The scaled boundary finite element method (SBFEM) is a semi-analytical numerical method, which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only. In a subdomain, all fields of state variables including displacement, stress, velocity and acceleration are semi-analytical, and the kinetic energy, strain energy and energy error are all integrated semi-analytically. These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains. Because only a small number of subdomains are subdivided, mesh refinement is very simple and efficient, and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate. Two 2D examples with stress wave propagation were modelled. The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses, using only a fraction of degrees of freedom required by adaptive finite element method.
Zhang, ZH., Yang, J., Liu, GH., & Hu, YJ. (2011). An adaptive scaled boundary finite element method by subdividing subdomains for elastodynamic problems. Science China Technological Sciences, 54(Supp 1), 101-110. https://doi.org/10.1007/s11431-011-4598-3