An efficient backward Euler time-integration method for nonlinear dynamic analysis of structures

Authors:
Tianyun Liu;Chongbin Zhao;Qingbin Li;Lihong Zhang
Affiliations:
State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing 100084, China;Computational Geosciences Research Centre, Central South University, Changsha 410083, China;State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing 100084, China;State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing 100084, China
Venue:
Computers and Structures
Year:
2012

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Abstract

This paper presents an efficient time-integration method for obtaining reliable solutions of the transient nonlinear dynamic problems and of the stiff systems in structural engineering. This method employs the backward Euler formulae for evaluating both displacements and velocities of structures. It is a self-starting, two-step, second-order accurate algorithm with the same computational effort as the trapezoidal rule. The evaluations of the stability and accuracy of the proposed method are also given in this paper. With some numerical damping introduced, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics: (1) it is applicable to linear as well as general nonlinear analyses; (2) it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; (3) it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and (4) it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses.