The analysis of the Generalized-α method for non-linear dynamic problems

By Silvano Erlicher, Luca Bonaventura, O. Bursi. 2002

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On the advantages of using the first-order generalised-alpha scheme for structural dynamic problems (2017, background): “[16] have proven the ove rshoot behaviour of CHα scheme in the context of nonlinear dynamic problems.”
Convergence of the generalized-α scheme for constrained mechanical systems (2007, methodology): “It is possible to eliminate a from the integration formulae at time steps tn−1 → tn and tn → tn+1, leading to a two-step formulation [10] 2 ∑”
Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-α scheme (2014, unknown): “[23], the generalized-α method is mathematically equivalent to a two-step method for the velocity variable ˜ v and to a three-step method for the position variable ˜ q .”
Accuracy of a composite implicit time integration scheme for structural dynamics (2017, methodology): “However, it is shown in [18, 37] that the acceleration accuracy is only first order, and the three-point backward Euler method is a LMS method, which needs the former two steps to be second-order accuracy.”