Bilayer Plates: Model Reduction, Γ-Convergent Finite Element Approximation, and Discrete Gradient Flow
Bilayer Plates: Model Reduction, Γ-Convergent Finite Element Approximation, and Discrete Gradient Flow
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DOI：
10.1002/cpa.21626
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发表时间：
2017-03-01
影响因子：
3
通讯作者：
Nochetto, Ricardo H.
中科院分区：
文献类型：
--
作者：
Bartels, Soren;Bonito, Andrea;Nochetto, Ricardo H.
双层板的弯曲是一种机制，其允许通过底层材料的小的外部诱导的晶格失配而产生大的变形。其数学建模，本文讨论，由一个非线性四阶问题与逐点等距约束。设计了一种基于Kirchhoff四元数的离散化方法，并证明了其Gamma收敛性。提出了一种降低能量的迭代方法，并研究了其对稳态构型的收敛性。它的性能，以及减少模型的能力，探索通过几个有见地的数值实验，涉及大（几何非线性）变形。(C)2015 Wiley Periodicals，Inc.
The bending of bilayer plates is a mechanism that allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth-order problem with a pointwise isometry constraint. A discretization based on Kirchhoff quadrilaterals is devised and its Gamma-convergence is proved. An iterative method that decreases the energy is proposed, and its convergence to stationary configurations is investigated. Its performance, as well as reduced model capabilities, are explored via several insightful numerical experiments involving large (geometrically nonlinear) deformations. (C) 2015 Wiley Periodicals, Inc.