求解二维弹性问题的径向基差分法

Radial Basis Function-Finite Difference Method for Solving 2D Elastic Problem

常规的配点型无网格法在求解弹性力学问题中,存在求解精度差和纽曼边界条件处理等局限.为解决这一问题,通过利用流体力学中基于径向基构造的差分格式(RBF-FD),来求解弹性力学平面问题.同时,为了进一步提高求解精度,对纽曼边界条件采用Hermite插值进行处理.数值算例表明,该方法具备良好的收敛性,并有着较高的精度,可有效解决传统配点型无网格法精度差的问题.同时,也表明该方法可以应用于弹性力学问题的求解.

Poor precision and treatment of Neumann boundary conditions are two major limitations in conventional meshless collocation method. In order to overcome those limitations, radial basis function-finite difference method （RBF-FD）, which is widely used in computational fluid mechanics, was introduced to solve 2-dimensional problems in elasticity. Hermite interpolation was adopted to reduce the error arising from Neumann boundary conditions. Numerical case demonstrates that, the proposed method achieves good convergence as well as high accuracy. Limitation of poor precision in conventional meshless collocation method can be effectively overcome. The numerical method can also be applied to solve the problems in elasticity.