无单元法研究现状及展望  

CURRENT STUDY AND DEVELOPMENT OF ELEMENT-FREE GALERKIN METHOD

作　　者：周小平[1] 周瑞忠[1] 

机构地区：[1]福州大学土木建筑工程学院,福州350002

出　　处：《工程力学》2005年第1期12-20,共9页Engineering Mechanics

基　　金：福建省自然科学基金(E0310011)

摘　　要：无单元法是众多无网格方法中较有代表性的一种,形式简单、明确,计算精度高。因其具有仅需离散的结点信息、解答具有高次连续性、能较好地反映应力高梯度分布并便于跟踪裂纹的扩展过程等优点,无单元法自问世以来获得了广泛的重视,已成为计算力学领域的一个研究热点。文中着重分析了无单元法研究中的热点问题及解决方法,介绍了该方法目前的一些应用范围,并指出其可能的发展方向。Element-Free Galerkin Method (EFG) is a typical meshless method. Compared with other meshless methods, EFG method has simple, definite form, and can achieve highly accurate solution. There are also several notable advantages in the applications of EFG method, such as only required discrete nodal data, higher order continuity of the solutions, being able to represent high-gradient stress field and to track the spread process of crack propagation. At present, EFG method has become a study issue in computational mechanics field. This paper is concerned with the EFG method. Some major problems in EFG, such as choosing base function, determining radius of domain of influence, introducing essential boundary conditions, are addressed. Meanwhile, many results of applications of EFG are introduced. Finally, the prospect of EFG's development is discussed.

关 键 词：计算力学 无单元法 综述 无网格方法 滑动最小二乘法 

分 类 号：O302[理学—力学]