This paper presents a boundary moving least squares method (BMLS) for solving 3D linear elasticity problems. In the proposed method, moving least squares interpolant is used to construct the 1D shape function employing the boundary discrete points in each axis. Then, the Kronecker product is introduced to generate the tensor product points in the regular region coving the problem domain, which simply the 3D shape function of the conventional meshless method into 1D shape function for raising the efficiency of calculation in the BMLS. In addition, building a virtual boundary is employed to solve irregular domain problems. Numerical results show that the BMLS method gives accurate solutions and desirable convergence rates when comparing with the analytical solutions and the finite element method (FEM) solutions. Furthermore, the choices of the basis function and the weight functions are also discussed in this work.

本文提出了一种边界移动最小二乘法（BMLS），用于解决3D线性弹性问题。在所提出的方法中，移动最小二乘插值用于构造利用每个轴上的边界离散点的一维形状函数。然后，引入Kronecker乘积以在覆盖问题域的规则区域中生成张量积点，从而将常规无网格方法的3D形状函数简单地转换为1D形状函数以提高BMLS中的计算效率。另外，建立虚拟边界用于解决不规则域问题。数值结果表明，与解析解和有限元方法（FEM）相比，BMLS方法可提供准确的解和理想的收敛速度。此外，