Stability Analysis of Rectangular Plate Based on Catastrophe Theory

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.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

scholarly journals Postbuckling Analysis Of A Rectangular Plate Loaded In Compression

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Rectangular Plate ◽  
User Program ◽  
Nonlinear Fem ◽  
Buckling Mode ◽  
Energy Principle ◽  
Initial Imperfections ◽  
Potential Energy Principle ◽  
Total Potential ◽  
The Stability ◽  
Minimum Total Potential Energy

Abstract The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied.

Application of Catastrophe Theory in Surrounding Rock Stability

2013 ◽  
Vol 712-715 ◽  
pp. 974-978
Author(s):  
Din Ge Kong ◽  
Kai Hu
Keyword(s):  
Catastrophe Theory ◽  
Surrounding Rock ◽  
Underground Engineering ◽  
Rock System ◽  
Instability Problem ◽  
Rock Stability ◽  
Highly Nonlinear ◽  
Practical Engineering ◽  
Simplified Mechanical Model ◽  
Catastrophic Model

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.

scholarly journals Modelling of thermal and stress-strain state of transformable space structures from hybrid composite materials

2018 ◽  
Vol 194 ◽  
pp. 01039 ◽  
Author(s):  
Konstanitin Mikhaylovskiy ◽  
Pavel Prosuntsov
Keyword(s):  
Composite Materials ◽  
Thermal Regime ◽  
Circular Orbit ◽  
Hybrid Composite ◽  
Multilayer Structure ◽  
Strain State ◽  
Thermal Control ◽  
Space Structures ◽  
Plates And Shells ◽  
Shock Resistance

The strikes of the meteoroids represent a serious danger for transformable space structures. Multilayer plates and shells made of hybrid composite materials can be effectively used for protection and thermal control of such structures. The results of the analysis of the thermal regime and shock resistance of a multilayer structure flying in a circular orbit 400 km high are presented.

scholarly journals Pulmonary barotrauma in divers vs procedures initiated by emergency medical personel

2015 ◽  
Vol 53 (4) ◽  
Author(s):  
Martyna Krukowska ◽  
Katarzyna Jańczuk ◽  
Anna Ślifirczyk ◽  
Marta Kowalenko
Keyword(s):  
Preventive Measures ◽  
Medical Personnel ◽  
The Body ◽  
Necessary Condition ◽  
Hyperbaric Chamber ◽  
Pulmonary Barotrauma ◽  
Medical Control ◽  
The Moment ◽  
Medical Examinations ◽  
Rescue Procedure

Abstract Introduction: Pulmonary barotrauma consists in the damage of pulmonary tissues resulting from pressure differences in the body and the surroundings. Barotrauma may occur during diver's ascent with a held breath. Objective: Presentation of symptoms in divers performing dives at shallow depths. A detailed description of pulmonary barotrauma as a direct hazard to life. Rescue procedure in the case of an occurrence of pulmonary barotrauma, methods of prevention. Abridged description of the state of knowledge: Proper equipment preparation, systematic diving training, as well as systematic medical control aimed at conducting medical examinations with regard to staying under water, all constitute primary preventive measures. At the moment of an occurrence of pulmonary barotrauma in a diver it is necessary to perform first aid activities by qualified medical personnel and arrange for a quick transportation to the nearest hyperbaric centre. Summary: Commonly, pulmonary barotrauma concerns individuals diving at depths up to 10 metres. Pulmonary barotrauma is a state of danger to one's health and life. Proper procedures at the scene of an accident as well as quick transportation to a hyperbaric chamber increase the chance of one's recovery and may constitute the necessary condition during rescue activities.

A Model of a Trapped Particle Under a Plate Adhering to a Rigid Surface

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Joel R. Parent ◽  
George G. Adams
Keyword(s):  
Numerical Solution ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Plate Thickness ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Approximate Analytic Solution ◽  
Total Potential ◽  
Curve Fit ◽  
Deflection Theory

Micro and nanomechanics are growing fields in the semiconductor and related industries. Consequently obstacles, such as particles trapped between layers, are becoming more important and warrant further attention. In this paper a numerical solution to the von Kármán equations for moderately large deflection is used to model a plate deformed due to a trapped particle lying between it and a rigid substrate. Due to the small scales involved, the effect of adhesion is included. The recently developed moment-discontinuity method is used to relate the work of adhesion to the contact radius without the explicit need to calculate the total potential energy. Three different boundary conditions are considered—the full clamp, the partial clamp, and the compliant clamp. Curve-fit equations are found for the numerical solution to the nondimensional coupled nonlinear differential equations for moderately large deflection of an axisymmetric plate. These results are found to match the small deflection theory when the deflection is less than the plate thickness. When the maximum deflection is much greater than the plate thickness, these results represent the membrane theory for which an approximate analytic solution exists.

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