运动方程自适应步长求解的一个新进展——基于EEP超收敛计算的线性有限元法

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英文篇名：NEW DEVELOPMENT OF SOLUTION OF EQUATIONS OF MOTION WITH ADAPTIVE TIME-STEP SIZE——LINEAR FEM BASED ON EEP SUPERCONVERGENCE TECHNIQUE 作者：袁驷 ; 袁全 ; 闫维明 ; 李易 ; 邢沁妍 英文作者：YUAN Si;YUAN Quan;YAN Wei-ming;LI Yi;XING Qin-yan;Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Department of Civil Engineering, Tsinghua University;Beijing Key Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology; 关键词：Galerkin有限元法 ; 运动方程 ; EEP超收敛 ; 自适应步长 ; 结点位移精度修正 英文关键词：Galerkin FEM;;equations of motion;;EEP super-convergence;;adaptive time-step length;;recovery of nodal displacement accuracy 中文刊名：GCLX 英文刊名：Engineering Mechanics 机构：清华大学土木工程系土木工程安全与耐久教育部重点实验室;北京工业大学建筑工程学院工程抗震与结构诊治北京市重点实验室; 出版日期：2018-02-25 出版单位：工程力学 年：2018 期：v.35 基金：国家自然科学基金项目(51378293,51078199,51508305) 语种：中文; 页：GCLX201802004 页数：8 CN：02 ISSN：11-2595/O3 分类号：25-32

摘要

该文采用最简单的Galerkin型线性单元,对运动方程构建了简捷高效的单步法递推公式;进而基于EEP超收敛计算技术,开发了单元步长自动优化和结点位移精度修正两项关键技术,可在整个时域上得到误差分布均匀且逐点满足给定的误差限的解答——堪称数值解析解。该文给出了单自由度和多自由度的数值算例以验证本法的有效性。
        This paper uses the simplest linear finite elements of the Galerkin type and gives a compact and efficient recurrence solution formula for equations of motion. Further, based on the EEP(Element Energy Projection) super-convergence technique, two critical techniques, i.e. adaptive time-step size and recovery of nodal displacement accuracy, have been developed, enabling a linear finite element solution with errors uniformly distributed and satisfying the pre-specified error tolerance at any moment in the whole time domain. Numerical examples of both single and multiple degreed systems are given to verify the validity of the proposed method.

引文

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    该文在第26届结构工程学术会议(2017长沙)应邀作特邀报告