RIM-IGABEM and DRM-IGABEM in three-dimensional general anisotropic elastic problems with complex-shape cavities

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.