论文标题
具有梯度迪里奇特边界条件的Miura表面的计算
Computation of Miura surfaces with gradient Dirichlet boundary conditions
论文作者
论文摘要
Miura表面是约束非线性椭圆形系统的解决方案。该系统是由Miura Fold的均质化得出的，Miura Fold是一种折纸折叠，具有多种工程应用。先前的询问给出了存在解决方案的次优条件，并提出了$ h^2 $ - 符合条件的有限元方法来近似它们。在本文中，使用梯度公式研究了Miura表面的存在。还证明，在某些假设下，约束从边界传播到域内的内部。然后，引入了基于稳定的最小二乘公式，符合有限元和牛顿方法的数值方法，以近似Miura表面。事实证明，数值方法会收敛并进行数值测试以证明其稳健性。
Miura surfaces are the solutions of a constrained nonlinear elliptic system of equations. This system is derived by homogenization from the Miura fold, which is a type of origami fold with multiple applications in engineering. A previous inquiry, gave suboptimal conditions for existence of solutions and proposed an $H^2$-conformal finite element method to approximate them. In this paper, the existence of Miura surfaces is studied using a gradient formulation. It is also proved that, under some hypotheses, the constraints propagate from the boundary to the interior of the domain. Then, a numerical method based on a stabilized least-square formulation, conforming finite elements and a Newton method is introduced to approximate Miura surfaces. The numerical method is proved to converge and numerical tests are performed to demonstrate its robustness.
