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Stochastic finite element analyses of uncertain nonlinear plane trusses under random excitations

机译：随机激励下不确定非线性平面桁架的随机有限元分析

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摘要

A method of stochastic finite element analysis is developed in this study to solve for the response statistics and reliability of nonlinear truss structures with uncertain system parameters under random excitations. Emphasis is on structural nonlinear behavior due to both large deflection and inelastic deformation. The constitutive law is based on an explicit differential equation model, and the model parameters are determined in terms of material property constants according to plasticity theory. Random excitations are modeled as Gaussian filtered white noises, whereas uncertain system parameters are modeled as either random fields or random variables. Based on a total Lagrangian finite element formulation, a set of stochastic nonlinear equations of motion is obtained. A stochastic equivalent linearization method, in conjunction with a perturbation method, is then developed to solve for the total response statistics. A second order asymptotic method is proposed to evaluate the overall structural reliability.;Numerical studies indicate that the proposed method yields accurate results with much less computer time compared with the Monte-Carlo simulation method. It is found that the system uncertainties make a significant contribution to the total response statistics as well as to the overall probability of failure. Dominant system parameters are also identified by non-dimensional response sensitivity analyses.
机译：为了解决随机激励下具有不确定系统参数的非线性桁架结构的响应统计和可靠性问题，本文提出了一种随机有限元分析方法。重点是由于大挠度和非弹性变形而引起的结构非线性行为。本构律基于显式微分方程模型，并且根据塑性理论，根据材料属性常数确定模型参数。随机激励建模为高斯滤波的白噪声，而不确定的系统参数建模为随机场或随机变量。基于总的拉格朗日有限元公式，获得了一组随机的非线性运动方程。然后，开发了一种随机等效线性化方法和一种微扰方法来求解总响应统计量。提出了一种二阶渐近方法来评估整体结构的可靠性。数值研究表明，与蒙特卡洛模拟方法相比，该方法产生的准确结果所需的计算机时间更少。发现系统不确定性对总响应统计以及整个故障概率有重大贡献。还可以通过无量纲响应灵敏度分析来识别主要的系统参数。

著录项

  • 作者

    Cherng, Rwey-Hua.;

  • 作者单位

    University of Illinois at Urbana-Champaign.;

  • 授予单位 University of Illinois at Urbana-Champaign.;
  • 学科 Civil engineering.;Mechanics.
  • 学位 Ph.D.
  • 年度 1992
  • 页码 156 p.
  • 总页数 156
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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