Wolff Sebastian, Bucher Christian
Forschungsbereich für Baumechanik und Baudynamik, Technische Universität Wien Karlsplatz 13/E2063, 1040 Wien, Austria.
Int J Numer Methods Eng. 2013 Aug 17;95(7):562-586. doi: 10.1002/nme.4516. Epub 2013 Jul 3.
This article presents asynchronous collision integrators and a simple asynchronous method treating nodal restraints. Asynchronous discretizations allow individual time step sizes for each spatial region, improving the efficiency of explicit time stepping for finite element meshes with heterogeneous element sizes. The article first introduces asynchronous variational integration being expressed by drift and kick operators. Linear nodal restraint conditions are solved by a simple projection of the forces that is shown to be equivalent to RATTLE. Unilateral contact is solved by an asynchronous variant of decomposition contact response. Therein, velocities are modified avoiding penetrations. Although decomposition contact response is solving a large system of linear equations (being critical for the numerical efficiency of explicit time stepping schemes) and is needing special treatment regarding overconstraint and linear dependency of the contact constraints (for example from double-sided node-to-surface contact or self-contact), the asynchronous strategy handles these situations efficiently and robust. Only a single constraint involving a very small number of degrees of freedom is considered at once leading to a very efficient solution. The treatment of friction is exemplified for the Coulomb model. Special care needs the contact of nodes that are subject to restraints. Together with the aforementioned projection for restraints, a novel efficient solution scheme can be presented. The collision integrator does not influence the critical time step. Hence, the time step can be chosen independently from the underlying time-stepping scheme. The time step may be fixed or time-adaptive. New demands on global collision detection are discussed exemplified by position codes and node-to-segment integration. Numerical examples illustrate convergence and efficiency of the new contact algorithm. Copyright © 2013 The Authors. published by John Wiley & Sons, Ltd.
本文介绍了异步碰撞积分器以及一种处理节点约束的简单异步方法。异步离散化允许为每个空间区域设置单独的时间步长，提高了具有异构单元尺寸的有限元网格显式时间步长的效率。本文首先介绍了由漂移和踢腿算子表示的异步变分积分。线性节点约束条件通过力的简单投影来求解，该投影被证明等同于RATTLE。单边接触通过分解接触响应的异步变体来求解。其中，通过修改速度来避免穿透。尽管分解接触响应求解一个大型线性方程组（这对显式时间步长方案的数值效率至关重要），并且在处理接触约束的过约束和线性相关性（例如来自双面节点到表面接触或自接触）方面需要特殊处理，但异步策略能够高效且稳健地处理这些情况。一次只考虑一个涉及非常少量自由度的约束，从而得到非常高效的解决方案。以库仑模型为例说明了摩擦的处理。对于受约束的节点接触需要特别小心。结合上述对约束的投影，可以提出一种新颖的高效求解方案。碰撞积分器不影响临界时间步长。因此，可以独立于基础时间步长方案选择时间步长。时间步长可以是固定的或时间自适应的。通过位置编码和节点到线段积分举例讨论了对全局碰撞检测的新要求。数值示例说明了新接触算法的收敛性和效率。版权所有© 2013作者。由约翰·威利父子有限公司出版。
