Abstract
In selecting rational types of underground structures resisting explosion, in order to improve stress states of the structural section and make full use of material strength of each part of the section, the research method of composite structures is presented. Adopting the analysis method of micro-section free body, equilibrium equations, constraint equations and deformation coordination equations are given. Making use of the concept of generalized work and directly introducing Lagrange multiplier specific in physical meaning, the validity of the constructed generalized functional is proved by using variation method. The rational rigidity matching relationship of composite structure section is presented through example calculations.
Similar content being viewed by others
References
WU Xiang-yu, ZHAO Yu-xiang. On basic way to dramatically increase the bearing capacity of underground engineering in rock mass[J].Chinese Journal of Rock Mechanics and Engineering, 2003,22(2):263. (in Chinese)
ZHAO Xiao-bing, FAN Qin. Vibration analysis of underground plane arched-bar structures under explosive loading[J].Defense Engineering, 1999, (3): 20–25. (in Chinese)
ZHAO Yu-xiang, SONG Xi-tai, QIAN Er-xuan. Fundamental of dynamical analysis of the blastresistant underground structures[J].Applied Mathematics and Mechanics (English Edition), 1993,14(5):407–416.
CHIEN Wei-zang.Variation Method and Finite Element[M]. Beijing: Science Press, 1980. (in Chinese)
XUE Da-wei. Generalized variational principles on nonlinear theory of elasticity with finite displacements[J].Applied Mathematics and Mechanics (English Edition), 1991,12(3):227–236.
ZHAO Yu-xiang. Dynamic analysis of underground cylindrical structures considering interaction of loads, structure and media[J].Underground Engineering, 1978, (6):22–25. (in Chinese)
Golubisky M, Schaeffer D G.Singularities and Groups in Bifurcan’ on Theory(Vol.1)[M]. New York: Springer, 1985.
Bogoliubov N, Mitropolsky Y A.Asymptotic Methods in the Theory of Nonlinear Oscillations[M]. New York: Gordon & Breach, 1961.
Nayfeh A H, Mook D T.Nonlinear Osci Uations[M]. New York: Wiley, 1979.
Abed E H, Wang H O, Chen R C. Stabilization of period doubling bifurcation and implications for control of chaos[J].Physica D, 1994,70(1):154–164.
Wang H O, Abed E H. Bifurcation control of a chaotic system[J].Automatica, 1995,31(9): 1213–1226.
Kang W. Bifurcation and normal form of nonlinear control systems—Parts I and II[J].SIAM J Contr Optim, 1998.36(1):193–232.
Chen G, Dong X.From Chaos to Order: Methodologies, Perspectives and Applications[M]. Singapore: World Scientific Pub Co, 1998.
Abed E H. Bifurcation-theoretic issues in the control of voltage collapse[A]. In: Chow J H, Kokotovic P V Thomas R J Eds.Proc IMA Workshop on Systems and Control Theory for Power Sys [C]. New York: Springer, 1995, 1–21.
Chen G, Lu J, Yap K C. Controlling Hopf bifurcation[A]. In: Veta T, Chen G Eds.Proc Int Symp Circ Sys[C].3. USA: Monterey, C A, 1998, 693–642.
Basso M, Evangelisti A, Genesio R,et al. On bifurcation control in time delay feedback systems [J].Int J Bifur Chaos, 1998,8(4):713–721.
Chen G.Controlling Chaos and Bifurcation in Engineering Systems[M]. Boca Raton, FL: CRC Press, 1999.
Chen G, Moiola J L, Wang H O. Bifurcation control: theories, methods and applications[J].Int J Bifur Chaos, 2000,10(3):511–548.
CHEN Yu-shu, Leung Andrew Y T.Bifurcation and Chaos in Engineering[M]. London: Springer, 1998.
CHEN Yu-shu, YANG Cai-xia, WU Zhi-qiang,et al. 1∶2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities[J].Applied Mathematics and Mechanics (English Edition), 2001,22(8):917–924.
LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang,et al. Bifurcation of nonlinear normal modes of M-DOF systems with internal resonance[J].Acta Mechanica Sinica, 2002,34(3):104–407.
Sundararajan P, Noah S. Dynamics of forced nonlinear systems using shooting arc length contination method[J].ASME J Vib Acoustics, 1995,119(1):9–20.
Author information
Authors and Affiliations
Additional information
Contributed by Xue Da-wei
Biographies: Zhao Xiao-bing (1976≈), Doctor; Zhao Yu-xiang (Corresponding author
Rights and permissions
About this article
Cite this article
Xiao-bing, Z., Da-wei, X. & Yu-xiang, Z. Dynamic analysis of underground composite structures under explosion loading. Appl Math Mech 25, 272–278 (2004). https://doi.org/10.1007/BF02437330
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02437330