新型无网格法(IMLS方形域法)的研究及其应用

Study of a new meshless method(IMLS Method of Square Sphere) and its application

根据最新无网格法的前沿研究,提出了一种新型无网格法-IMLS方形域法。该法在场函数近似、权函数选取以及方形域数值积分等方面给出了全新的格式。方法中未知变量的近似采用IMLS技术,局部影响域形状采用方形几何形态。这些技术的具体实施展现了节点布置和数值积分的无网格特点,并自然满足Dirichlet边界条件。该方法可以容易求解偏微分方程初值或边值问题上实现,此外,计算了一维固结问题、二维弹性力学平面问题的算例,所得计算结果证明:该方法是一种具有收敛快、精度高、简便有效的通用方法,在工程中具有广阔的应用前景。

According to some recent studies of meshless methods, a new technique of meshless methods was presented - the meshless Interpolating Moving Least Square （IMLS） method in square sphere. The method showed new formula in the approximations of the unknown variable, the choice of weighted function and the numerical integration in the square sphere. Concerning the method, the technique of IMLS was adopted for the approximations of the unknown variable, and the square sphere was used for the geometric form of the local influence field. The adoption of these techniques presented the features of mesh free that the nodes were placed and the numerical integration was performed without a mesh. The Dirichlet boundary condition was also satisfied. The method could be easily applied to initial or boundary value problems of PDE. Besides, excellent convergence rate, high accuracy and good efficiency of the method were demonstrated by the examples in the problem of 1D consolidation and the 2D elastic mechanics. It was very promising in engineering applications.