An extended finite element method for pipe-embedded plane thermal analysis

• A extended finite element is proposed for the pipe embeded thermal analysis.
• Using the proposed method can avoid the difficulty of modeling refined meshes and effectively improve the solving speed.
• The enrichment shape function is constructed based on the theoritical solution.
• The Dirichlet boundary condition inside the element is transformed into in-element Robin boundary.
• Multiple-pipes problems can be solved by the proposed method.

In thermal analysis of concrete with cooling pipes by conventional FEM (finite element method), extremely refined conforming meshes have to be generated around the pipe axis to obtain precise temperature field. It makes the meshing process demanding and cumbersome, especially in 3D cases. To avoid the difficulty of refining meshes in conventional FEM, an extended finite element method (XFEM) is proposed in this paper with which thermal analysis with pipes can be performed on coarse meshes instead of refined conforming meshes. The enrichment shape function is constructed in the proposed XFEM based on analytical solution and the Dirichlet boundary condition of the cooling pipe is numerically approximated by in-element Robin boundary condition. Thermal analysis of a concrete slab with a cooling pipe in the center is performed by XFEM with coarse meshes and by conventional FEM with refined conforming meshes respectively. The results demonstrate that the temperature field obtained by XFEM has a comparable accuracy level with the conventional FEM. The accuracy and reliability are further validated with three other numerical cases including the varying cooling boundary case, the internal heat source case and the multiple-pipe case.