Postbuckling Analysis of Continuous, Elastic Systems Under Multiple Loads—Part 2: Applications

1979 ◽  
Vol 46 (2) ◽  
pp. 398-403 ◽  
Author(s):  
R. H. Plaut
Keyword(s):  
Axial Load ◽  
The Other ◽  
Follower Load ◽  
Axial Loads ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Shallow Arch ◽  
Multiple Loads ◽  
Elastic Systems ◽  
Nonconservative Loading

In Part 1, a theoretical stability analysis of continuous, elastic systems subjected to multiple independent loads was developed. Postbuckling behavior and imperfection-sensitivity were investigated. Three examples are presented here to illustrate the procedures and results of that study. The first example consists of a cantilever subjected to a pair of concentrated axial loads, one applied at the tip and the other at midspan. In the second example, involving nonconservative loading, an axial load and a follower load are applied at the tip of a cantilever. Finally, a shallow arch under three concentrated vertical loads is considered, in order to demonstrate a case with prebuckling deformations.

Branching Analysis at Coincident Buckling Loads of Nonconservative Elastic Systems

1977 ◽  
Vol 44 (2) ◽  
pp. 317-321 ◽  
Author(s):  
R. H. Plaut
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Power Laws ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Buckling Loads ◽  
Elastic Systems

Discrete nonconservative elastic systems which lose stability by buckling (divergence) are considered. Simple (distinct) critical points were treated previously, and the case of coincident buckling loads is analyzed here. An asymptotic procedure in the neighborhood of the critical point is used to determine postbuckling behavior and imperfection-sensitivity. It is shown that the system may exhibit no bifurcation at all. In other cases postbuckling paths may be tangential to the fundamental path at the critical point. The sensitivity to imperfections is shown to be more severe than for systems with distinct buckling loads (e.g., one-third, one-fourth, and one-fifth power laws are obtained for certain cases).

Postbuckling Analysis of Continuous, Elastic Systems Under Multiple Loads—Part 1: Theory

1979 ◽  
Vol 46 (2) ◽  
pp. 393-397 ◽  
Author(s):  
R. H. Plaut
Keyword(s):  
Perturbation Technique ◽  
Type Systems ◽  
Parameter Perturbation ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Finite Degree ◽  
Elastic Systems ◽  
Multiple Parameter ◽  
Nonlinear Equilibrium ◽  
The Stability

The stability of continuous, elastic systems subjected to multiple independent loads is considered. The analysis includes nonconservative loads as well as conservative loads, provided that instability is of the static, type. Systems exhibiting prebuckling deformations are included. A multiple-parameter perturbation technique is applied to the nonlinear equilibrium equation in the neighborhood of a critical point, and the postbuckling behavior and imperfection-sensitivity of the system are investigated. Critical points are classified as “general” or “special”, in analogy with Huseyin’s definitions for finite-degree-of-freedom, conservative systems. The results can be applied to study the interaction effects of the independent loads on stability. The theory is given in the present paper, while applications to columns and arches will be presented in the sequel.

scholarly journals Improved design criterion for frictionally engaged contacts in overrunning clutches

2021 ◽  
Author(s):  
Nadine Nagler ◽  
Armin Lohrengel
Keyword(s):  
Design Process ◽  
Contact Area ◽  
Axial Load ◽  
State Of The Art ◽  
Tangential Force ◽  
Design Criterion ◽  
Hertzian Contact ◽  
Loss Of Function ◽  
Axial Loads ◽  
Improved Design

AbstractOverrunning clutches, also known as freewheel clutches, are frictionally engaged, directional clutches; they transmit torque depending on the Freewheel clutch rings’ rotation directions. The torque causes a tangential force in the Hertzian contact area. The hitherto “state-of-the-art design criterion” bases on this load situation. In practice, axial loads additionally act on the frictionally engaged Hertzian contact area. This additional axial load can cause the loss of the friction connection and so the freewheel clutch slips. This publication presents an improved design criterion for frictionally engaged contacts in freewheel clutches. It allows to consider tangential as well as axial loads during the design process. Additionally, it offers the possibility to estimate the probability of frictional engagement loss and gross slip based on the freewheel clutch’s application scenario. This publication points out how to use the improved design criterion to design freewheel clutches that are more robust against a loss of function.

An Approximate Procedure for the Solution of a Class of Transient-Wave Diffraction Problems

1966 ◽  
Vol 33 (1) ◽  
pp. 168-172 ◽  
Author(s):  
L. A. Peralta ◽  
G. F. Carrier ◽  
C. C. Mow
Keyword(s):  
Harmonic Wave ◽  
Elastic Solid ◽  
The Other ◽  
Wave Problem ◽  
Transient Wave ◽  
Harmonic Response ◽  
Elastic Systems ◽  
Computational Difficulty ◽  
Approximate Procedure ◽  
Potential Use

The description of even the gross features of the response to an incident stress pulse of an infinite elastic solid with a hole or obstruction requires very extensive calculations [1]. On the other hand, the response of such elastic systems to a harmonic incident wave is much less intricate. It is well known that the response to any given incident pulse can be constructed from the solution of the harmonic wave problem. Furthermore, it is clear that the computational difficulty associated with this synthesis can be reduced enormously when a suitable, algebraically simple approximation to the harmonic response can be found. In this paper, a useful rule for choosing the appropriate approximation to the harmonic wave response is presented. This method is shown to give results in agreement with known solutions. The procedure is also applied to problems where only solutions to the harmonic wave case are available. The most important potential use of the technique lies in the possibility that, for some classes of structures, one may be able to identify the parameters of the approximate harmonic response with simple macroscopic properties of the system. Such an identification would not only save much labor but would also identify design criteria for the optimization of the system.

Nonlinear Bending of a Stress Corrosion Specimen

1966 ◽  
Vol 88 (1) ◽  
pp. 31-36
Author(s):  
Paul E. Wilson ◽  
Edward E. Spier
Keyword(s):  
Stress Corrosion ◽  
Flexural Rigidity ◽  
Axial Loads ◽  
Postbuckling Behavior ◽  
Nonlinear Bending ◽  
Corrosion Studies ◽  
Plate Strip ◽  
Stress States ◽  
Center Section

This paper presents an analysis of the postbuckling behavior of an initially straight plate strip of variable flexural rigidity whose ends are subjected to opposing “axial” loads. Bending action takes place only in the center section of the strip, since the symmetric end portions are considered to be rigid. Pertinent postbuckling load-deflection curves are deduced by using the nonlinear bending theory of a plate strip, and the maximum stress is obtained as a function of the half-distance between the loaded ends. Numerical results are presented in nondimensional form, and the theoretical solution is shown to compare favorably with a major portion of the experimental stress and deflection data. Information given here has an important and direct application to the determination of bending stress states in the lateral faces of a wide class of tensile test coupons used in stress corrosion studies.

End moments in open web steel joists

1980 ◽  
Vol 7 (1) ◽  
pp. 114-124
Author(s):  
S. C. Shrivastava ◽  
R. G. Redwood ◽  
P. J. Harris ◽  
A. A. Ettehadieh
Keyword(s):  
Significant Influence ◽  
The Other ◽  
Bending Moments ◽  
Axial Loads ◽  
Simply Supported ◽  
Gravity Load ◽  
Negative Bending

A study is made of the behaviour of open web steel joists having both top and bottom chords connected to a column when the end is subjected to negative bending moments. Six tests are described, three of which examine the behaviour with typical standard connections as detailed and supplied by manufacturers; the other three involve modifications to these connections in an attempt to minimize connection eccentricity. It is shown that the eccentricities inherent in the standard connections examined can have a significant influence on the behaviour and strength of a joist, whereas if the eccentricities are eliminated, reasonably predictable behaviour, based upon the member resistances under axial loads, can be achieved. These results are examined in relation to tie joists, which are designed to be simply supported under gravity load but have the bottom chord extended and attached to a column, and also in relation to joists designed as framing members.

Imperfection Sensitivity of Compressed Circular Cylindrical Shells Under Periodic Axial Loads

2009 ◽  
Author(s):  
Francesco Pellicano
Keyword(s):  
Differential Equations ◽  
Dynamic Stability ◽  
Cylindrical Shells ◽  
Nonlinear Partial Differential Equations ◽  
Excitation Frequency ◽  
Finite Amplitude ◽  
Axial Loads ◽  
Imperfection Sensitivity ◽  
Lagrange Equations ◽  
Circular Cylindrical Shells

In the present paper the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature.

scholarly journals Results of theoretical and experimental studies on determining the coefficient of subgrade reaction of sleepers for the conditions of main railways with axial loads of 30-35 tons per axle

2018 ◽  
Vol 230 ◽  
pp. 01003
Author(s):  
Oleksandr Darenskiy ◽  
Eduard Bielikov ◽  
Olexii Dudin ◽  
Alina Zvierieva ◽  
Anatolii Oleshchenko
Keyword(s):  
Sustainable Development ◽  
Reinforced Concrete ◽  
Axial Load ◽  
Experimental Studies ◽  
Operating Conditions ◽  
Railway Track ◽  
Rolling Stock ◽  
Subgrade Reaction ◽  
Axial Loads ◽  
Interaction Dynamics

The article considers obtaining numerical values of the coefficient of subgrade reaction of wooden and reinforced concrete sleepers with axial loads up to 30-35 tons per axle. It has been concluded that using the rolling stock with axial loads of up to 35 tons per axle is necessary in order to ensure sustainable development of the railway complex. The performance of the railway track thus should be investigated in order to predict its operation in such conditions. Generally, such studies are performed using numerical methods. One of the parameters that are required for such calculations is the parameter which is commonly called the coefficient of subgrade reaction. Empirical dependencies of the coefficient of subgrade reaction of wooden and reinforced concrete sleepers on the axial load and on the operating conditions of the track have been obtained. The obtained results can be used in studies of the interaction dynamics of the track of main railways with rolling stock with axial loads of 30-35 tons per axle, which will give an opportunity to provide well-grounded recommendations on the rules for the arrangement and maintenance of the track in such conditions.

Shell Stability

1983 ◽  
Vol 50 (4b) ◽  
pp. 935-940 ◽  
Author(s):  
C. D. Babcock
Keyword(s):  
Dynamic Buckling ◽  
Recent History ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Plastic Buckling ◽  
Shell Stability ◽  
Current Trends ◽  
Shell Buckling ◽  
History Of ◽  
Subject Areas

Recent advances in shell buckling research are reviewed. Five separate subject areas are covered: elastic postbuckling behavior and imperfection sensitivity, plastic buckling, dynamic buckling, experiments and computations. Recent history of the research is presented emphasizing important advances in understanding. Areas of needed research and current trends are pointed out.

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