Accurate solution of wave propagation problems in elasticity. (June 2021) - Kim, Ki-Tae; Bathe, Klaus-Jürgen
Highlights: We present a solution scheme for the accurate solution of wave propagations in general solids. The procedure is based on the use of overlapping finite elements and direct time integration. The solution converges monotonically as the spatial discretization and time stepping become finer. We present the accurate solutions of some wave propagation problems that are difficult to solve accurately. The problems solved may be benchmark problems in the evaluations of computational schemes. Abstract: The accurate solution of wave propagations in general two- and three-dimensional solids is still difficult and frequently impossible to achieve with the current computational schemes and computers available. We present in this paper a solution scheme that has much promise for the accurate solution of wave propagations in general solids. The procedure is based on the use of "overlapping finite elements" and direct time integration. The overlapping finite elements are effective because the spatial dispersion error is relatively small and can be monotonically reduced using a finer mesh. Similarly, the time integration dispersion errors can also be reduced monotonically as the time step becomes smaller. Hence the key property of the solution scheme is that the total dispersion error in the simulation of multiple waves traveling through solids is monotonically reduced as the spatial discretization and time stepping become finer. We summarize the ingredients of the solution scheme and illustrate the characteristics in the solution of some wave propagation problems that are difficult to solve accurately. These solutions may be benchmark solutions to use in the evaluations of other computational schemes.