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

doi:10.1007/s10483-018-2330-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (5): 703-716.doi: https://doi.org/10.1007/s10483-018-2330-6

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

Weibin WEN^1,2,3, Shibin LUO¹, Shengyu DUAN², Jun LIANG², Daining FANG^2,3

1. School of Civil Engineering, Central South University, Changsha 410083, China;
2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China;
3. College of Engineering, Peking University, Beijing 100871, China

收稿日期:2017-09-11 修回日期:2017-10-24 出版日期:2018-05-01 发布日期:2018-05-01
通讯作者: Shengyu DUAN,E-mail:syduan@bit.edu.cn E-mail:syduan@bit.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11602004 and 11325210)

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

Weibin WEN^1,2,3, Shibin LUO¹, Shengyu DUAN², Jun LIANG², Daining FANG^2,3

1. School of Civil Engineering, Central South University, Changsha 410083, China;
2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China;
3. College of Engineering, Peking University, Beijing 100871, China

Received:2017-09-11 Revised:2017-10-24 Online:2018-05-01 Published:2018-05-01
Contact: Shengyu DUAN E-mail:syduan@bit.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11602004 and 11325210)

摘要/Abstract

摘要：

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-FriedrichsLewy (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.

关键词: wave propagation, structural dynamics, time integration, subdifferential, generalized mean value theorem, convexity, Lipschitz, monotone, isogeometric analysis (IGA), numerical dissipation

Abstract:

Key words: wave propagation, subdifferential, generalized mean value theorem, convexity, Lipschitz, monotone, time integration, isogeometric analysis (IGA), structural dynamics, numerical dissipation

中图分类号:

74S30
34N05

Weibin WEN, Shibin LUO, Shengyu DUAN, Jun LIANG, Daining FANG. Improved quadratic isogeometric element simulation of one-dimensional elastic wave propagation with central difference method[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 703-716.

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

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

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