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Improved quadratic isogeometric element simulation of one-dimensional elastic wave propagation with central difference method

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Abstract

Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation problems. In the proposed procedures, the lumped matrices corresponding to the isogeometric elements are obtained. The stability conditions of the solution procedures are also acquired. The dispersion analysis is conducted to obtain the optimal Courant-Friedrichs-Lewy (CFL) number or time-step sizes corresponding to the spatial isogeometric elements. The dispersion analysis shows that the isogeometric quadratic element of the fourth-order dispersion error (called the isogeometric analysis (IGA)-f quadratic element) provides far more desirable numerical dissipation/dispersion than the element of the second-order dispersion error (called the IGA-s quadratic element) when appropriate time-step sizes are selected. The numerical simulations of one-dimensional (1D) transient wave propagation problems demonstrate the effectiveness of the proposed solution procedures.

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410083, China

    Weibin Wen & Shibin Luo

  2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Weibin Wen, Shengyu Duan, Jun Liang & Daining Fang

  3. College of Engineering, Peking University, Beijing, 100871, China

    Weibin Wen & Daining Fang

Authors
  1. Weibin Wen
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  2. Shibin Luo
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  3. Shengyu Duan
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  4. Jun Liang
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  5. Daining Fang
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Correspondence to Shengyu Duan.

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Project supported by the National Natural Science Foundation of China (Nos. 11602004 and 11325210)

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Wen, W., Luo, S., Duan, S. et al. Improved quadratic isogeometric element simulation of one-dimensional elastic wave propagation with central difference method. Appl. Math. Mech.-Engl. Ed. 39, 703–716 (2018). https://doi.org/10.1007/s10483-018-2330-6

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  • DOI: https://doi.org/10.1007/s10483-018-2330-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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