Abstract
This paper focuses on approximation properties for strong/weak discontinuities in the PU-based finite element methods. The extended finite element method (X-FEM), which is one of the PU-based FEM, enables us to approximate the discontinuous deformation due to crack/interface with the enrichment functions. In contrast, the finite cover method (FCM), which is also one of the PU-based FEM, is capable of representing discontinuous behavior by defining the multiple sets of finite covers (elements) instead of using the enrichment functions. We examine the properties and the effects of these different PU-based approximations for strong/weak discontinuities in this paper. Section 2 shows two types of approximations of strong/weak discontinuities in the PU-based FEM by taking X-FEM and FCM for instance, and explains the equivalence of them. Several numerical examples are presented to examine the analysis accuracy and effi ciency for structures involving a line crack, a branched crack and a material interface in Section 3.
