Snapping of Low Pinned Arches on an Elastic Foundation

1973 ◽  
Vol 40 (3) ◽  
pp. 741-744 ◽  
Author(s):  
G. J. Simitses
Keyword(s):  
Critical Load ◽  
Elastic Foundation ◽  
Critical Loads ◽  
Entire Range ◽  
Buckling Load ◽  
Stability Studies ◽  
Deflection Curve ◽  
The Stability ◽  
Load Deflection Curve ◽  
Range Of Values

The problem of a low half-sine pinned arch under a quasi-statically applied half-sine load is considered. The low arch is resting on an elastic foundation. Critical loads are obtained by investigating the stability of the equilibrium positions by considering all possible modes of deformation. It is assumed that the behavior of the arch is linearly elastic up to the critical load. The entire range of values for the modulus of the foundation is considered. The results are presented graphically as either critical load (snap-through) or classical buckling load (stable bifurcation) versus the rise parameters for a large number of values of the modulus of foundations. This investigation presents an interesting model for stability studies, because, depending on the value of the rise parameter and the modulus of the foundation, the load-deflection curve exhibits the possibilities of the top-of-the-knee buckling, snap-through buckling through unstable bifurcation, and classical buckling (stable bifurcation).

The estimation of the critical load of a braced framework

1955 ◽  
Vol 231 (1184) ◽  
pp. 25-36 ◽  
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
The Other ◽  
Simple Criterion ◽  
Relaxation Methods ◽  
The Stability

With present methods of estimating the critical loads of triangulated frameworks by relaxation methods it is difficult to decide near the critical load whether the process is converging and the structure is stable, or whether the process is diverging and the structure unstable. This difficulty does not arise in the method presented here. Each triangle of the framework in turn is replaced by a hypothetical member until finally only one member of the truss remains, and this member has been modified in such a way as to take into account the stiffnesses of all the other members of the truss. A simple criterion for the stability of this final equivalent member is established and an example of the application of the method given.

CRITICAL LOADS OF SQUARE PLATES UNDER DIFFERENT INPLANE LOAD CONFIGURATIONS ON OPPOSITE EDGES

2001 ◽  
Vol 01 (02) ◽  
pp. 283-291 ◽  
Author(s):  
S. G. LEE ◽  
S. C. KIM ◽  
J. G. SONG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Critical Load ◽  
Critical Loads ◽  
Patch Load ◽  
Fixity Factor ◽  
The Stability ◽  
Opposite Tendency ◽  
Width Factor

The elastic critical load coefficients of square plates, under different inplane load configurations on opposite plate edges, are determined and the results compared. The stability analysis was performed by a finite element method that was developed by the authors. The parameters considered in the analysis are the Kinney's fixity factor, and the width factor of the patch load. It was found that the coefficients of the critical loads increase with increasing values of fixity and width factors. The opposite tendency is that a plate under a patch loaded towards the two corners of an edge is more stable than a plate loaded concentrically at the center of the edge.

scholarly journals Snapping of a Planar Elastica With Fixed End Slopes

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Jen-San Chen ◽  
Yong-Zhi Lin
Keyword(s):  
Theoretical Prediction ◽  
Static Load ◽  
Natural Frequencies ◽  
Equilibrium Configuration ◽  
The Other ◽  
Deflection Curve ◽  
Slope Difference ◽  
The Stability ◽  
Fixed End ◽  
Load Deflection Curve

In this paper, we study the deformation and stability of a planar elastica. One end of the elastica is clamped and fixed in space. The other end of the elastica is also clamped, but the clamp itself is allowed to slide along a linear track with a slope different from that of the fixed clamp. The elastica deforms after it is subjected to an external pushing force on the moving clamp. It is observed that when the pushing force reaches a critical value, snapping may occur as the elastica jumps from one configuration to another remotely away from the original one. In the theoretical investigation, we calculate the static load-deflection curve for a specified slope difference between the fixed clamp and the moving clamp. To study the stability of the equilibrium configuration, we superpose the equilibrium configuration with a small perturbation and calculate the natural frequencies of the deformed elastica. An experimental setup is designed to measure the load-deflection curve and the natural frequencies of the elastica. The measured load-deflection relation agrees with the theoretical prediction very well. On the other hand, the measured natural frequencies do not agree very well with the theoretical prediction, unless the mass of the moving clamp is taken into account.

Modeling of effects of adhesive interlayers on contact-induced radial cracking in brittle coatings on substrates

2003 ◽  
Vol 18 (6) ◽  
pp. 1481-1486 ◽  
Author(s):  
Chun-Hway Hsueh ◽  
Jong Ho Kim ◽  
Do Kyung Kim
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Critical Load ◽  
Elastic Foundation ◽  
Critical Loads ◽  
Glass Substrates ◽  
Adhesive Interlayer ◽  
Semiempirical Equation ◽  
Radial Cracks ◽  
Fitting Parameters

The effects of soft adhesive interlayers on contact-induced radial cracking in brittle coatings on supporting substrates were investigated recently. A semiempirical equation for the critical load to initiate radial cracking was derived, which used three fitting parameters obtained by comparison with the finite element results. An analytical model is derived in the present study to illustrate the effects of adhesive interlayers. This is achieved by adopting the analogy between the coating/substrate system and a plate on an elastic foundation. In the presence of an adhesive interlayer, the interlayer/substrate bilayer is treated as the effective elastic foundation. The effective modulus of foundation for the bilayer is derived, and the solution for coating/interlayer/substrate systems can be obtained from the existing solution for coating/substrate systems by replacing the modulus of foundation. Specific results are calculated for critical loads to initiate radial cracks in silicon coatings bonded by adhesive interlayers of different materials and thicknesses to glass substrates. The present analytical solution provides an alternative other than the existing semiempirical equation in predicting the effects of adhesive interlayers.

On the Sufficiency of the Energy Criterion for the Stability of Certain Nonconservative Systems of the Follower-Load Type

1972 ◽  
Vol 39 (3) ◽  
pp. 717-722 ◽  
Author(s):  
H. H. E. Leipholz
Keyword(s):  
Lower Bound ◽  
Critical Load ◽  
Energy Criterion ◽  
Conservative System ◽  
Buckling Load ◽  
Follower Load ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
Divergence Type ◽  
The Stability

Using Galerkin’s method it is shown that in the domain of divergence, the nonconservative system of the follower-load type is always more stable than the corresponding conservative system. Hence, for nonconservative systems of the divergence type, the critical load of the corresponding conservative system becomes a lower bound for the buckling load, and the energy criterion remains sufficient for predicting stability. Moreover, it is proven that even for more general nonconservative systems, the energy criterion is sufficient under certain restrictions.

scholarly journals Research on Voltage Stabilizing Control Strategy of Critical Load in Unplanned Island Based on Electric Spring

Electronics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 80
Author(s):  
Hongjun Wang ◽  
Chunchao Song ◽  
Youjun Yue ◽  
Hui Zhao
Keyword(s):  
Critical Load ◽  
Control Strategy ◽  
Critical Loads ◽  
Control Mode ◽  
Experimental Simulation ◽  
Hybrid Microgrid ◽  
Stabilizing Control ◽  
Working Principle ◽  
Bus Voltage ◽  
The Stability

Aiming to solve the problem of voltage fluctuation of critical load caused by lack of control when an unplanned island occurs in a microgrid, a voltage stabilizing control strategy of critical load based on electric spring is proposed in this paper. When unplanned islanding occurs in a microgrid system, the system bus voltage fluctuates dramatically due to instantaneous power imbalance, compromising the power supply safety of important loads on the bus. In this paper, the electric spring control mode is integrated into the voltage stabilizing control strategy of critical loads in an unplanned island for the first time to realize the protection of critical loads. First of all, a model of an optical storage AC/DC hybrid microgrid is built, the overall system architecture is determined, and the microgrid is divided into four working states. Second, the working principle of electric spring is introduced, and a decoupling control strategy based on double closed loop is proposed. Finally, the experimental simulation of the proposed control strategy is experimentally simulated in Matlab/Simulink environment. The simulation findings show that when the bus voltage and current of microgrid change due to an unplanned island, the proposed control strategy based on electric spring may achieve the stability of voltage and current on critical loads.

The Approximate Elastic Critical Loads of Continuous Struts

1962 ◽  
Vol 66 (622) ◽  
pp. 652-654
Author(s):  
H. Waters
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
Axial Load ◽  
Simultaneous Equations ◽  
The Stability

The determination of the critical axial load of a strut having one or more intermediate supports and varying stiffness is made difficult by the highly transcendental nature of the simultaneous equations involved. It is therefore usual to make a test of the stability of the strut at some arbitrarily chosen load, as for example when applying the convergence technique. The behaviour of the strut then indicates whether the chosen load is too high or too low, and another load is selected and another test made. Although the true critical load is eventually reached, it is clear that if its value can be fairly closely approximated at the outset, then the labour of calculation will be greatly reduced.

Optimization of the time the chromatograph thermostats exit to a given temperature

2020 ◽  
pp. 40-45
Author(s):  
Nadezhda O. Vzduleva ◽  
Valery B. Gitlin
Keyword(s):  
Heating Rate ◽  
Entire Range ◽  
Gas Chromatograph ◽  
Heating And Cooling ◽  
Operating Temperatures ◽  
The Stability

The problems of ensuring the stability of the temperature of the chromatographic experiment carried out using a serial gas chromatograph LGH-3000 are considered. Limiting the permissible heating rate of the chromatograph thermostats does not allow a quick transition to the new conditions of the chromatographic experiment in accordance with the requirements of the technical conditions. The processes of heating and cooling the thermostat are analyzed. It is shown that the ratio of the duration of the interval equal to the sum of the durations of the heating and cooling intervals to the duration of the heating interval is inversely proportional to the temperature of the chromatographic experiment. Based on this situation, an empirical algorithm is proposed for heating the thermostat to a given temperature, which made it possible to reduce the time it takes to reach a given temperature in the entire range of operating temperatures.

AN IMPROVED METHOD FOR THE ASSAY OF PROGESTERONE BY COMPETITIVE PROTEIN BINDING

1970 ◽  
Vol 63 (2) ◽  
pp. 225-241 ◽  
Author(s):  
B. D. Reeves ◽  
M. L. A. de Souza ◽  
I. E. Thompson ◽  
E. Diczfalusy
Keyword(s):  
Protein Binding ◽  
Binding Sites ◽  
Entire Range ◽  
Improved Method ◽  
Plasma Progesterone ◽  
Extraction And Purification ◽  
Corticosteroid Binding Globulin ◽  
Competitive Protein Binding ◽  
The Individual ◽  
Range Of Values

ABSTRACT An improved method for the assay of plasma progesterone by competitive protein binding is described. The improvement is based upon rigorous control of the variables, the compensation for and standardisation of interfering factors inherent in the method and the use of a human corticosteroid binding globulin, that meets the requirements for sensitivity at levels of 1.0 ng of progesterone and below. The assessment of the reliability of the individual steps in the method as well as that of the complete method is presented. The sensitivity of the method is around 0.2 ng progesterone per ml plasma. Accuracy was measured by adding progesterone in amounts ranging from 0.0 to 1.0 ng to 1.0 ml plasma. There was a linear relationship between the progesterone added and recovered throughout the entire range of values, with a coefficient of correlation (r) of 0.94. Of 52 related steroids tested, none was found which would remain associated with progesterone following extraction and purification and which would also compete with progesterone for binding sites.

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