MICHELL TRUSSES AND LINES OF PRINCIPAL ACTION
MICHELL TRUSSES AND LINES OF PRINCIPAL ACTION
复制标题
米歇尔桁架和主要作用线
DOI：
10.1142/s0218202508003133
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发表时间：
2008
影响因子：
3.5
通讯作者：
P. Seppecher
中科院分区：
文献类型：
--
作者：
G. Bouchitté;W. Gangbo;P. Seppecher
研究了当平衡力系为紧支集向量测度时Michell桁架的问题。我们引入了一类应力张量，它可以写成由曲线（主应变线）承载的一阶张量的叠加。最优性条件给出这样的家庭，特别是最佳应力张量进行相互正交的曲线族。该方法说明了一个具体的例子，唯一性可以证明通过研究一个不寻常的双曲型偏微分方程系统。我们在这里解决的问题是感兴趣的弹性理论，最优设计，以及在功能分析。
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.