一种新的无网格方法与有限元耦合法

A New Coupled Meshless-finite Element Method

本文分析了Belytschko和Huerta提出的无网格方法和有限元耦合法各自存在的问题,提出了一种新的无网格方法与有限元耦合法。Belytschko提出的方法的缺点是,无网格方法子域和有限元法子域的界面必须是规则的,交界域内有限元不能随意划分,交界域内无网格方法的节点也不能随意分布。Huerta提出的方法的缺点是对交界域内无网格方法的节点影响域可能无法覆盖交界域。本文提出的无网格方法与有限元耦合法解决了以上两种方法存在的问题,并保留了无网格方法随意配点的优点、交界面可以不规则、提高了无网格子域内的求解精度,从而提高问题的整体求解精度。然后,建立了弹性力学的无网格方法与有限元法的耦合法。最后给出了数值算例。

The coupled meshless-finite element methods presented by Belytschko and Huerta are discussed first, and the disadvantages of the methods are explained. Then a new coupled meshless-finite element method is presented. The disadvantages of the Belytschko＇s method are that the interface between meshless method sub-domain and finite element sub-domain must be regular, and that the finite element mesh can not be discretized arbitrarily and the meshless nodes can not be distributed arbitrarily in the interface sub-domain. The disadvantage of the Huerta＇s method is that the domains of influence of the meshless nodes can not cover the interface sub-domain. Our coupled meshless-finite element method can overcome all the disadvantages of Belytschko＇s and Huerta＇s methods. Moreover, the nodes are arbitrary, and that the interface between the meshless subdomain and the finite element subdomain can be irregular. And the solution precision in the meshless subdomain is greater, and thus the solution precision in the whole domain is greater. Then the formulae of the new coupled meshless-finite element method for elasticity are obtained. Some numerical examples are given at last.