Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent need generate conformal meshes, this work uses extended method (XFEM) discretize governing equations on non-conforming, embedding meshes. A flexible approach create truncated hierarchical B-splines discretizations is presented. enables refinement each state variable field individually meet field-specific accuracy requirements. obtain immersed geometry representation that consistent across all hierarchically B-spline discretizations, into a single mesh, XFEM background which constructed from union An extraction operator introduced represent bases in terms Lagrange shape functions mesh without loss accuracy. The are enriched generalized Heaviside enrichment strategy accommodate small geometric features and multi-material problems. augmented by formulation face-oriented ghost stabilization enhanced for bases. We present examples two- three-dimensional linear elastic thermo-elastic numerical results validate our framework. also demonstrate applicability proposed large, geometrically