An adaptive recursive SBFE algorithm for the dynamic analysis of Viscoelastic problems

Abstract Integrating the advantages of the Scaled Boundary Finite Element Method (SBFEM) and a temporally piecewise adaptive algorithm (TPAA), an effective numerical approach is developed for the dynamic analysis of viscoelastic problems. By virtue of a piecewise variables separation, a temporally and spatially coupled dynamic viscoelastic problem is decoupled into a series of recursive spatial problems which are solved by SBFEM. A stable and accurate temporal solution can be achieved via an adaptive process when the step size varies, and the convenience for the treatment of stress singularity and mesh generation in the viscoelastic dynamic analysis can be provided by SBFEM. Numerical tests are conducted to verify the effectiveness of the proposed approach and to highlight the advantages introducing SBFEM over the conventional methods in the dynamic analysis, and the proposed results agree well with references.