Stability Analysis of Rectangular Plate Based on Catastrophe Theory

Abstract:

Plates and shells are well used in structures. In order to study the nonlinear stability of plate, the total potential energy expression was deduced after analyzing the geometrical conditions of four ends simply supported rectangular plate on large deflection, the cusp catastrophic model of the rectangular plate was established based on catastrophe theory, and the bifurcation set that makes the system unstable was obtained to analyze the instability conditions of rectangular plate. The instability conditions of rectangular plate were analyzed based on this set, the critical inner stress is at the cusp point, the necessary condition of instability is σ>σ_cr , but the plate is stable when the movement path of control variables composed by inner stress and landscape load not across the bifurcation curves in the control space. Structures in some projects can be predigested to such a rectangular plate and this cusp catastrophic model can be used for analyzing its instability conditions for taking preventive measures.

• Periodical: Applied Mechanics and Materials (Volumes 148-149)
• Pages: 968-972
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.148-149.968
• Online since: December 2011
• Authors: Guo Feng Jin, Wei Zhang, Yuan Jia Song, Zheng Wei Yang, Gan Tian
• Keywords: Catastrophe Theory, Cusp Catastrophe Model, Rectangular Plate, Stability

References

[1] M. Golubitsky: Society for Industrial and Applied Mathematics Vol. 20 (1978), pp.352-387.

[2] X. A. Lignos, G. A. R. Parke, J. E. Harding and A. N. Kounadis: submitted to International Journal for Numerical Methods in Engineering (2002).

[3] CHEN L: submitted to Chinese Journal of Applied Mechanics (2003).

[4] G. I. Ioannidis and I. G. Raftoyiannis: Comput Mech Vol. 35 (2005), pp.127-133.

[5] M. Carricato, J. Duffy and V. Parenti-Castelli: Mechanism and Machine Theory Vol. 37 (2002), pp.693-716.

DOI: 10.1016/s0094-114x(02)00012-5

[6] M. Potier-Feny: Int. J Engng Sci. Vol. 23 (1985), pp.821-837.

[7] A. Carpinteri: submitted to International Journal of Fracture (1990).

[8] CHEN G C: submitted to Journal of Fujian College of Architecture & C. E. (2002).

[9] CHEN G C. submitted to Journal of Fujian Agriculture and Forestry University (Natural Science Edition) (2003).

[10] CHEN G C. submitted to Journal of Fujian University of Technology (2003).

[11] MIAO X X, LI S C and CHEN Z Q: Mining Science and Technology Vol. 19 (2009), pp.1-7.

[12] ZHONG G S, JIANG W W and XU G Y: submitted to Journal of Liaoning Technical University, (2007).

[13] LI S G, ZHANG T J: Mining Science and Technology Vol. 20 (2010), pp.209-214.

[14] TAN M L and JIANG L H: submitted to Journal of mechanical strength (2010).

[15] HUANG K Z, XIA Z X, XUE D M and REN W M: Theory of Plate and Shell (Tsinghua University Press, Beijing 1987).

[16] LIU R H: Plate and Shell Mechanics (China machine press, Beijing 1990).