Discussion of paper ‘Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation’ by Chinmoy Kolay and James M. Ricles, Earthquake Engineering and Structural Dynamics 2014; 43:1361–1380

Abstract

SummaryIt seems that the explicit KR‐α method (KRM), which was developed by Kolay and Ricles, is promising for the step‐by‐step integration because it simultaneously integrates unconditional stability, explicit formulation, and numerical dissipation together. It was shown that KRM can inherit the numerical dispersion and energy dissipation properties of the generalized‐α method [1] for a linear elastic system, and it reduces to CR method (CRM), which was developed by Chen and Ricles [2] if ρ∞ = 1 is adopted, where ρ∞ is the spectral radius of the amplification matrix of KRM as the product of the natural frequency and the step size tends to infinity. However, two unusual properties were found for KRM and CRM, and they might limit their application to solve either linear elastic or nonlinear systems. One is the lack of capability to capture the structural nonlinearity, and the other is that it is unable to realistically reflect the dynamic loading. Copyright © 2014 John Wiley & Sons, Ltd.