Strategy for accurately and efficiently modelling an internal traction-free boundary based on the s-version finite element method: Problem clarification and solutions verification

In this study, a strategy based on the s-version finite element method (S-method) for accurately and efficiently modelling an internal traction-free boundary of a solid body was established utilising the Neumann boundary conditions of the local mesh. In conventional studies, the internal boundary is modelled only considering the Neumann conditions of the local mesh; the global mesh is defined independently of the geometry of the internal boundary. Although this conventional method is effective in simplifying the meshing procedure for problems of a solid body with an internal boundary, its verification has not been sufficiently investigated. This study first clarifies the limitations of the conventional method based on strict verification and discussions of the weak form of the S-method. Three methods are proposed to solve the clarified issue: (i) FCM-based, (ii) IBM-based, and (iii) XFEM-based methods. The numerical results of the respective methods showed better accuracy than that of the conventional method. Particularly, the XFEM-based method demonstrated significantly higher accuracy and successfully solved the clarified issue. Consequently, the intrinsic strengths of the S-method, which are local high accuracy with low numerical costs and simplicity in the meshing procedure, are effectively utilised for the problems of a solid body with an internal boundary by the proposed strategy of the XFEM-based method. [Display omitted] •A strategy to accurately model the internal traction-free boundary was established.•The Neumann boundary conditions of the local mesh in the S-method were utilised.•The issues of the conventional S-method were clarified by strict verification.•The proposed XFEM-based method successfully solved the clarified issue.•The intrinsic strengths of the S-method can be utilised by the proposed method.