轻结构的Optimization：质量消失猜想
Optimization of light structures: the vanishing mass conjecture
摘要：
我们考虑的形状最优化问题，其中包括在放置一个给定的质量$m$的弹性材料在设计区域，使符合是最小的。考虑到最佳的轻结构，我们的目的是要表明，找到最硬的形状配置的问题简化为总质量$m$趋于零：我们提出了一个明确的放松制定后出现的顺应性作为一个凸泛函的相对质量密度重新缩放。这使我们能够按照最近在[5]中发展的Monge-Kantorovich方法写出轻结构的必要和充分最优性条件。
英文摘要：
We consider the shape optimization problem which consists in placing a given mass $m$ of elastic material in a design region so that the compliance is minimal. Having in mind optimal light structures, our purpose is to show that the problem of finding the stiffest shape configuration simplifies as the total mass $m$ tends to zero: we propose an explicit relaxed formulation where the compliance appears after rescaling as a convex functional of the relative density of mass. This allows us to write necessary and sufficient optimality conditions for light structures following the Monge-Kantorovich approach developed recently in [5].
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