2 Amson (1974) catastrophic model' of

Surrounding rock system of underground engineering is highly nonlinear, and there is no unified cognition for its stability criteria. Introduces the basic principle of catastrophe theory, focusing on the cusp catastrophic model, build a simplified mechanical model for the surrounding rock, and the instability of surrounding rock of the cusp catastrophic model is obtained. In practical engineering, it is show that catastrophe theory is an effective method to study the instability problem of the tunnel.

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Study on effects of thickness on airfoil-stall at low Reynolds numbers by cusp-catastrophic model based on GA(W)-1 airfoil

Chinese Journal of Aeronautics ◽

10.1016/j.cja.2019.12.024 ◽

2020 ◽

Vol 33 (5) ◽

pp. 1444-1453

Author(s):

Zhiping LI ◽

Peng ZHANG ◽

Tianyu PAN ◽

Qiushi LI ◽

Jian ZHANG

Keyword(s):

Reynolds Numbers ◽

Low Reynolds Numbers ◽

Model Based ◽

Low Reynolds ◽

Catastrophic Model

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A catastrophic model for vibrational buckling of elastic arches

Applied Mathematics and Mechanics ◽

10.1007/bf02016620 ◽

1990 ◽

Vol 11 (12) ◽

pp. 1171-1174 ◽

Cited By ~ 3

Author(s):

Shen Mao-shan ◽

Wei De-min

Keyword(s):

Catastrophic Model

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Mafic enclaves in granitoid intrusions: a catastrophic model of rheological behaviour

Terra Nova ◽

10.1111/j.1365-3121.1994.tb00524.x ◽

1994 ◽

Vol 6 (6) ◽

pp. 575-581 ◽

Cited By ~ 1

Author(s):

A. Pesquera

Keyword(s):

Rheological Behaviour ◽

Mafic Enclaves ◽

Granitoid Intrusions ◽

Catastrophic Model

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Stability Analysis of Rectangular Plate Based on Catastrophe Theory

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.148-149.968 ◽

2011 ◽

Vol 148-149 ◽

pp. 968-972

Author(s):

Guo Feng Jin ◽

Wei Zhang ◽

Yuan Jia Song ◽

Zheng Wei Yang ◽

Gan Tian

Keyword(s):

Rectangular Plate ◽

Catastrophe Theory ◽

Large Deflection ◽

Preventive Measures ◽

Space Structures ◽

Necessary Condition ◽

Control Space ◽

Total Potential ◽

Plates And Shells ◽

Catastrophic Model

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>σcr, 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.

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Hysteresis behaviors of compressor rotating stall with cusp catastrophic model

Chinese Journal of Aeronautics ◽

10.1016/j.cja.2018.02.010 ◽

2018 ◽

Vol 31 (5) ◽

pp. 1075-1084 ◽

Cited By ~ 4

Author(s):

Zhiping LI ◽

Peng ZHANG ◽

Tianyu PAN ◽

Qiushi LI ◽

Jian ZHANG

Keyword(s):

Rotating Stall ◽

Catastrophic Model

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Model Analysis for Comprehensive Transportation Structure Evolution Based on Catastrophe Theory

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.444-445.801 ◽

2013 ◽

Vol 444-445 ◽

pp. 801-805

Author(s):

Li Ping Wu ◽

Chun Ping Pang ◽

Bin Qian

Keyword(s):

Catastrophe Theory ◽

Turning Point ◽

Transportation System ◽

Model Analysis ◽

Structure Evolution ◽

Development Pattern ◽

Basic Principles ◽

Model Based ◽

Fast Optimization ◽

Catastrophic Model

The cusp catastrophic model based on catastrophe theory is presented to analyze the development pattern evolution of comprehensive transportation system (CTS for short). By establishing cusp catastastrophe model of development pattern we obtain that the construction of comprehensive transportation system should include two parts, the first part is the stock optimization and the second part is the increment construction. With the increment construction as the turning point, promoting the fast optimization of the stock should be the basic principles of the construction and development of CTS.

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