The dual interpolation boundary face method (DiBFM) proposed recently has been successfully applied to solve various problems in two dimensions. Compared with the conventional boundary element method (BEM), it has been proved that the DiBFM has the advantages of higher accuracy, convergence rate and computational efficiency. In addition, the DiBFM is suitable to unify the conforming and nonconforming elements in the BEM implementation, as well as to approximate both continuous and discontinuous fields. Moreover, there are no geometric errors by the DiBFM in the computational process. In this paper, the DiBFM is extended successfully to solve the elasticity problems in three-dimensions (3D) with formulations derived in details. A number of numerical examples are presented in order to validate the accuracy and convergence rate of the proposed method.

最近提出的双插值边界面方法（DiBFM）已成功地应用于解决二维的各种问题。与传统的边界元法（BEM）相比，已证明DiBFM具有更高的精度，收敛速度和计算效率。另外，DiBFM适用于统一BEM实现中的合格元素和不合格元素，以及近似连续和不连续字段。而且，DiBFM在计算过程中没有几何误差。本文成功地扩展了DiBFM，以详细推导的公式解决了三维（3D）的弹性问题。为了验证所提方法的准确性和收敛速度，给出了许多数值例子。