On Godunov Schemes for Combined Longitudinal and Torsional Elastic-Plastic Waves in Thin-Walled Tubes

摘要

A high-order Godunov scheme is developed and the Riemann problem is discussed for combined longitudinal and torsional elastic-plastic waves in thin-walled tubes. The scheme is based on characteristic theory of the system, uses uniform formulation for all kinds of loading paths, and thus is easy to be implemented in an actual simulation. The scheme is tested through numerical examples including steepening of waves and step loading. It is shown that the scheme keeps the principle advantages of Godunov schemes, i.e., the robust operation in the presence of strong waves, thin fronts of discontinuities with little attendant noise generated. It is turned out that the solution of a Riemann problem in the model depends on the internal structure of the initial discontinuity.