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力学与实践 ›› 2017, Vol. 39 ›› Issue (5): 433-440.doi: 10.6052/1000-0879-17-115

• 专题综述 • 上一篇    下一篇

Trefftz有限元法的研究进展

王克用, 李培超   

  1. 上海工程技术大学机械工程学院, 上海 201620
  • 收稿日期:2017-04-05 修回日期:2017-05-03 出版日期:2017-10-15 发布日期:2017-11-06
  • 作者简介:王克用,博士,副教授,主要研究方向为Trefftz有限元法和多孔介质传热.E-mail:k.y.wang@126.com

RESEARCH ADVANCES IN THE TREFFTZ FINITE ELEMENT METHOD

WANG Keyong, LI Peichao   

  1. School of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China
  • Received:2017-04-05 Revised:2017-05-03 Online:2017-10-15 Published:2017-11-06

摘要:

Trefftz有限元法(Trefftz finite element method,TFEM)是一种高效的数值计算方法,兼有传统有限元法和边界元法的诸多优点.基于双独立插值模式,结合杂交泛函和高斯散度定理,推得仅含边界积分的有限元格式.简述了过去10年间(2007-2016) Trefftz有限元法在单元域内插值函数、源项处理、特殊功能单元以及非各向同性材料等方面的研究进展,并对未来的发展趋势给出了几点展望.

关键词:

Trefftz有限元法|域内插值函数|边界积分|特殊功能单元|无源化处理

Abstract:

The Trefftz finite element method (TFEM) is an efficient numerical approach with many joint advantages of the conventinal finite and boundary element methods. Based on the mutual independent interpolation modes, the finite element formulation involving the boundary integrations only is derived by incorporating the hybrid functional and the Gaussian divergence theorem. The research advances in the internal interpolation function, the treatment of the source term, the special-purpose element and the nonisotropic material during the past decade (2007-2016) are reviewed and several directions are pointed out for the future development.

Key words:

Trefftz finite element method|internal interpolation function|boundary integration|specialpurpose element|non-source treatment

中图分类号: 

  • O343.1