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A post‐processing technique and an a posteriori error estimate for the newmark method in dynamic analysis
Author(s) -
Wiberg N.E.,
Li X. D.
Publication year - 1993
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290220602
Subject(s) - newmark beta method , a priori and a posteriori , norm (philosophy) , taylor series , mathematics , algorithm , energy (signal processing) , mathematical optimization , computer science , finite element method , mathematical analysis , engineering , statistics , structural engineering , philosophy , epistemology , political science , law
In this paper, we present a post‐processing technique and an a posteriori error estimate for the Newmark method in structural dynamic analysis. By post‐processing the Newmark solutions, we derive a simple formulation for linearly varied third‐order derivatives. By comparing the Newmark solutions with the exact solutions expanded in the Taylor series, we achieve the local post‐processed solutions which are of fifth‐order accuracy for displacements and fourth‐order accuracy for velocities in one step. Based on the post‐processing technique, a posteriori local error estimates for displacements, velocities and, thus, also the total energy norm error estimate are obtained. If the Newmark solutions are corrected at each step, the post‐processed solutions are of third‐order accuracy in the global sense, i.e. one‐order improvement for the original Newmark solutions is achieved. We also discuss a method for estimating the global time integration error. We find that, when the total energy norm is used, the sum of the local error estimates will give a reasonable estimate for the global error. We present numerical studies on a SDOF and a 2‐DOF example in order to demonstrate the performance of the proposed technique.