论文标题
稳定的梯度流离散化，用于模拟具有等距和障碍物约束的双层板弯曲
Stable Gradient Flow Discretizations for Simulating Bilayer Plate Bending with Isometry and Obstacle Constraints
论文作者
论文摘要
双层板是复合材料，在暴露于环境变化时表现出较大的弯曲变形，从而导致所涉及材料的机械响应不同。在本文中，讨论了一种新的数值方法，适用于模拟双层板中给定材料不匹配诱导的等距变形。弯曲能的尺寸降低的配方在抽象环境中被离散化，并为离散的Kirchhoff三角形指定；证明了与连续配方的融合。采用等轴测限制线性化的实用半无用的离散梯度流是一种迭代方法，以最大程度地减少弯曲能的迭代方法；证明了稳定性和违反等轴测限制的束缚。讨论了障碍物的融合，并通过涉及模拟大弯曲变形和接触现象的研究的数值实验来说明该方法的实际性能。
Bilayer plates are compound materials that exhibit large bending deformations when exposed to environmental changes that lead to different mechanical responses in the involved materials. In this article a new numerical method which is suitable for simulating the isometric deformation induced by a given material mismatch in a bilayer plate is discussed. A dimensionally reduced formulation of the bending energy is discretized generically in an abstract setting and specified for discrete Kirchhoff triangles; convergence towards the continuous formulation is proved. A practical semi-implicit discrete gradient flow employing a linearization of the isometry constraint is proposed as an iterative method for the minimization of the bending energy; stability and a bound on the violation of the isometry constraint are proved. The incorporation of obstacles is discussed and the practical performance of the method is illustrated with numerical experiments involving the simulation of large bending deformations and investigation of contact phenomena.
