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郭书祥,吕震宙.线性区间有限元静力控制方程的组合解法[J].计算力学学报,2003,20(1):34~38
线性区间有限元静力控制方程的组合解法
Advanced combinatorial methods for solving the governing equations of linear static interval finite element method
  修订日期:2000-12-14
DOI:10.7511/jslx20031008
中文关键词:  有限元方法 区间有限元 控制方程 组合解法
英文关键词:finite element method,interval finite element method,governing equations,combinatorial method
基金项目:国家自然科学基金(59575040,59775032),航空基金(00B53010)资助项目.
郭书祥  吕震宙
[1]空军工程大学工程学院力学教研室,陕西西安710038 [2]西北工业大学飞机工程系,陕西西安710072
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中文摘要:
      区间有限元的静力控制方程常被归结为区间方程组来求解。但实际上两者并不等价。本文根据不确定结构有限元分析的力学背景,直接从问题的基本参量的不确定性出发,将基本区间参量的边界组合与求解区间方程组的有关解法相结合,提出了线性区间有限元静力控制方程的两种组合解法-参量边界全组合法和组合迭代法。可以以较小的计算量获得或逼近位移和应力区间的准确界限。且不受基本参量变化范围的限制。算例分析表明文中方法是实用和可行的。
英文摘要:
      The static governing equations of interval finite element method (FEM) are always transformed into interval equations to solve. But, in fact, they are not equivalent. In this paper, the mechanical background of the finite element analysis of uncertain structures are taken into account, and starting directly from the uncertainties of the basic parameters, two combinatorial procedures for solving the governing equations of linear static interval FEM are presented. In our procedures, the combination of the bounds of basic interval parameters is combined with the methods that we have given in some previous papers for solving the interval equations of interval analysis of structures. The presented procedures may have a high accuracy and low computational burden, and does not restricted by the ranges of variation of the basic parameters. Two numerical examples illustrated the applicability and effectiveness of the proposed procedures.
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