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Optimal distribution of multimaterial composites for torsional beams

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Abstract

In this paper, we consider the optimal design of torsional beams using an arbitrary number of materials. The problem is initially ill-posed, and must be relaxed by the introduction of multimaterial composites. The optimization algorithm for multimaterial composites is described and computational results for both perturbations and asymptotical cases are presented. It is noticed that the case for three or more composites undergoes a phenomenon very much like a phase transition when certain conditions are satisfied.

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References

  • Balay, S.; Gropp, W.; McInness, L.C.; Smith, B. 1996:PETSc 2.0 user's manual. Mathematics and Computer Science Division, Argonne National Laboratory

  • Bendsøe, M.P. 1995:Optimization of structural topology, shape, and material. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Cherkaev, A.; Kohn, R. (eds.) 1996:Topics in the mathematical modelling of composite materials. New York: Birkhauser

    Google Scholar 

  • Cherkaev, A.V.; Lavrov, N.A.; Lurie, K.A. 1980: Nonuniform rod of extremal torsional stiffness.Mech. of Solids 15, 75–80

    Google Scholar 

  • Cherkaev, A.V.; Lurie, K.A.; Fedorov, A.V. 1982: Regularization of optimal design problems for bars and plates i, ii.J. Optimiz. Theory Appl. 37, 499–524

    Google Scholar 

  • Ekeland, I.; Temam, R. 1976:Convex analysis and variational problems. North-Holland Publishing Company

  • Klosowicz, B.; Lurie, K.A. 1971: On the optimal nonhomogeneity of a torsional elastic bar.Arch. Mech.,24, 239–249

    Google Scholar 

  • Goodman, J.; Kohn, R.V.; Reyna, L. 1986: Numerical study of a relaxed variational problem from optimal design.Comp. Meth. Appl. Mech. Eng. 57, 107–127

    Google Scholar 

  • Kohn, R.V.; Strang, G. 1986: Optimal design and relaxation of variational problems.Comm. Pure Appl. Math. 39, 113–137

    Google Scholar 

  • Landau, L.D. 1986:Theory of elasticity. Oxford: Pergamon Press

    Google Scholar 

  • Lurie, K.A.; Cherkaev, A.V. 1984: Exact estimates of the conductivity of mixtures formed of two materials in a given proportion.Proc. Roy. Soc. Edin. 99A, 71–87

    Google Scholar 

  • Lurie, K.A.; Cherkaev, A.V. 1986: The effective characteristics of composite materials and optimal design of construction (in Russian).Adv. in Mech. 9(2), 3–81

    Google Scholar 

  • Schrieber, R.; Keller, H.B. 1983: Driven cavity flows by efficient numerical techniques.J. Comp. Phys. 49, 310–333

    Google Scholar 

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Authors and Affiliations

  1. Utah Supercomputing Institute, University of Utah, 84112, Salt Lake City, UT, USA

    T. Burns

  2. Department of Mathematics, University of Utah, 84112, Salt Lake City, UT, USA

    A. Cherkaev

Authors
  1. T. Burns
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  2. A. Cherkaev
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Burns, T., Cherkaev, A. Optimal distribution of multimaterial composites for torsional beams. Structural Optimization 13, 4–11 (1997). https://doi.org/10.1007/BF01198369

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  • DOI: https://doi.org/10.1007/BF01198369

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