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Geometrically nonlinear analysis of discretized structures by the group theoretic approach.

机译：离散理论的几何非线性分析的群理论方法。

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摘要

This thesis is concerned with the static and dynamic response analysis of large, geometrically nonlinear structures with symmetry by using a reduction technique, the Group Theoretic Approach (GTA).; In engineering practice, there are many structures that have symmetric properties. The GTA introduced provides a way in which the abstract symmetric group ideas from group theory can be applied to engineering problems, and can dramatically reduce the problem of the analysis of a large scale structure to a smaller problem which captures identical solutions to those for the original structure.; The emphasis has been on developing and using the GTA for the static and dynamic analysis of large scale geometrically nonlinear structures with symmetry.; In construction of a reduced problem for the original structure, group representation theory and projection operator theory were adopted to find symmetry modes for the configuration space of the structure. The symmetry modes were actually a set of basis vectors in the sub-space for a reduced problem, and they were used to form the transformation matrix by which the original structure was reduced to a smaller problem.; A relatively large collection of linear and geometrically nonlinear symmetric structures were treated by using the GTA. The significant numerical savings, as well as the identical solution offered by the GTA, have been demonstrated by consideration of several typical numerical problems. Various kinds of engineering structures, such as trusses, frames and membrane structures, were evaluated. It is observed that the solutions computed by the GTA in the reduced sub-space were identical to those obtained in the original full space when true symmetry exists in the structure. When the symmetry is not perfect, the GTA yields approximations, the accuracy depending upon the amount of asymmetry.; This investigation has demonstrated that the GTA is mathematically very elegant and rigorous. The GTA has a great potential in analysis of any symmetric problem which can be solved by the finite element method. This investigation also has opened a door to much wider application of the GTA.
机译：本文涉及通过使用归约技术-群理论法（GTA）-对具有对称性的大型几何非线性结构进行静态和动态响应分析。在工程实践中，有许多具有对称特性的结构。引入的GTA提供了一种方法，可以将来自群论的抽象对称群思想应用于工程问题，并且可以将大型结构分析的问题显着减少为较小的问题，从而获得与原始问题相同的解决方案结构体。;重点是开发和使用GTA进行具有对称性的大规模几何非线性结构的静态和动态分析。在构造原始结构的简化问题时，采用群表示理论和投影算子理论来寻找结构构型空间的对称模式。对称模式实际上是子空间中用于简化问题的一组基向量，并且它们用于形成变换矩阵，通过该变换矩阵将原始结构简化为较小的问题。使用GTA处理了相对较大的线性和几何非线性对称结构集合。通过考虑几个典型的数值问题，已证明了显着的数值节省以及GTA提供的相同解决方案。评估了各种工程结构，例如桁架，框架和膜结构。可以观察到，当结构中存在真正的对称性时，GTA在缩小子空间中计算出的解与在原始完整空间中获得的解相同。当对称性不理想时，GTA会得出近似值，其准确性取决于不对称性的数量。这项调查表明，GTA在数学上非常优雅且严格。 GTA在分析任何可以通过有限元方法解决的对称问题方面具有巨大潜力。这项调查也为GTA的广泛应用打开了一扇门。

著录项

  • 作者

    Li, Lingchuan.;

  • 作者单位

    The University of Western Ontario (Canada).;

  • 授予单位 The University of Western Ontario (Canada).;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 1999
  • 页码 213 p.
  • 总页数 213
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

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