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.

拟议的研究项目的目的是开发用于选择性缩放惯性和应变的变异方法，以进行显式动态有限元分析，以开发有效，准确的四面体有限元，以进行非线性动力学和波浪传播。对于复杂的几何形状，四面体有限元在有限元网格中通常是必不可少的。由于以下问题，现有的四面体有限元素的性能受到限制：锁定，高CPU成本，高数值分散体和异质媒体中的大量反射传输错误。到目前为止，不存在通用准确的高性能四面体。为了减少锁定效应和CPU成本，这是非线性结构动力学中重要问题的CPU成本，提出了各种选择性惯性和应变缩放。基本的假设是，应应变缩放在四面体元素中的应用，容易锁定的元素，以及用于计算昂贵的元素（例如具有Allmans旋转的元素和复合有限元素的元素）的应用，可以在同一时间的准确元素中开发有效的元素。对于波传播问题，可以通过惯性定制获得高阶四面体元素的优化分散行为。最后，通过降低反射传输 - 纠正率提高了异质介质中模拟的准确性。