论文标题
薄结构变形的数值近似
Numerical approximations of thin structure deformations
论文作者
论文摘要
我们使用弯曲作为主要机制来审查薄结构的不同（简化）模型，以经历大变形。每个模型都在于最小化第四阶能量，可能受到非凸约限制。使用局部不连续的Galerkin（LDG）有限元素近似平衡变形。离散能量的设计取决于与分段Hessian相比，在具有更好近似属性的不连续函数上定义的离散Hessian操作员。离散的梯度流进行适当的速度以驱动最小化过程。他们的选择是因为其稳健性和保留非凸约限制的能力。提出了一些数值实验，以展示这些模型可以实现的各种形状。
We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin (LDG) finite elements. The design of the discrete energies relies on a discrete Hessian operator defined on discontinuous functions with better approximation properties than the piecewise Hessian. Discrete gradient flows are put in place to drive the minimization process. They are chosen for their robustness and ability to preserve the nonconvex constraint. Several numerical experiments are presented to showcase the large variety of shapes that can be achieved with these models.
