论文标题
光结构的优化：消失的质量猜想
Optimization of light structures: the vanishing mass conjecture
论文作者
论文摘要
我们认为形状优化问题包括将给定的质量$ M $ M $弹性材料放在设计区域中，从而使合规性很小。考虑到最佳的光结构，我们的目的是表明，随着总质量$ m $倾向于零，找到最僵硬的形状构型的问题简化了：我们提出了一种明确的放松配方，其中合规性作为质量相对密度的凸功能后出现后的合规性出现。这使我们能够在最近在[5]中开发的Monge-Kantorovich方法之后，为光结构编写必要和足够的最佳条件。
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].
