Variational methods for mass scaling

质量缩放的变分方法

基本信息

批准号：
279006948
负责人：
Professor Dr.-Ing. Manfred Bischoff
金额：
--
依托单位：
Institut für Baustatik und Baudynamik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2015
资助国家：
德国
起止时间：
2014-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/279006948?language=en
关键词：
Variational methods mass scaling

项目摘要

The subject of the proposed research project is the development of new variational methods for selective mass scaling in the context of explicit dynamic finite element analysis with the aim to achieve substantial speed-up for modern industrial applications. There are three fundamental innovations which we seek to develop and advance: First, a method for direct and sparse construction of consistent inverse mass matrices will be developed. Such matrices allow trivial computation of the nodal accelerations from the global force vector, i. e. no cost-intensive matrix inversion is required. Preliminary work has shown that application of selective mass scaling onto these inverse mass matrices allows to increase the critical time step by a factor of two while keeping accuracy of thecomputational results close to the ones obtained with a diagonalized mass matrix. Here, further effort is needed to extend the method for a broader range of solid finite elements and to assess accuracy, critical time step and stability of the newly obtained mass matrices via grid dispersion and eigenvalue analyses. Second, an efficient treatment of geometrically non-linear problems, unilateral contact, multi-point constraints and prescribed velocity boundary conditions together with the new mass matrices is developed. Third, variational selective mass scaling methods are extended to solid shell elements. So far only algebraic methods for selective mass scaling have been applied to this family of elements.

拟议研究项目的主题是在显式动态有限元分析的背景下开发用于选择性质量缩放的新变分方法，旨在显着加速现代工业应用。我们寻求开发和推进三项基本创新：首先，将开发一种直接稀疏构造一致逆质量矩阵的方法。这样的矩阵允许根据全局力矢量 i 来简单地计算节点加速度。 e.不需要成本密集的矩阵求逆。初步工作表明，在这些逆质量矩阵上应用选择性质量缩放可以将临界时间步长增加两倍，同时保持计算结果的精度接近使用对角化质量矩阵获得的结果。在这里，需要进一步努力将该方法扩展到更广泛的固体有限元范围，并通过网格色散和特征值分析来评估新获得的质量矩阵的准确性、关键时间步长和稳定性。其次，开发了几何非线性问题、单边接触、多点约束和规定速度边界条件以及新质量矩阵的有效处理方法。第三，变分选择性质量缩放方法扩展到固体壳单元。到目前为止，只有选择性质量缩放的代数方法已应用于该元素族。