Discretization of geometrically exact elasto-plastic Cosserat shells using geodesic finite elements

使用测地有限元对几何精确的弹塑性 Cosserat 壳进行离散化

基本信息

批准号：
245812845
负责人：
Professor Dr. Oliver Sander
金额：
--
依托单位：
Scientific Computing Center (SCC)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2016-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/245812845?language=en
关键词：
Discretization geometrically exact elasto plastic

项目摘要

Cosserat materials are a generalization of the classic continuum mechanics model. In addition to the usual displacement field, a field of rotations is considered. In the case of shell models, these rotations can be interpreted naturally as the orientation and torsion of the shell normal vector. They hence lead to a natural extension of the Mindlin-Reissner model for large strains.The discretization of such models is notoriously difficult. The usual finite elements cannot be used, since the configuration space has the structure of a nonlinear manifold. Existing approaches suffer from instabilities and outright crashes when dealing with large rotations, and in many cases they do not preserve the objectivity of continuous models.During the last few years, geodesic finite elements (GFE) have been developed by the applicant. These generalize normal Lagrange elements to the case of functions with values in a nonlinear manifold. As a special case, finite elements of arbitrary order for Cosserat materials are obtained. The discretization allows rotations of any size, and provably preserves the objectivity of continuous models.The goal of this project is to apply geodesic finite elements for the discretization of Cosserat shells. For this, a sequence of shell models of increasing complexity will be treated. Preliminary work covering the purely elastic case is already available.

Cosserat材料是经典连续机械模型的概括。除了通常的位移场外，还考虑了旋转场。在壳模型的情况下，这些旋转可以自然解释为壳正常向量的方向和扭转。因此，它们导致了Mindlin-Reissner模型的自然扩展，以实现大型菌株。众所周知，这种模型的离散化是困难的。由于配置空间具有非线性歧管的结构，因此无法使用通常的有限元素。现有的方法在处理大型轮换时会遭受不稳定性和彻底的崩溃，并且在许多情况下，它们并不保留连续模型的客观性。在过去的几年中，申请人已经开发了大地测量有限元素（GFE）。这些将正常的lagrange元素推广到具有非线性歧管中值的函数情况。作为特殊情况，获得了哥塞拉特材料的任意订单的有限要素。离散化允许旋转任何大小，并证明可以保留连续模型的客观性。该项目的目的是将地理有限元元素应用于Cosserat shell的离散化。为此，将处理一系列复杂性的壳模型。涵盖纯弹性情况的初步工作已经可用。