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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 907023, 11 pages
Research Article

A Robust and Efficient Composite Time Integration Algorithm for Nonlinear Structural Dynamic Analysis

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China

Received 28 August 2014; Accepted 30 September 2014

Academic Editor: Song Cen

Copyright © 2015 Lihong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a new robust and efficient time integration algorithm suitable for various complex nonlinear structural dynamic finite element problems. Based on the idea of composition, the three-point backward difference formula and a generalized central difference formula are combined to constitute the implicit algorithm. Theoretical analysis indicates that the composite algorithm is a single-solver algorithm with satisfactory accuracy, unconditional stability, and second-order convergence rate. Moreover, without any additional parameters, the composite algorithm maintains a symmetric effective stiffness matrix and the computational cost is the same as that of the trapezoidal rule. And more merits of the proposed algorithm are revealed through several representative finite element examples by comparing with analytical solutions or solutions provided by other numerical techniques. Results show that not only the linear stiff problem but also the nonlinear problems involving nonlinearities of geometry, contact, and material can be solved efficiently and successfully by this composite algorithm. Thus the prospect of its implementation in existing finite element codes can be foreseen.