爆炸作用下围岩稳定性样条小波三维数值模拟

PDF(1570 KB)

振动与冲击 ›› 2016, Vol. 35 ›› Issue (19) : 26-30.

论文

孙惠香1胡平2梁丽娜1刘远飞1康婷1于媛1

作者信息 +

The Three-DimensionSpline Wavelet numericalsimulation on adjoining rock stabilityunder explosionaction

SUN Huixiang1,HU Ping2, LING Lina1,LIU Yuanfei1, KANG Ting 1YU Yuan1

Author information +

文章历史 +

摘要

爆炸具有高压瞬时的特点，地下结构模拟属于半无限域，应用传统有限元模拟时单元划分较多，计算效率低。样条小波有限元具有良好的数值逼近性，一个单元具有多个节点。推导了三维小波转换矩阵，应用构造了三维区间B样条圆环、扇形小波单元。结合工程实例通过Matlab软件编程，对爆炸作用地下拱形结构围岩稳定性进行了三维数值模拟，模拟结果与现场采集数据基本一致，计算效率高于传统有限元。

Abstract

Blasting load has the characteristics of high pressure and transient. Underground structure belongs to semi infinite domain in traditional simulation. And the computation is inefficient because of the numerous elements. The Wavelets Finite element has characteristics of good digital approximation. And one element hasmanynodes. The three-dimension transition matrix was derived. The new elements of three-dimension interval B-spline annulus sector wavelet elementand sector wavelet element were constructed. And it was used to study the adjoining rock stability of underground arch structure under blasting Load through programming with Matlab software. The numerical result is basically consistent with the data collected at blasting excavation scene. And thecomputation efficiency is improved compared with traditional finite element.

导出引用

孙惠香1胡平2梁丽娜1刘远飞1康婷1于媛1. 爆炸作用下围岩稳定性样条小波三维数值模拟[J]. 振动与冲击, 2016, 35(19): 26-30

SUN Huixiang1,HU Ping2, LING Lina1,LIU Yuanfei1, KANG Ting 1YU Yuan1. The Three-DimensionSpline Wavelet numericalsimulation on adjoining rock stabilityunder explosionaction[J]. Journal of Vibration and Shock, 2016, 35(19): 26-30

参考文献

[1] 何正嘉，陈雪峰等.小波有限元理论及其工程应用[M].北京：科学出版社，2006，30.
He Z J,Chen X Fet al. Wavelet element theory and Engineering applications[M]. Beijing: Science press, 2006,30.
[2] 秦荣.计算结构力学[M].北京：科学出版社，2003.
Qin R. Computational Structure Mechanics[M]. Beijing: Science press, 2003.
[3] A Practical Guide to Splines.World Book Publishing Company, 2000.
[4] 陈雪峰，向家伟，何正嘉.区间B样条小波薄壳截锥单元构造[J].应用力学学报，2007 (12)：599-603.
Chen X F,Xiang J W,He Z J. Construction of Thin Truncated ConicalShell Elements by Inteval B-spline Wavelet[A]. Cinese Journal of Applied Mechanics. 2007(12):599-603.
[5] 向家伟，陈雪峰等.一维区间B样条小波单元的构造研究[J].应用力学学报，2006（6）：222-227.
Xiang J W, Chen X Fet al. Construction of One-Dimensional Elements with B-Spline Wavelet[A]. Cinese Journal of Applied Mechanics. 2006(6):222-227.
[6] Goswami J C, Chan A K, Chui C K. On solving first-kindintegral equations using wavelets on a bounded interval[J].IEEE Transactions on Antennas and Propagation, 1995, 436142622.
[7] JiangZ W.Cubic spline wavelet bases of sobolev spaces and multilevel interpolat ion[J].Applied and Computational Harmonic Analysis，1996(3)：154-163.
[8] 张雄，王天舒.计算动力学[M].北京：清华大学出版社.2007：5-29
Zhang X，Wang T S. Computational Dynamics [M]. Beijing: Tsinghua University Press. 2007:5-29.
[9] 张波，盛和太.ANSYS有限元数值分析原理与工程应用[M].北京：清华大学出版社, 2005：216-270.
Zhang B, Sheng T H. ANSYS Numerical Analysis Principle and Engineering Application [M]. Beijing: Tsinghua University Press. 2007: 216-270.
[10] 孙惠香，邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社，1997.Wang M C, Shao M.
The Finite Element Principle and Numerical Method [M]. Beijing: Tsinghua University Press. 1997.
[11] 孙惠香，许金余等. 爆炸作用下跨度对地下结构破坏形态的影响[J]，空军工程大学学报，2013, 14(2)：90-94.
Sun H X. Xu J Y. The influence of span for deep underground arch structure on failure modes under blast loading [J]. Journal of Air Force Engineering University, 2013， 14(2)：90-94.
[12] 孔大庆，孙惠香等. 爆炸作用下岩体特性对围岩与地下结构动力相互作用影响[J]，空军工程大学学报，2014， 15(6)：77-81.
Sun H X. Xu J Y. The influence of span for deep underground arch structure on failure modes under blast loading [J]. Journal of Air Force Engineering University, 2013， 14(2)：90-94.