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

作　　者：Weibin WEN Shibin LUO Shengyu DUAN Jun LIANG Daining FANG 

机构地区：[1]School of Civil Engineering, Central South University [2]State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology [3]College of Engineering, Peking University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第5期703-716,共14页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11602004 and11325210)

摘　　要：Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation prob- lems. In the proposed procedures, the lumped matrices corresponding to the isogeomet- ric 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 dis- persion 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.Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation prob- lems. In the proposed procedures, the lumped matrices corresponding to the isogeomet- ric 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 dis- persion 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：structural dynamics wave propagation isogeometric analysis （IGA） numerical dissipation time integration 

分 类 号：O241[理学—计算数学]