Effect of Initial Imperfections on the Instability of a Ring Confined in an Imperfect Rigid Boundary

1967 ◽  
Vol 34 (4) ◽  
pp. 979-984 ◽  
Author(s):  
L. L. Bucciarelli ◽  
T. H. H. Pian
Keyword(s):  
Limit Point ◽  
Stability Limit ◽  
Circular Ring ◽  
Load Level ◽  
Shallow Arch ◽  
Rigid Boundary ◽  
Initial Imperfections ◽  
Buckling Behavior ◽  
Initial Geometric Imperfections ◽  
The Stability

The stability of a radially constrained, complete, circular ring subjected to thermal stress and of a similarly restrained portion of a circular ring under circumferential end load is investigated. The effect of three types of initial geometric imperfections on the buckling behavior is determined. Results obtained, employing shallow arch approximations, show that this behavior depends on the assumed form of imperfection. In one case, no bifurcation or limit point exists at finite load level; in the second case, bifurcation and snap buckling may occur; in the third case, the system admits of a limit point. A design curve is proposed which can be used to estimate the stability limit of a circular ring exhibiting a certain “out-of-roundness.”

On the Buckling of Axially Compressed Imperfect Cylindrical Shells

1974 ◽  
Vol 41 (3) ◽  
pp. 737-743 ◽  
Author(s):  
J. Arbocz ◽  
E. E. Sechler
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Limit Point ◽  
Axial Load ◽  
Shooting Method ◽  
Response Pattern ◽  
Load Level ◽  
Nonlinear Ordinary Differential Equations ◽  
Point Boundary ◽  
Buckling Behavior

A theoretical investigation of the buckling behavior of imperfect isotropic shells with edge constraints and under axial compression was carried out. The nonlinear Donnell equations for imperfect isotropic shells have been reduced to an equivalent set of nonlinear ordinary differential equations. The resulting two-point boundary-value problem was solved numerically by the “shooting method.” The use of this method made it possible to investigate how the axial load level at the limit point is affected by the following factors: the rigorous enforcing of the experimental boundary conditions, the prebuckling growth caused by the edge constraint, the overall symmetry of the response pattern, and the orientation and shape of the axisymmetric and asymmetric imperfection components.

One-Way Buckling of Circular Rings Confined Within a Rigid Boundary

1995 ◽  
Vol 117 (2) ◽  
pp. 162-169 ◽  
Author(s):  
C. Sun ◽  
W. J. D. Shaw ◽  
A. M. Vinogradov
Keyword(s):  
Critical Condition ◽  
Experimental Approach ◽  
Equilibrium Analysis ◽  
Initial Deflection ◽  
Rigid Boundary ◽  
Geometric Imperfections ◽  
Circular Rings ◽  
Initial Geometric Imperfections ◽  
The Stability ◽  
Theoretical Results

The stability of a ring confined by a rigid boundary, subjected to circumferential end loads, is investigated both theoretically and experimentally. The effect of initial geometric imperfections on the buckling load is determined by assuming an initial deflection configuration as a simple sine form and the critical condition was derived from equilibrium analysis. An experimental approach was designed to verify the analytical results. Comparison with other theoretical results are also made.

scholarly journals Some aspects of consideration of initial imperfections in the calculations of stability of thin-walled elements of open profile

2021 ◽  
pp. 122-128
Author(s):  
Ivan Okhten ◽  
Olha Lukianchenko
Keyword(s):  
Middle Surface ◽  
Stability Loss ◽  
Critical Force ◽  
The Finite Element Method ◽  
Geometric Imperfections ◽  
Initial Imperfections ◽  
General Stability ◽  
Initial Geometric Imperfections ◽  
Linear And Nonlinear ◽  
The Stability

Performed analysis of the initial geometric imperfections influence on the stability of the open C-shaped bars. Test tasks were solved in MSC Nastran, which is based on the finite element method. Imperfections are given in different formulations: the general stability loss of an ideal bar, of wavy bulging of walls and shelves, of deplanation of a bar. To model imperfections, has been developed a program which for the formation of new coordinates of the nodes of the "deformed" model, the components of a vector similar to the form of stability loss are added to the corresponding coordinates of the middle surface of the bar. In this way, you can set initial imperfections in the forms of stability loss of the bar with different amplitude. Researches made with different values of the imperfection amplitude and eccentricity of applied efforts. All tasks are performed in linear and nonlinear staging. The conclusion is made regarding the influence of initial imperfections form and imperfection amplitude on the critical force in nonlinear calculations. It was found that the most affected are imperfections, which are given in the form of total loss of stability. It was revealed the influence of the imperfection amplitude on the magnitude of the critical force for such imperfections. The influence of imperfections amplitude given in the form of wavy bulging walls and in the form of deplanations is not affected on the value of the critical force.

Appraisal of Allowable Loads by Simplified Rules

1986 ◽  
Vol 108 (2) ◽  
pp. 131-137
Author(s):  
D. Moulin
Keyword(s):  
Experimental Investigation ◽  
Plastic Region ◽  
Thin Structures ◽  
Geometric Imperfections ◽  
Buckling Behavior ◽  
Simplified Method ◽  
Post Buckling ◽  
Initial Geometric Imperfections ◽  
Fast Breeder Reactors ◽  
Breeder Reactors

This paper presents a simplified method to analyze the buckling of thin structures like those of Liquid Metal Fast Breeder Reactors (LMFBR). The method is very similar to those used for the buckling of beams and columns with initial geometric imperfections, buckling in the plastic region. Special attention is paid to the strain hardening of material involved and to possible unstable post-buckling behavior. The analytical method uses elastic calculations and diagrams that account for various initial geometric defects. An application of the method is given. A comparison is made with an experimental investigation concerning a representative LMFBR component.

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.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

Some difficulties associated with the limit equilibrium method of slices

1983 ◽  
Vol 20 (4) ◽  
pp. 661-672 ◽  
Author(s):  
R. K. H. Ching ◽  
D. G. Fredlund
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Stability Limit ◽  
Limit Equilibrium Method ◽  
Soil Conditions ◽  
Side Force ◽  
Limit Equilibrium Methods ◽  
Equilibrium Method ◽  
The Stability

Several commonly encountered problems associated with the limit equilibrium methods of slices are discussed. These problems are primarily related to the assumptions used to render the inherently indeterminate analysis determinate. When these problems occur in the stability computations, unreasonable solutions are often obtained. It appears that problems occur mainly in situations where the assumption to render the analysis determinate seriously departs from realistic soil conditions. These problems should not, in general, discourage the use of the method of slices. Example problems are presented to illustrate these difficulties and suggestions are proposed to resolve these problems. Keywords: slope stability, limit equilibrium, method of slices, factor of safety, side force function.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Stability of Heat Pipes in Vapor-Dominated Systems

1999 ◽  
Author(s):  
Pouya Amili ◽  
Yanis C. Yortsos
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Oil Recovery ◽  
Critical Rayleigh Number ◽  
Stability Limit ◽  
Wave Number ◽  
Nuclear Waste Repository ◽  
Geothermal Systems ◽  
Dimensionless Numbers ◽  
The Stability

Abstract We study the linear stability of a two-phase heat pipe zone (vapor-liquid counterflow) in a porous medium, overlying a superheated vapor zone. The competing effects of gravity, condensation and heat transfer on the stability of a planar base state are analyzed in the linear stability limit. The rate of growth of unstable disturbances is expressed in terms of the wave number of the disturbance, and dimensionless numbers, such as the Rayleigh number, a dimensionless heat flux and other parameters. A critical Rayleigh number is identified and shown to be different than in natural convection under single phase conditions. The results find applications to geothermal systems, to enhanced oil recovery using steam injection, as well as to the conditions of the proposed Yucca Mountain nuclear waste repository. This study complements recent work of the stability of boiling by Ramesh and Torrance (1993).

An Analytical Design Method for Milling Cutters With Non-Constant Pitch to Increase Stability

2000 ◽  
Author(s):  
Erhan Budak
Keyword(s):  
Surface Finish ◽  
Design Method ◽  
Stability Limit ◽  
Analytical Stability ◽  
Chatter Vibrations ◽  
Constant Pitch ◽  
Improved Stability ◽  
Limited Frequency ◽  
The Stability ◽  
Explicit Relation

Abstract Chatter vibrations result in reduced productivity, poor surface finish and decreased cutting tool life. Milling cutters with non-constant pitch angles can be very effective in improving the stability of the process against chatter. In this paper, an analytical stability model and a design method are presented for non-constant pitch cutters. An explicit relation is obtained between the stability limit and the pitch variation which leads to a simple equation for optimal pitch angles. A certain pitch variation is effective for limited frequency and speed ranges which are also predicted by the model. The improved stability, productivity and surface finish are demonstrated by several examples.

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