The paper establishes the pure boundary integral equations of the isogeometric boundary element method (IGABEM) based on isotropic fundamental solutions to solve three-dimensional (3D) general anisotropic elastic problems including various complex cavities. The residual method is employed which introduces the fictitious body force causing the domain integral. Subsequently, the radial integration method (RIM) and the dual reciprocity method (DRM) are utilized to transform the domain integral to the boundary integral, respectively. Moreover, the Bézier extraction technique are used to facilitate the incorporation of NURBS into boundary element codes. Based on this, a novel scheme to determine the location of the collocation points in NURBS elements is proposed. Finally, the theoretical frameworks of the RIM-IGABEM and the DRM-IGABEM are developed, which retain the advantages of BEM and IGA, i.e. only boundary is discretized and complex geometry is described exactly, and the schemes are adaptable that only require to change pre-processing of a considered anisotropic problems, including the material properties and the geometry. Several numerical examples are used to demonstrate effectiveness of the schemes, and the effects of the material properties and the geometric shape on the distribution of displacements are discussed in detail.

中文翻译：

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RIM-IGABEM 和 DRM-IGABEM 在复杂形状空腔的三维一般各向异性弹性问题中的应用


该文基于各向同性基本解建立了等几何边界元法 （IGABEM） 的纯边界积分方程，用于求解包括各种复杂空腔在内的三维 （3D） 一般各向异性弹性问题。采用残差方法，引入导致域积分的虚构体力。随后，利用径向积分法 （RIM） 和对偶互易法 （DRM） 分别将域积分转换为边界积分。此外，贝塞尔提取技术用于促进将 NURBS 合并到边界元代码中。基于此，提出了一种确定 NURBS 单元中配置点位置的新方案。最后，开发了 RIM-IGABEM 和 DRM-IGABEM 的理论框架，它们保留了边界元法和 IGA 的优点，即仅离散边界，精确描述复杂几何形状，并且方案适应性强，只需要改变所考虑的各向异性问题的预处理，包括材料属性和几何形状。使用几个数值示例来证明这些方案的有效性，并详细讨论了材料属性和几何形状对位移分布的影响。