. Part II: unsymmetric cantilevers. Int J Mech Sci 36:399–419

  7. Novozhilov VV (1962) Theory of thin shells, 2nd edn. Sudpromgiz, Leningrad (in Russian)

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Correspondence to C. Graczykowski.

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Graczykowski, C., Lewiński, T. Michell cantilevers constructed within trapezoidal domains—Part III: force fields. Struct Multidisc Optim 33, 1–19 (2007). https://doi.org/10.1007/s00158-005-0601-6

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Keywords

  • Internal Force
  • Point Load
  • Straight Segment
  • Longitudinal Force
  • Circular Domain