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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都具有多尺度的性质。在这类问题中，结构的整体行为受到发生在比所研究结构的尺寸小几个数量级的尺度上的现象的影响。这种情况发生在几乎所有的工程应用中，如土木工程、造船或机械工程。因此，为了可靠地模拟结构力学中的多尺度问题，必须发展有效的数值方法。尽管最近在计算能力方面取得了进展，但基于标准方法（如有限元法）对所有尺度进行这种模拟是当今计算机系统无法达到的。在本研究计划的头两年期间，我们通过进一步发展有限细胞方法（FCM），解决了与多尺度行为相关的弹性静力学问题的几个方面。我们取得的主要成就之一是为FCM开发了一种分层优化策略，使我们能够有效地计算多尺度问题。在第二个项目期间，我们希望将分层FCM扩展到弹性动力学中出现的三维问题。在这方面，我们将通过进一步发展FCM来解决波在非均质材料和复合材料中的传播模拟，以提供一种有效的模拟方法。我们期望开发的新方法将极大地扩展波传播模拟的可能性，以支持通过应用高频加载来检测工程结构损伤的结构健康监测等技术。