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Regularization of optimal design problems for bars and plates, part 2

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Abstract

For the problems of optimal design considered in Ref. 1, contradictions arising in the necessary conditions of optimality are eliminated by suitable extension of the initially given class of admissible materials. The extended class includes composites of some special (layered) microstructure. Elastic properties of such composites are described, and alternative (regularized) formulations of the optimal design problems are given. Necessary conditions of Weierstrass are shown to be satisfied, both for the case in which the strip of variations is small compared with the width of the layers and for the opposite case. Numerical results are given for the regularized problem of a bar of extremal torsional rigidity.

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References

  1. Lurie, K. A., Cherkaev, A. V., andFedorov, A. V.,Regularization of Optimal Design Problems for Bars and Plates, Part 1, Journal of Optimization Theory and Applications, Vol. 37, No. 4, 1982.

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Authors and Affiliations

  1. A. F. Ioffe Physical-Technical Institute, Academy of Sciences of the USSR, Leningrad, USSR

    K. A. Lurie (Senior Research Worker), A. V. Cherkaev (Research Worker) & A. V. Fedorov (Research Worker)

Authors
  1. K. A. Lurie
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  2. A. V. Cherkaev
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  3. A. V. Fedorov
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Additional information

The authors are indebted to Dr. N. A. Lavrov for performing numerical calculations.

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Lurie, K.A., Cherkaev, A.V. & Fedorov, A.V. Regularization of optimal design problems for bars and plates, part 2. J Optim Theory Appl 37, 523–543 (1982). https://doi.org/10.1007/BF00934954

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  • DOI: https://doi.org/10.1007/BF00934954

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