Non‐linear space‐time elasticity
Non‐linear space‐time elasticity
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非线性时空弹性
DOI：
10.1002/nme.7194
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发表时间：
2023
影响因子：
2.9
通讯作者：
C. Hesch
中科院分区：
文献类型：
--
作者：
S. Schuß;S. Glas;C. Hesch
在这篇文章中，我们介绍了一种新的非线性弹性时空公式，能够使用时空圆柱体中的结构化和非结构化网格高效地计算大变形和位移，而不改变所需的规则性，从而能够使用拉格朗日形函数，包括四面体和超四面体或超正方体元素。对空间和时间方向的共同和不加区别的处理使我们能够消除并行计算中的一个主要瓶颈：时间步进方案的设计，它既不能在时间上有效地并行化，也不允许局部细化，因为不可能在时间上向后传输信息。此外，时间步长格式的稳定性取决于每个时间步长中局部逼近误差的累积，与时空格式相反，时空格式具有增强的稳定性和鲁棒性。最后，我们将使用各种示例（包括非线性弹性背景下的高灵敏度系统）来证明相对于经典时间步进格式的收敛优势。
In this contribution we introduce a novel space‐time formulation for non‐linear elasticity, able to calculate large deformations and displacements with high efficiency using structured and unstructured meshes in the space‐time cylinder without changing the required regularity and thus, enabling the use of Lagrangian shape functions including tetrahedron and hypertetrahedron or tesseract elements. The common and indiscriminate treatment of spatial and temporal directions allows us to remove one of the major bottlenecks in parallel computations: The design of time‐stepping schemes, which can neither been parallelized efficiently in time nor allow for local refinements as no information transfer backwards in time is possible. Moreover, stability of time‐stepping schemes depend on the accumulation of local approximation errors in each time‐step, in contrast to space‐time formulation, characterized by enhanced stability and robustness. Eventually, we will demonstrate superiority in the convergence against classical time‐stepping schemes using various examples including highly sensitive systems in the context of non‐linear elasticity.
DOI：
10.1016/j.cma.2017.08.020
发表时间：
2017-11
影响因子：
7.2
作者：
C. Hesch;S. Schuß;M. Dittmann;S. Eugster;M. Favino;R. Krause
通讯作者：
C. Hesch;S. Schuß;M. Dittmann;S. Eugster;M. Favino;R. Krause