二阶一致无网格与有限元耦合离散研究  

STUDY OF THE COUPLED DISCRETIZATION OF QUADRATICALLY CONSISTENT MESHFREE AND FINITE ELEMENT METHODS

作　　者：高欣[1] 王冰冰[1] 段庆林[1] 李锡夔[1] 陈飙松[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《固体力学学报》2014年第4期325-333,共9页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(11102036;11232003;11372066);973计划(2010CB731502);中央高校基本科研业务费专项资金(DUT12LK08);教育部留学回国人员科研启动基金资助

摘　　要：为准确方便地施加本质边界条件,在连续掺混法(Continuous Blending Method,CBM)的框架下,通过增加一个边中节点,发展了采用二阶基底的无网格与二阶有限元的耦合离散方法.Galerkin弱形式的数值积分采用具二阶一致性的3点积分方法(Quadratically Consistent 3-point integration method,QC3).与原本在QC3中采用的Nitsche法相比,所发展的耦合离散方法可像有限元法一样简单高效地施加本质边界条件,不向弱形式中引入额外项,也不依赖于任何人工参数.而且,数值结果还表明,QC3的计算精度也得到进一步提高.A coupled discretization scheme of meshfree methods using second-order basis and quadratic finite elements is proposed in the framework of continuous blending method （CBM）. An additional node on the center of each edge on the boundary is introduced into the proposed scheme such that the essential boundary conditions can be straightforwardly enforced as in the finite element method. The Galerkin weak form is numerically integrated by the quadratically consistent 3-point （QC3） integration method. In com- parison to the Nitsche＇s method originally used in QC3 to enforce essential boundary conditions, the pro- posed scheme does not introduce additional terms into the weak form and no artificial parameters are in- volved. In addition, numerical results also show that the accuracy of the QC3 method is further improved by proposed coupled scheme.

关 键 词：无网格 连续掺混法 QC3 一致性 有限元 

分 类 号：O241.82[理学—计算数学]