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

doi:10.1007/s10483-018-2330-6

Abstract

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-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.

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

2010 MSC Number:

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. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 703-716.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-018-2330-6

https://www.amm.shu.edu.cn/EN/Y2018/V39/I5/703

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

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