The enriched degree of freedom method for the absorbing boundary and its application to XFEM in elastodynamic problems

For elastodynamic problems, significant effort has been exerted by numerical researchers to eliminate the reflection of outgoing elastic waves at the boundary of the computational domain. Eliminating these reflection is very important for correctly analyzing the dynamic response of various structures. In this paper, the enriched degree of freedom method is first proposed to absorb outgoing elastic waves; degrees of freedom are added to the nodes in the absorbing domain by using a user-defined function. Next, the gradually increasing mass matrix is derived to further dampen the elastic waves based on the theory of the perfectly matched layer. Then, a novel damping method is proposed based on the enriched degree of freedom method, and it is appropriately coupled with the XFEM and the modi-fied Newmark algorithm to solve elastodynamic problems with infinite boundaries. Finally, the numerical results show that the proposed method is feasible and applicable for ab-sorbing the outgoing elastic waves. Importantly, the proposed method is independent of the frequency; it can be used to simulate the field-scale model and the laboratory-scale model, and it is effective in solving problems with multiple cracks.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper proposes a method that combines the enriched degree of freedom method with a damping method to solve the issue of boundary reflection in elastodynamic problems. The method is versatile, applicable to various structures and problems with multiple cracks, and is not affected by frequency.