工程力学 ›› 2019, Vol. 36 ›› Issue (9): 40-49,59.doi: 10.6052/j.issn.1000-4750.2018.07.0383

• 基本方法 • 上一篇    下一篇

基于隔离非线性的实体单元模型与计算效率分析

李佳龙1, 李钢1, 李宏男1,2   

  1. 1. 大连理工大学海岸和近海工程国家重点实验室, 辽宁, 大连 116024;
    2. 沈阳建筑大学土木工程学院, 辽宁, 沈阳 110168
  • 收稿日期:2018-07-13 修回日期:2019-01-04 出版日期:2019-09-25 发布日期:2019-04-10
  • 通讯作者: 李钢(1979-),男,辽宁葫芦岛人,教授,博士,博导,主要从事结构工程抗震等研究(E-mail:gli@dlut.edu.cn). E-mail:gli@dlut.edu.cn
  • 作者简介:李佳龙(1991-),男,四川遂宁人,博士生,主要从事结构非线性分析等研究(E-mail:wekalee@163.com);李宏男(1957-),男,辽宁沈阳人,教授,博士,博导,主要从事结构工程抗震和结构健康检测等研究(E-mail:hnli@dlut.edu.cn).
  • 基金资助:
    国家自然科学基金项目(51878112);中央高校基本科研业务费专项资金项目(DUT17ZD220);大连市高层次人才创新支持计划项目(2015R044,2017RD04)

THE INELASTICITY-SEPARATED SOLID ELEMENT MODEL AND COMPUTATIONAL EFFICIENCY ANALYSIS

LI Jia-long1, LI Gang1, LI Hong-nan1,2   

  1. 1. State Key Laboratory of Costal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China;
    2. College of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, China
  • Received:2018-07-13 Revised:2019-01-04 Online:2019-09-25 Published:2019-04-10

摘要: 实体有限元模型计算中往往需要较多的计算单元与结点数量,且这些单元状态判定以及大规模的刚度矩阵分解将消耗大量的计算资源,计算效率低。该文基于隔离非线性法理论建立了线性四面体与六面体等参单元分析模型,采用直接积分格式的6积分点替代六面体等参单元的8高斯点作为非线性应变插值点,能够在保证计算精度的同时提高单元状态判定效率。控制方程采用Woodbury公式与组合近似法联合求解,使得整个求解过程只有矩阵回代以及矩阵与向量的乘积,进一步提高了求解效率。基于时间复杂度的计算效率分析表明:随着结点自由度数目的增加,该文方法的计算效率相对传统变刚度法显著提高,数值算例验证了实体单元模型的正确性以及算法的高效性。

关键词: 隔离非线性法, 实体单元, 直接积分, Woodbury公式, 组合近似法, 效率分析

Abstract: Due to the large number of elements required in the calculation of solid finite element models, large computational resource is consumed in the element state determination process and the factorization of the global tangent stiffness matrix with large dimensions, thus resulting in low efficiency. In this paper, linear tetrahedron and hexahedron isoparametric elements are established based on the inelasticity-separated finite element method. Six direct integration points are considered for hexahedron elements as the nonlinear strain interpolation points instead of eight gauss integration points, of which the computational accuracy is stable and the efficiency is improved. In addition, the main solving process of the governing equation is only the back substitution of the initial stiffness matrix and the matrix-vector multiplication by using the Woodbury formula and combined approximation approach. Therefore, the efficiency is significantly improved. Finally, the computational efficiency of the proposed method based on the time complexity theory indicates that, with the increase of the number of nodal degrees of freedom, the computational efficiency of the proposed method is significantly improved as compared with the traditional variable stiffness method. The numerical examples verify the correctness of the proposed solid element model and the high efficiency of the proposed algorithm.

Key words: inelasticity-separated finite element method, solid element, direct integration, Woodbury formula, combined approximations approach, efficiency analysis

中图分类号: 

  • TU375.6
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