论文标题
LDG的大变形板的近似
LDG approximation of large deformations of prestrained plates
论文作者
论文摘要
较小的板板大变形模型的模型包括最大程度地减少弯曲能量的二阶弯曲能量，但受到非凸度度量的约束。前者涉及中间板的第二种基本形式，后来是对其第一种基本形式的限制。我们讨论了该简化模型的形式推导以及等效公式，该公式使其在计算上可正常。我们提出了一种局部不连续的Galerkin（LDG）有限元方法，该方法取决于重建的Hessian概念。我们设计离散的梯度流以最大程度地减少随之而来的非凸问题并找到合适的初始变形。我们提出了一些有见地的数值实验，这是一些实际的兴趣，并评估了近似过程的各个计算方面。
A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the later is a restriction on its first fundamental form. We discuss a formal derivation of this reduced model along with an equivalent formulation that makes it amenable computationally. We propose a local discontinuous Galerkin (LDG) finite element approach that hinges on the notion of reconstructed Hessian. We design discrete gradient flows to minimize the ensuing nonconvex problem and to find a suitable initial deformation. We present several insightful numerical experiments, some of practical interest, and assess various computational aspects of the approximation process.
