拟协调元研究综述

SURVEY OF QUASI-CONFORMING FINITE ELEMENT METHOD

拟协调元是有限元中十分重要的、具有特色的一种列式体系.拟协调元列式简单、灵活,统一了协调元、非协调元等列式方法.在列式中,拟协调元将几何方程和平衡方程同时弱化,并强调基函数在有限元空间中的重要作用;借助对位移和应变离散精度的控制,拟协调元保障了单元的收敛性,并可以利用泰勒展开校核进行简便直接的收敛性分析.研究者们利用拟协调元已经构造了大量的优秀的单元,并广泛地应用到结构问题、流体流动问题、非线性分析、稳定性和破坏分析等方面.这些工作集中体现了拟协调元的理论价值和工程应用价值.对拟协调列式方法、列式理论和已发表文献中的主要拟协调单元进行了总结.最后对拟协调的研究工作进行了展望.

Quasi-conforming analysis is an important and characteristic finite element method. The formula- tion of quasi-conforming element is simple and flexible, which unifies the conforming and non-conforming finite element method. In quasi-conforming formulation, the equilibrium equations as well as strain-displacement equations are weakened and the importance of basis functions of finite element space is emphasized. The convergence of quasi-conforming elements is guarded by the control of discrete precision of displacements and strains. The Taylor expansion test can also be used for direct analysis of convergence. Many excellent quasi- conforming elements have been constructed and applied widely in engineering analysis, which is the reflection of the value of quasi-conforming finite element method. The formulation process, theory and the important ele- ments of quasi-conforming are summarized in this paper. Finally prospective developments of quasi-conforming are suggested. The research on quasi-conforming is an original and fundamental work, which contributes to the development of computational mechanics.