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Methods for selective scaling of strain and inertia for explicit dynamics with tetrahedral finite elements

四面体有限元显式动力学的应变和惯性选择性缩放方法

基本信息

批准号：
326748051
负责人：
Professor Dr.-Ing. Anton Tkachuk
金额：
--
依托单位：
Institutionen för ingenjörsvetenskap och fysik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/326748051?language=en
关键词：
Methods selective scaling strain inertia

项目摘要

Purpose of the proposed research project is the development of variational methods for selective scaling of inertia and strain for explicit dynamic finite element analysis to develop efficient and accurate tetrahedral finite elements for non-linear dynamics and wave propagation. For complex geometries, tetrahedral finite elements are often indispensable in finite element meshes. Existing tetrahedral finite elements are limited in their performance due to the following issues: Locking, high CPU cost, high numerical dispersion and large reflection-transmission errors in heterogeneous media. So far, the universal accurate high-performance tetrahedral does not exist. To reduce locking effects and CPU cost, which are important issues in non-linear structural dynamics, variational selective inertia and strain scaling is proposed. The basic hypothesis is that the application of strain scaling for tetrahedral elements prone to locking and the application of inertia scaling for computationally expensive elements like elements with Allmans rotations and composite finite elements enables the development of efficient and at the same time accurate elements. For wave propagation problems, an optimized dispersion behavior of higher-order tetrahedral elements may be obtained by inertia customization. Finally, the accuracy for simulation in heterogeneous media is improved by a reduction of the reflection-transmission-error.

拟议研究项目的目的是开发用于显式动态有限元分析的惯性和应变选择性缩放的变分方法，以开发用于非线性动力学和波传播的高效且准确的四面体有限元。对于复杂的几何形状，四面体有限元往往是不可缺少的有限元网格。现有的四面体有限元由于以下问题而在性能上受到限制：锁定、高CPU成本、高数值色散和在非均匀介质中的大反射-透射误差。到目前为止，还不存在普遍精确的高性能四面体。为了减少非线性结构动力学中的重要问题锁定效应和CPU成本，提出了变分选择惯性和应变缩放。基本的假设是，应变缩放的四面体元素的应用程序容易锁定和计算昂贵的元素，如元素与Allmans旋转和复合有限元的惯性缩放的应用程序，使开发高效，同时准确的元素。对于波传播问题，可以通过惯性定制来获得高阶四面体单元的优化色散行为。最后，通过减小反射透射误差，提高了非均匀介质中的模拟精度。