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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2008

Michell Trusses and Lines of Principal Action

Résumé

We study the problem of Michell trusses when the system of applied equilibrated forces is a vector measure with compact support. We introduce a class of stress tensors which can be written as a superposition of rank-one tensors carried by curves (lines of principal strains). Optimality conditions are given for such families showing in particular that optimal stress tensors are carried by mutually orthogonal families of curves. The method is illustrated on a specific example where uniqueness can be proved by studying an unusual system of hyperbolic PDEs. The questions we address here are of interest in elasticity theory, optimal designs, as well as in functional analysis.
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Dates et versions

hal-00528973 , version 1 (23-10-2010)

Identifiants

  • HAL Id : hal-00528973 , version 1

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Guy Bouchitté, Wilfrid Gangbo, Pierre Seppecher. Michell Trusses and Lines of Principal Action. Mathematical Models and Methods in Applied Sciences, 2008, 18 (9), pp.1571-1603. ⟨hal-00528973⟩
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