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首页> 外文学位 >FINITE ELEMENT ANALYSIS OF SYSTEM STOCHASTICITY (NEUMANN, MONTE CARLO).
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FINITE ELEMENT ANALYSIS OF SYSTEM STOCHASTICITY (NEUMANN, MONTE CARLO).

机译：系统随机性的有限元分析（纽曼，蒙特卡洛）。

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摘要

The first part of this dissertation deals with the response variability of an axially loaded prismatic bar which is subjected to static loads of a deterministic nature. The response variability arises from the spatial randomness of the elastic modulus of the bar. The problem is analyzed using the finite element method along with a Neumann expansion of the stillness matrix in order to obtain an analytic expression for the covariance matrix of the response displacement vector. The finite element size necessary to obtain sufficiently accurate values of the stochastic response parameters is examined thoroughly.; The second part deals with the stochastic finite element analysis of a wave propagation problem, consisting of a statically determinate rod having an elastic modulus varying randomly along its length and loaded with a deterministic dynamic axial load. Monte Carlo simulation techniques are used in order to analyze the system. This part has two purposes: first to find the statistical distribution functions the response quantities of the system will follow and second to examine how the input parameters of the problem affect the response variability of the system.; The third part deals with the stochastic finite element analysis of a nonlinear structural dynamic problem, consisting of a linearly elastic beam lying on a nonlinear foundation and loaded with a deterministic transverse dynamic load. The beam can be simply-supported or fixed at both ends. Monte Carlo simulation techniques are used in order to analyze the system. This part has the same two purposes as the second one.; Finally, the fourth part deals with the stochastic finite element analysis of nonlinear structural dynamic problems, consisting of a linearly elastic plate lying on a nonlinear foundation and loaded with a deterministic uniform transverse dynamic load. The plate can be simply-supported or fixed all-around. The stochasticity of the problem arises from the spatial randomness of the elastic modulus of the plate and/or from the spatial randomness of a coefficient controlling the degree of nonlinearity of the foundation. Monte Carlo simulation techniques are used in order to analyze the system. This part has again the same two purposes as the second and third ones. (Abstract shortened with permission of author.)
机译：本文的第一部分研究轴向载荷的棱柱杆的响应变化性，该杆件承受确定性的静态载荷。响应的可变性是由棒的弹性模量的空间随机性引起的。使用有限元方法以及静止矩阵的Neumann展开对问题进行分析，以获得响应位移矢量协方差矩阵的解析表达式。彻底检查了获得足够准确的随机响应参数值所需的有限元素大小。第二部分处理波传播问题的随机有限元分析，该分析由静态确定的杆组成，该杆的弹性模量沿其长度随机变化，并承受确定的动态轴向载荷。为了分析系统，使用了蒙特卡洛仿真技术。这部分有两个目的：第一，找到系统响应量所遵循的统计分布函数，第二，检查问题的输入参数如何影响系统的响应可变性。第三部分处理非线性结构动力问题的随机有限元分析，该问题由位于弹性地基上并承受确定性横向动态载荷的线性弹性梁组成。梁可以简单地支撑或固定在两端。为了分析系统，使用了蒙特卡洛仿真技术。这一部分具有与第二个目的相同的两个目的。最后，第四部分处理非线性结构动力问题的随机有限元分析，该分析由位于非线性基础上并承受确定性均匀横向动态载荷的线性弹性板组成。该板可以简单地支撑或全方位固定。问题的随机性是由于板的弹性模量的空间随机性和/或控制基础非线性程度的系数的空间随机性引起的。为了分析系统，使用了蒙特卡洛仿真技术。这部分又具有与第二和第三目的相同的两个目的。 （摘要经作者许可缩短。）

著录项

  • 作者

    DEODATIS, GEORGIOS.;

  • 作者单位

    Columbia University.;

  • 授予单位 Columbia University.;
  • 学科 Engineering Civil.
  • 学位 Ph.D.
  • 年度 1987
  • 页码 209 p.
  • 总页数 209
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 建筑科学;
  • 关键词

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