When the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

当使用基于全空间弹力基本解的对称Galerkin边界元方法（SGBEM）来解决Neumann问题时，由于涉及不可避免的刚体运动项，因此无法唯一确定位移解。引入了几种用于消除非唯一性的方法，包括附加点支持，特征分解，奇异系统的正则化和修改后的边界积分方程，以修正SGBEM，并进行了验证，以消除溶液中的刚体运动。全空间外部Neumann问题。由于半空间问题在岩土工程实践中很常见，并且通常是诺伊曼（Neumann）问题，因此还使用带有截断的自由表面网格的修正SGBEM对典型的半空间问题进行了分析。然而，对于研究的所有消除不均匀性的方法，显示出各种级别的错误。其中，基于Fredholm理论的修正边界积分方程组相对更可取，因为它在加载区域内部和附近具有精确的结果，尤其是在变形显着变化的地方。