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Optimality Conditions for Mass Design Problems and Applications to Thin Plates

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Abstract

We derive necessary and sufficient optimality conditions for a quite large class of structural design problems which can be formulated as follows: under a given load and a total volume constraint, minimize a suitable notion of compliance among all admissible mass distributions, represented by positive measures with prescribed integral mean. As a special case, we focus attention on the optimization of thin plates; we detail the corresponding optimality conditions and we show how they can be handled in order to determine analytically some optimal plates.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Toulon et du Var, La Gard Cedex, France

    Guy Bouchitté

  2. Dipartimento di Matematica – Politecnico, Piazza Leonardo Da Vinci, 32, 20133, Milano, Italy

    Ilaria Fragalà

Authors
  1. Guy Bouchitté
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  2. Ilaria Fragalà
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Correspondence to Guy Bouchitté.

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Communicated by L. Ambrosio

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Bouchitté, G., Fragalà, I. Optimality Conditions for Mass Design Problems and Applications to Thin Plates. Arch Rational Mech Anal 184, 257–284 (2007). https://doi.org/10.1007/s00205-006-0022-8

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  • DOI: https://doi.org/10.1007/s00205-006-0022-8

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