权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

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 材料是经典连续介质力学模型的推广。除了通常的位移场之外，还考虑旋转场。对于壳模型，这些旋转可以自然地解释为壳法向量的方向和扭转。因此，它们导致了 Mindlin-Reissner 模型对于大应变的自然扩展。众所周知，此类模型的离散化非常困难。不能使用通常的有限元，因为配置空间具有非线性流形的结构。现有方法在处理大旋转时会遇到不稳定和彻底崩溃的问题，并且在许多情况下它们不能保持连续模型的客观性。在过去几年中，申请人开发了测地有限元（GFE）。这些将正常拉格朗日元素推广到具有非线性流形值的函数的情况。作为一个特例，获得了 Cosserat 材料的任意阶有限元。离散化允许任何大小的旋转，并可证明保留连续模型的客观性。该项目的目标是应用测地线有限元来离散化 Cosserat 壳。为此，将处理一系列复杂性不断增加的壳模型。覆盖纯弹性外壳的初步工作已经完成。