An Analytical Method in the Dynamical Analysis of the Rock Cavity

Abstract

In this paper,an analytical method in dynamical analysis of the rock cavity is given based on interacted construction of numerical analysis and analytical solution.An example is used to show how to get it in practice.

FullText(HTML)

References(4)

References

[1]	Yang Sheng-tian and Zhan Yao-qin,Finite element analysis of a cavity in rock subjected to blast loading,Proceeding of the ICFEM,8(1982).
[2]	杨异田,侧向爆炸荷载下直墙拱形岩洞强度的近似分析,爆炸与冲击,2,4(1982).
[3]	曹志远、杨异田,关于受弯构件力学计算的一种表达式,科学通报,24,3(1979).
[4]	Мусхслишвили Н.И.,《数学弹性力学的几个基本问题》(赵惠元译),科学出版社(1958)．

Relative Articles

[1]	LIU Wei, TONG Xiaolong, JIN Rong. An Integration Method With Controllable Numerical Damping Dissipation for Structural Dynamic Equations[J]. Applied Mathematics and Mechanics, 2024, 45(7): 922-935. doi: 10.21656/1000-0887.440292
[2]	LIN Yong-xin, CHEN Yu-shu, WANG Dan, CAO Qing-jie. New Approach to the Correlation Measurement for Subsystems in a Complex Giant System[J]. Applied Mathematics and Mechanics, 2013, 34(9): 917-928. doi: 10.3879/j.issn.1000-0887.2013.09.005
[3]	XIANG Yu, HUANG Yu-ying, LU Jing, YUAN Li-yun, ZOU Shi-zhi. A New Matrix Method for Analyzing Vibration and Damping Effect of a Sandwich Circular Cylindrical Shell With a Viscoelastic Core[J]. Applied Mathematics and Mechanics, 2008, 29(12): 1443-1456.
[4]	S. Abbasbandy, LIAO Shi-jun. A New Modification of False Position Method Based on the Homotopy Analysis Method[J]. Applied Mathematics and Mechanics, 2008, 29(2): 203-208.
[5]	GONG Wen-hui, XIE Hong-yang, WANG Yuan-han. Semi-Analytical and Semi-Numerical Method for Dynamic Analysis of Foundation[J]. Applied Mathematics and Mechanics, 2006, 27(5): 539-546.
[6]	YAN Xiang-qiao. An Effective Boundary Element Method for Analysis of Crack Problems in a Plane Elastic Plate[J]. Applied Mathematics and Mechanics, 2005, 26(6): 749-756.
[7]	TAN Mei-lan, WANG Xin-wei. New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings[J]. Applied Mathematics and Mechanics, 2005, 26(7): 847-853.
[8]	LIU Zhao-rong, XU Gang, CHEN Yong, TENG Zhong-zhao, QIN Kai-rong. An Analysis Model of Pulsatile Blood Flow in Arteries[J]. Applied Mathematics and Mechanics, 2003, 24(2): 205-214.
[9]	ZHANG Wei-yi, Koncay Huseyin, YE Min. The Application of a Modified Normal Form Approach[J]. Applied Mathematics and Mechanics, 2001, 22(7): 713-718.
[10]	Liao Shijun, . Homotopy Analysis Method: a New Analytic Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 1998, 19(10): 885-890.
[11]	Zhao Lei, Chen Qiu. An Equivalent Nonlinearization Method for Analysing Response of Nonlinear Systems to Random Excitations[J]. Applied Mathematics and Mechanics, 1997, 18(6): 513-521.
[12]	Chen Mengcheng, Tang Renji. An Approximate Method of Response Analysis of Vibrations for Cracked Beams[J]. Applied Mathematics and Mechanics, 1997, 18(3): 203-209.
[13]	Shui Xiaoping, Zhang Yongfa. A Method for Solving the Dynamics of Multibody Systems With Rheonomic and Nonholonomic Constraints[J]. Applied Mathematics and Mechanics, 1996, 17(6): 551-557.
[14]	Zeng Zhao-jing, Dai Shu-he. A New Method for Analyzing Surface Cracks[J]. Applied Mathematics and Mechanics, 1993, 14(8): 747-752.
[15]	Loo wen-da, Yang Zheng-wen. Finite Layer Analysis for Semi-Infinite Soils(Ⅱ)——Special Cases and Numerical Examples[J]. Applied Mathematics and Mechanics, 1992, 13(11): 945-950.
[16]	Yang Zheng-wen, Loo Wen-da. Finite Layer Analysis for Semi-Infinite Soils (Ⅰ)——General Theory[J]. Applied Mathematics and Mechanics, 1992, 13(10): 881-890.
[17]	Liu Tie-niu, Xu Dao-lin. Large Range Analysis for Nonlinear Dynamic Systems——Element Mapping Method[J]. Applied Mathematics and Mechanics, 1992, 13(6): 553-561.
[18]	Zheng Xiao-ping Ye Tian-qi Chen Bai-ping, . An Analytical Method for a Mixed Boundary Value Problem of Circular Plates under Arbitrary Lateral Loads[J]. Applied Mathematics and Mechanics, 1991, 12(9): 787-793.
[19]	Liu Zheng-rong, Zhou Shi-gang, Liu Er-ning. A Method to Calculate Period Doubling Bifurcation[J]. Applied Mathematics and Mechanics, 1987, 8(7): 633-637.
[20]	Yang Sheng-tian, Cao Zhi-yuan. An Analytical Solution for Underground Structure-Country Rock Dynamic Interaction[J]. Applied Mathematics and Mechanics, 1983, 4(6): 861-868.