Estimation of Stability Limit Based on Gershgorin's Theorem for Explicit Contact-Impact Analysis Signorini Problem Using Bipenalty Approach

Abstract

Abstract. The stability properties of the bipenalty method presented in Reference [4] is studied in application to one-dimensional bipenalized Signorini problem. The attention has been paid on the critical Courant numbers estimation based on Gershgorin's theorem. It is shown that Gershgorin's formula overestimates maximum eigenfrequency for all penalty ratios with exception of the critical penalty ratio. Thus, smaller safer values of critical Courant numbers are obtained in comparison with exact ones calculated from the solution of eigenvalue problem.

Time Step Estimates for Reciprocal Mass Matrices Using Ostrowski's Bounds

“…More studies are necessary for irregular meshes and other shell element types, e.g. 4 Table 5: Comparison of estimated time steps for panel example with 3-node shell elements.…”

“…Nodal time estimates, which were proposed in the 1980s [10,8], have recently obtained attention in several applications of explicit dynamics [12,2,4]. First, the nodal time estimates have allowable cost and they use only local information contained in the row or/and the column associated with a nodal degree of freedom.…”