Engineering Mechanics ›› 2018, Vol. 35 ›› Issue (10): 1-9,36.doi: 10.6052/j.issn.1000-4750.2017.06.0434

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AN ENERGY CONSISTENT INTEGRATION METHOD FOR TRUSS ELEMENTS

PAN Tian-lin1,2, WU Bin2,3   

  1. 1. School of Civil Engineering and Architecture, Northeast Electric Power University, Jilin 132012, China;
    2. School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China;
    3. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China
  • Received:2017-06-06 Revised:2018-01-10 Online:2018-10-12 Published:2018-10-12

Abstract: Based on the energy equilibrium theory, an energy consistent integration method for truss elements is proposed in this paper. The method is unconditionally stable in nonlinear systems, and its accuracy is second order. The existence of algorithm parameters is proved by mean value theorem, and the solution form of the parameters is also provided. The discrete dynamic equations are linearized to obtain the equivalent stiffness matrices for iteration. The new algorithm is embedded in a nonlinear finite element program. On the basis of this program, the nonlinear dynamic analysis of a single pendulum and a transmission tower structure is completed. The numerical results show that the classic average acceleration method and implicit midpoint method are both energy inconsistent and may even produce divergent results. In contrast, the proposed method has good stability within different time steps.

Key words: engineering mechanics, time integration algorithm, energy-consistent, unconditional stability, average acceleration method, truss elements

CLC Number: 

  • TU311.4
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