On a composite implicit time integration procedure for nonlinear dynamics

By Klaus-Jürgen Bathe, Mirza M. Irfan Baig. 2005

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Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme (2007, methodology): “[14] and [15] .”
Performance of an implicit time integration scheme in the analysis of wave propagations (2013, background): “In earlier work an effective implicit time integration scheme was proposed for the finite element solution of nonlinear dynamic problems [1,2].”
Accuracy of a composite implicit time integration scheme for structural dynamics (2017, methodology): “Because it is well known that there is no numerical damping in the Newmark method when ı D 1=2, the well-known three-point backward Euler formula is employed and aimed to display some numerical damping and to stabilize the time integration scheme [20].”
Insight into an implicit time integration scheme for structural dynamics (2012, methodology): “[1,2] referred to herein as the ‘Bathe method’.”
On the advantages of using the first-order generalised-alpha scheme for structural dynamic problems (2017, methodology): “Two-step composite scheme by Bathe and Baig [18] and the three-step scheme by Wen et al.”
Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements (2017, background): “Thus, the system of equations (21) should be rearranged into the linearized form as [33]:”