A structure theorem for shape functions defined on submanifolds
A structure theorem for shape functions defined on submanifolds
复制标题
子流形上定义的形函数的结构定理
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
K. Sturm
中科院分区：
文献类型：
--
作者：
K. Sturm
本文研究了依赖于闭子流形的形函数。我们证明了一个新的结构定理，建立了这种类型的形状函数的形状导数的一般结构。作为一个特例，我们得到了经典的Hadamard-Zol'esio结构定理，而且裂集的结构定理也可以被改写到我们的框架中。作为一个应用，我们研究了几个无约束的形状函数所产生的微分几何和断裂力学。
In this paper, we study shape functions depending on closed submanifolds. We prove a new structure theorem that establishes the general structure of the shape derivative for this type of shape function. As a special case we obtain the classical Hadamard-Zol'esio structure theorem, but also the structure theorem for cracked sets can be recast into our framework. As an application we investigate several unconstrained shape functions arising from differential geometry and fracture mechanics.