The local boundary integral equation (LBIE) method is a pure meshless integral method proposed by Atluri and co-workers. Since the fundamental solutions are used as the test functions, the sub-domain can be very small and the LBIE method is a promising method for solving problems of elasticity with nonhomogeneous material properties. In this paper, the subtraction technique is introduced to remove the strong singularity that results in a regularized local boundary integral equation (RLBIE) method. The formula is rather straightforward and more accurate than other treatment techniques. Compared with other meshless methods, more geometrical parameters need to be assigned in the method. If the parameters change a little bit, the solutions obtained from the method may fluctuate quickly and uncertainly. Therefore the effects of weight function, support domain, sub-domain, and monomial basis are investigated and how to select the parameters is discussed. The appropriate parameters can be determined and the meshless RLBIE method is an accurate and robust method.

局部边界积分方程（LBIE）方法是Atluri及其同事提出的纯无网格积分方法。由于将基本解用作测试函数，因此子域可能非常小，并且LBIE方法是解决具有非均质材料特性的弹性问题的有前途的方法。本文介绍了减法技术，以消除导致规则化局部边界积分方程（RLBIE）方法的强奇异性。该公式相当简单，比其他处理技术更准确。与其他无网格方法相比，该方法需要分配更多的几何参数。如果参数稍有变化，则从该方法获得的解可能会快速不确定地波动。因此权重函数的作用 研究了支持域，子域和单项式基础，并讨论了如何选择参数。可以确定适当的参数，并且无网格RLBIE方法是一种准确而可靠的方法。