稳定相容节点积分的无网格算法

首先形成了弹性力学控制方程的等效积分弱形式.针对域内高斯积分的缺陷以及直接节点积分的不稳定性，采用了基于应变光滑理论的稳定相容节点积分方案，从而改进了二维问题的无网格全局弱形式.该方案的积分域 Voronoi图是伴随于域节点的，是“天然”的网格形式.选择了添加多项式项的径向基点插值形函数，以便容易地施加本质边界条件.算例显示该方法的数值结果与解析解吻合良好，从而展现了其稳定性、精确性以及很好的鲁棒性.

A meshless method using stabilized conforming nodal integration

The equivalent integral weak form of the elastic mechanics control equation is formed.Because of the disadvantages of Guass integration and instability of direct nodal integration,the stabilized conforming nodal integration scheme is adopted based on strain smoothing theory,which improves the meshless global weak form of the 2D problem.The integral fields of this scheme,Voronoi diagram, are with grids accompanied with field nodes.Radial basis point interpolation shape function augmented with polynomial terms is selected in order to easily apply the essential boundary conditions.Numerical examples show that the numerical results have good agreement with the analytical ones,and also establish the stability,accuracy,and good robustness of the present method.