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Effective loading algorithm associated with explicit dynamic relaxation method for simulating static problems

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Abstract

Based on the fact that a static problem has an equivalent wave speed of infinity and a dynamic problem has a wave speed of finite value, an effective loading algorithm associated with the explicit dynamic relaxation method was presented to produce meaningful numerical solutions for static problems. The central part of the explicit dynamic relaxation method is to turn a time-independent static problem into an artificial time-dependent dynamic problem. The related numerical testing results demonstrate that: (1) the proposed effective loading algorithm is capable of enabling an applied load in a static problem to be propagated throughout the whole system within a given loading increment, so that the time-independent solution of the static problem can be obtained; (2) the proposed effective loading algorithm can be straightforwardly applied to the particle simulation method for solving a wide range of static problems.

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Authors and Affiliations

  1. Computational Geosciences Research Centre, Central South University, Changsha, 410083, China

    Chong-bin Zhao  (赵崇斌), Sheng-lin Peng  (彭省临) & Liang-ming Liu  (刘亮明)

  2. CSIRO Division of Exploration and Mining, P. O. Box 1130, Bentley, WA, 6102, Australia

    Chong-bin Zhao  (赵崇斌), B. E. Hobbs & A. Ord

Authors
  1. Chong-bin Zhao  (赵崇斌)
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  2. Sheng-lin Peng  (彭省临)
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  3. Liang-ming Liu  (刘亮明)
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  4. B. E. Hobbs
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  5. A. Ord
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Corresponding author

Correspondence to Chong-bin Zhao  (赵崇斌).

Additional information

Foundation item: Projects(10872219; 10672190) supported by the National Natural Science Foundation of China

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Zhao, Cb., Peng, Sl., Liu, Lm. et al. Effective loading algorithm associated with explicit dynamic relaxation method for simulating static problems. J. Cent. South Univ. Technol. 16, 125–130 (2009). https://doi.org/10.1007/s11771-009-0021-7

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  • DOI: https://doi.org/10.1007/s11771-009-0021-7

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