On an analytical method to solve singular integrals both in space and time for 2-D elastodynamics by TD-BEM

A joint analytical–numerical integration method is proposed to solve the time domain boundary integral equations for 2-D elastodynamics. The analytical integration method is adopted to solve the discrete boundary integral equations for elastodynamics with singular integrals, while the numerical integration method is conventionally adopted to solve the discrete boundary integral equations for elastodynamics without singular integrals. Accurate quantitative relationships for G and H matrices between elastostatics and elastodynamics are established, under certain assumptions. All the singularities in G and H matrices for 2-D elastodynamics are analytically solved in the process of the discretization in space and time. The analytical method to solve singular integrals in space and time is verified by the examples of 1-D rod and 2-D cantilever beam under sudden loads.