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冰川冻土 ›› 2016, Vol. 38 ›› Issue (4): 1044-1051.doi: 10.7522/j.issn.1000-0240.2016.0121

• 特殊土的力学特性与工程问题 • 上一篇    下一篇

带相变瞬态温度场问题的扩展有限元解析

何敏1 2, 李宁1, 高焕焕2, 刘乃飞1   

  1. 1. 西安理工大学 岩土工程研究所, 陕西 西安 710048;
    2. 西北勘测设计研究院有限公司, 陕西 西安 710065
  • 收稿日期:2016-05-28 修回日期:2016-07-11 出版日期:2016-08-25 发布日期:2016-09-19
  • 作者简介:何敏(1981-),男,湖北随州人,高级工程师,2013年在西安理工大学获博士学位,现从事水电站设计及寒区岩土工程三场耦合方面的研究.E-mail:hem81@163.com
  • 基金资助:
    国家自然科学基金项目(11572246;5117913);西安理工大学博士学位论文创新基金项目(207-002J1306)资助

Extended finite element method analysis for the transient temperature field with phase change

HE Min1 2, LI Ning1, GAO Huanhuan2, LIU Naifei1   

  1. 1. Institute of Geotechnical Engineering, Xi'an University of Technology, Xi'an 710048, China;
    2. Xibei Engineering Corporation Limited of the Power Construction Corporation of China, Xi'an 710065, China
  • Received:2016-05-28 Revised:2016-07-11 Online:2016-08-25 Published:2016-09-19

摘要: 带相变瞬态传热问题是寒区工程多场耦合问题求解的关键.在剖析常规有限元法在求解带相变瞬态温度场问题的不足的基础上,结合冻土冻融温度变化的特点,提出采用扩展有限元法求解冻土工程带相变瞬态传热问题的新方法,以四边形单元为例推导了冻土工程温度场的求解格式,详细剖析了瞬态传热过程中移动界面水平集函数的构造、单元刚度矩阵的形成及高斯积分的求解.据此编写了相应的扩展有限元程序,通过经典Stefan问题全面验证了程序的正确性与合理性.

关键词: 水热力耦合, 相变, 瞬态温度场, 扩展有限元

Abstract: Transient heat transfer with phase change is the key to the solving of the multi-field coupling problems in cold regions. The freezing process of frozen soil can be divided into four stages based on the measured freezing curves in Changchun. Analyzing the shortage of the traditional finite element method in solving the phase change problem and the characteristic of frozen soil's freezing process, the extended finite element method (XFEM) was proposed for solving the transient heat transfer problem with phase change for permafrost engineering. The XFEM interpolating function and solving format of temperature field with phase change was derived that taking quadrilateral element as an example. Based on the study of the constructing and solving of the level set function, building of the stiffness matrix and subdividing of the elements, a XFEM program for the transient heat transfer problem with phase change was proposed in this paper which has been verified by classical Stefan problem.

Key words: THM coupling, ice-water phase change, transient temperature field, extended finite element method

中图分类号: 

  • P642.14