Time‐Discrete Geodesics in the Space of Shells
Time‐Discrete Geodesics in the Space of Shells
复制标题
DOI：
10.1111/j.1467-8659.2012.03180.x
复制
发表时间：
2012-08
影响因子：
2.5
通讯作者：
Behrend Heeren;M. Rumpf;M. Wardetzky;B. Wirth
中科院分区：
文献类型：
--
作者：
Behrend Heeren;M. Rumpf;M. Wardetzky;B. Wirth
从连续介质力学的概念的基础上，我们提供了一个计算模型的测地线在薄壳的空间，与度量，反映物理变形薄壳所需的粘性耗散。与以前的工作不同，我们将弯曲的贡献到我们的变形能量上的膜失真项，以获得一个物理上合理的概念壳之间的距离，这不需要额外的平滑。我们的弯曲能公式依赖于所谓的相对Weingarten映射，我们基于离散微分几何的原理提供了一个离散模拟。我们的计算结果强调了强烈的影响，物理参数的演变壳形状沿着测地线路径。
Building on concepts from continuum mechanics, we offer a computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell. Different from previous work, we incorporate bending contributions into our deformation energy on top of membrane distortion terms in order to obtain a physically sound notion of distance between shells, which does not require additional smoothing. Our bending energy formulation depends on the so‐called relative Weingarten map, for which we provide a discrete analogue based on principles of discrete differential geometry. Our computational results emphasize the strong impact of physical parameters on the evolution of a shell shape along a geodesic path.