论文标题
$ h^2 $ - 符合Miura表面的近似
$H^2$-conformal approximation of Miura surfaces
论文作者
论文摘要
Miura Ori是一种非常经典的折纸模式，用于工程中的许多应用。对使用这种模式表面表面的形状的研究仍然缺乏。最近已经建立了一个约束的非线性偏微分方程（PDE），该方程已建立了周期性的Miura tessellation可能采取的可能形状的均匀化极限，并且仅在特定情况下仅解决。在本文中，对于一般的Dirichlet边界条件，证明了对无约束PDE的解决方案的存在和独特性。然后，引入了$ h^2 $ - 合格的离散化，以近似PDE的解决方案与牛顿方法耦合以解决相关的离散问题。给出了该方法的收敛证明以及收敛速率。最后，数值实验显示了该方法的鲁棒性，并且可以使用周期性的miura tessellations来实现非微不足道的形状。
The Miura ori is a very classical origami pattern used in numerous applications in Engineering. A study of the shapes that surfaces using this pattern can assume is still lacking. A constrained nonlinear partial differential equation (PDE) that models the possible shapes that a periodic Miura tessellation can take in the homogenization limit has been established recently and solved only in specific cases. In this paper, the existence and uniqueness of a solution to the unconstrained PDE is proved for general Dirichlet boundary conditions. Then a $H^2$-conforming discretization is introduced to approximate the solution of the PDE coupled to a Newton method to solve the associated discrete problem. A convergence proof for the method is given as well as a convergence rate. Finally, numerical experiments show the robustness of the method and that non trivial shapes can be achieved using periodic Miura tessellations.
