论文标题
最佳的弹性斗篷
Optimal Elastostatic Cloaks
论文作者
论文摘要
弹性斗篷掩盖了弹性场的一个孔或不均匀性。在本文中，基于伴随状态方法的弹性斗篷的最佳设计的公式，其中提出了线性动量的平衡作为约束。设计参数是披风的弹性模量，而目标函数是物理和虚拟体中解决方案之间距离的量度。假定弹性培养基和斗篷都是由各向同性线性弹性材料制成的。为了确保披风中平滑的不均匀弹性模量，添加了惩罚项。混合有限元用于离散优化问题的弱公式。提出了为单个和多个负载设计的最佳弹性斗篷的几个数值示例。我们考虑不同的几何形状和加载类型，并观察到在某些情况下，最佳的弹性披风（腔孔）是由辅助材料制成的。
An elastic cloak hides a hole or an inhomogeneity from elastic fields. In this paper, a formulation of the optimal design of elastic cloaks based on the adjoint state method, in which the balance of linear momentum is enforced as a constraint, is presented. The design parameters are the elastic moduli of the cloak, while the objective function is a measure of the distance between the solutions in the physical and in the virtual bodies. Both the elastic medium and the cloak are assumed to be made of isotropic linear elastic materials. In order to guarantee smooth inhomogeneous elastic moduli within the cloak a penalization term is added to the objective function. Mixed finite elements are used for discretizing the weak formulation of the optimization problem. Several numerical examples of optimal elastic cloaks designed for both single and multiple loads are presented. We consider different geometries and loading types and observe that in some cases the optimal elastic cloaks for cloaking holes (cavities) are made of auxetic materials.
