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$H^2$-conformal approximation of Miura surfaces

Frederic Marazzato
Feb 2022
摘要
A nonlinear partial differential equation (PDE) that models the possibleshapes that a periodic Miura tessellation can take in the homogenization limithas been established recently and solved only in specific cases. In this paper,the existence and uniqueness of a solution to the PDE is proved for generalDirichlet boundary conditions. Then a H^2-conforming discretization isintroduced to approximate the solution of the PDE and a fixed point algorithmis proposed to solve the associated discrete problem. A convergence proof forthe method is given as well as a convergence rate. Finally, numericalexperiments show the robustness of the method and that non trivial shapes canbe achieved using periodic Miura tessellations.
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