工程力学 ›› 2020, Vol. 37 ›› Issue (3): 18-27.doi: 10.6052/j.issn.1000-4750.2019.01.0189

• 基本方法 • 上一篇    下一篇

隔离非线性分层壳有限单元法

李钢, 吕志超, 余丁浩   

  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
  • 收稿日期:2019-04-14 修回日期:2019-10-24 出版日期:2020-03-25 发布日期:2020-03-07
  • 通讯作者: 李钢(1979-),男,辽宁人,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:吕志超(1993-),男,黑龙江人,硕士生,主要从事结构非线性分析等研究(E-mail:2858468050@qq.com);余丁浩(1989-),男,河北人,博士生,主要从事结构非线性分析等研究(E-mail:954545127@qq.com).
  • 基金资助:
    国家重点研发计划项目(2018YFD1100404);大连市高层次人才创新支持计划项目(2017RD04)

THE FINITE ELEMENT MODEL FOR INELASTICITY-SEPARATED MULTI-LAYER SHELL

LI Gang, Lü Zhi-chao, YU Ding-hao   

  1. State Key Laboratory of Costal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China
  • Received:2019-04-14 Revised:2019-10-24 Online:2020-03-25 Published:2020-03-07

摘要: 分层壳单元由于其模型简单,物理意义清晰,被广泛应用于建筑结构的有限元数值模拟中。该文基于隔离非线性有限元法提出了分层壳单元的高效非线性分析模型,将分层壳单元的截面变形(应变和曲率)分解为线弹性变形和非线性变形,以单元中面的高斯积分点作为非线性变形插值结点,建立了非线性变形场,并根据虚功原理,推导了分层壳单元的隔离非线性控制方程,采用Woodbury公式和组合近似法联合求解控制方程。依据时间复杂度理论的统计分析表明:该文建立的方法相较于传统变刚度有限元方法在非线性分析效率方面具有显著优势。并与有限元软件ANSYS的计算结果进行对比,验证了该文方法的准确性。

关键词: 隔离非线性有限元法, 分层壳单元, Woodbury公式, 组合近似法, 时间复杂度理论

Abstract: The multi-layer shell element is widely used for the numerical simulation of engineering structures because of its simple model and clear physical property. An efficient nonlinear analysis model for the multi-layer shell element is proposed based on the theory of the inelasticity-separated finite element method (IS FEM), in which the section deformation of the element is decomposed into linear elastic and nonlinear components, and the nonlinear deformation field is established by using Gaussian integration in the middle of the element as the interpolation point. Based on the principle of virtual work, a governing equation for the multi-layer shell element with the IS FEM form is derived by treating the decomposed nonlinear deformation as additional degrees of freedom. Moreover, the governing equation can be solved efficiently by incorporating the combined approximations method into Woodbury formula. The time complexity theory is used to evaluate the computational efficiency of both the proposed method and the conventional finite element method, and the results show that the present method has significant advantages in structural nonlinear analysis. Finally, two numerical examples are used to verify the accuracy and efficiency of the proposed algorithm by comparing the results with ANSYS results.

Key words: inelasticity-separated finite element method, multi-layer shell element, Woodbury formula, combined approximations method, time complexity theory

中图分类号: 

  • TU311.4
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