Retracted: 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

It seems that the explicit KR‐α method (KRM) 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 (GM) for a linear elastic system, and it reduces to CR method (CRM) if ρ_∞ = 1is 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.     

Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation

The implicit dissipative generalized‐ α method is analyzed using discrete control theory. Based on this analysis, a one‐parameter family of explicit direct integration algorithms with controllable numerical energy dissipation, referred to as the explicit KR‐α method, is developed for linear and nonlinear structural dynamic numerical analysis applications. Stability, numerical dispersion, and energy dissipation characteristics of the proposed algorithms are studied. It is shown that the algorithms are unconditionally stable for linear elastic and stiffness softening‐type nonlinear systems, where the latter indicates a reduction in post yield stiffness in the force–deformation response. The amount of numerical damping is controlled by a single parameter, which provides a measure of the numerical energy dissipation at higher frequencies. Thus, for a specific value of this parameter, the resulting algorithm is shown to produce no numerical energy dissipation. Furthermore, it is shown that the influence of the numerical damping on the lower mode response is negligible. It is further shown that the numerical dispersion and energy dissipation characteristics of the proposed explicit algorithms are the same as that of the implicit generalized‐ α method. A numerical example is presented to demonstrate the potential of the proposed algorithms in reducing participation of undesired higher modes by using numerical energy dissipation to damp out these modes. Copyright © 2014 John Wiley & Sons, Ltd.     

A two-step unconditionally stable explicit method with controllable numerical dissipations

A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By the consistent and stability analysis, the proposed algorithms achieve the second-order accuracy and are unconditionally stable under the condition that α≥-0.5, β≤ 0.5 and γ≥-(1+α)/2. Compared with other unconditionally stable algorithms, such as Chang's algorithms and CR algorithm, the proposed algorithms are found to be superior in terms of the controllable numerical damping ratios. The unconditional stability and numerical damping ratios of the proposed algorithms are examined by three numerical examples. The results demonstrate that the proposed algorithms have a superior performance and can be used expediently in solving linear elastic dynamics problems.     

Discussion of paper ‘Simulation of floor response spectra in shake table experiments’ by G. Maddaloni,K. P. Ryu and A. M. Reinhorn,Earthquake Engineering and Structural Dynamics 2011; 40(6): 591‐604

Three main topics including the floor motion action mechanism, the test frame design, and the target spectrum simulation presented in the paper are discussed specifically. Floor motion action mechanism is critical in understanding the seismic performance of architectural nonstructural components. Seismic sensitiveness and earthquake response properties of the nonstructural components should be considered in the design of the test frame for the shaking table test. Target spectrum simulation is also a challenging job in the shaking table test, in which dynamic characteristics of the specimen, performance of the shaking table facilities, and the control techniques should be all considered. Copyright © 2011 John Wiley & Sons, Ltd.