Time‐domain transient elastodynamic analysis of 3‐D solids by BEM

The numerical implementation of the Direct Boundary Element formulation for time‐domain transient analysis of three‐dimensional solids is presented in a most general and complete manner. The present formulation employs the space and time dependent fundamental solution (Stokes' solution) and Graffi's dynamic reciprocal theorem to derive the boundary integral equations in the time domain. A time‐stepping scheme is then used to solve the boundary initial value problem by marching forward in time. Higher order shape functions are used to approximate the field quantities in space as well as in time, and a combination of analytical (time‐integration) and numerical (spatial‐integration) integration is carried out to form a system of linear equations. At the end of each time step, these equations are solved to obtain the unknown field quantities at that time. Finally, the accuracy and reliability of this algorithm is demonstrated by solving a number of example problems and comparing the results against the available analytical and numerical solution.