The hierarchical finite cell method for multi-scale problems in structural mechanics

结构力学多尺度问题的分层有限元方法

基本信息

批准号：
183669279
负责人：
Professor Dr.-Ing. Alexander Düster
金额：
--
依托单位：
Direction de lènergie nuclèairc
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2010
资助国家：
德国
起止时间：
2009-12-31 至 2013-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/183669279?language=en
关键词：
hierarchical finite cell method multi

项目摘要

Many important problems in structural mechanics are of a multi-scale nature. In problems of this kind, the global behavior of the structure is influenced by phenomena occurring on scales that are orders of magnitude smaller than the dimensions of the structure under investigation. This situation occurs in almost all engineering applications such as civil engineering, naval architecture or mechanical engineering. In order to simulate multi-scale problems reliably in structural mechanics, it is therefore essential to develop efficient numerical methods. In spite of the recent progress made in terms of computing power, performing such simulations based on standard methods, like the finite element method, for all scales is beyond the reach of present-day computer systems. During the first, 2-year period of this research proposal, we tackled several aspects of elastostatic problems connected with multi-scale behavior by further developing the finite cell method (FCM). One of the main achievements we accomplished was to develop a hierarchical refinement strategy for the FCM, which enabled us to compute multi-scale problems efficiently. In the second project period, we wish to extend the hierarchical FCM to three-dimensional problems that crop up in elastodynamics. In this regard, we will address the simulation of wave propagationin heterogeneous materials and composites by developing the FCM further in orderto provide an efficient simulation method. We expect that the new method to be developed will significantly extend the possibilities of wave propagation simulation to support technologies such as structural health monitoring by applying high-frequency loading for detecting damage in engineering structures.

结构力学中的许多重要问题具有多尺度性质。在这种问题上，结构的全球行为受到在尺度上发生的现象的影响，而尺度的数量级小于所研究结构的维度。这种情况发生在几乎所有工程应用中，例如土木工程，海军建筑或机械工程。为了在结构力学中可靠地模拟多尺度问题，因此必须开发有效的数值方法。尽管在计算能力方面取得了最新的进展，但基于标准方法（例如有限元方法）对所有尺度进行的模拟都超出了当今的计算机系统的范围。在这项研究建议的第一个2年期间，我们通过进一步开发有限的细胞方法（FCM）解决了与多尺度行为相关的弹性静态问题的几个方面。我们取得的主要成就之一是为FCM制定层次结构策略，这使我们能够有效地计算多尺度问题。在第二个项目时期，我们希望将层次FCM扩展到弹性动力学中出现的三维问题。在这方面，我们将通过进一步开发FCM来解决在异质材料和复合材料中的波传播的模拟，以便提供有效的仿真方法。我们希望开发新的方法将大大扩展波传播模拟的可能性，从而通过应用高频加载来检测工程结构的损害来支持诸如结构健康监测的技术。