scholarly journals Influence of Uncertainties on the Dynamic Buckling Loads of Structures Liable to Asymmetric Postbuckling Behavior

2008 ◽  
Vol 2008 ◽  
pp. 1-24 ◽  
Author(s):  
Paulo B. Gonçalves ◽  
Donald Mark Santee
Keyword(s):  
Static Load ◽  
Basin Of Attraction ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Buckling Loads ◽  
Melnikov Criterion ◽  
Linear Buckling ◽  
The Stability

Structural systems liable to asymmetric bifurcation usually become unstable at static load levels lower than the linear buckling load of the perfect structure. This is mainly due to the imperfections present in real structures. The imperfection sensitivity of structures under static loading is well studied in literature, but little is know on the sensitivity of these structures under dynamic loads. The aim of the present work is to study the behavior of an archetypal model of a harmonically forced structure, which exhibits, under increasing static load, asymmetric bifurcation. First, the integrity of the system under static load is investigated in terms of the evolution of the safe basin of attraction. Then, the stability boundaries of the harmonically excited structure are obtained, considering different loading processes. The bifurcations connected with these boundaries are identified and their influence on the evolution of safe basins is investigated. Then, a parametric analysis is conducted to investigate the influence of uncertainties in system parameters and random perturbations of the forcing on the dynamic buckling load. Finally, a safe lower bound for the buckling load, obtained by the application of the Melnikov criterion, is proposed which compare well with the scatter of buckling loads obtained numerically.

scholarly journals ANÁLISE DA INTEGRIDADE E DA INSTABILIDADE DINÂMICA DE UM SISTEMA MECÂNICO SUJEITO A BIFURAÇÃO DO TIPO BUTTERFLY

2021 ◽  
Vol 12 (3) ◽  
pp. 14-22
Author(s):  
Michael Dowglas de Gois Silva ◽  
Fábio Roberto Chavarette ◽  
Milton Batista Ferreira Junior ◽  
Rodrigo Francisco Borges Lourenco
Keyword(s):  
Static Load ◽  
Structural Systems ◽  
Spring Stiffness ◽  
Bifurcation Diagrams ◽  
Model Uncertainties ◽  
Geometric Imperfections ◽  
Attraction Basin ◽  
Linear Buckling ◽  
Lower Load ◽  
The Stability

Slender structural systems susceptible to unstable buckling generally losestability at lower load levels than the linear buckling load of the perfect structure. This is mainly due to the geometric imperfections present in real structures. The objective of this work is to determine the integrity measures, together with the stability of the post-critical solutions of a mechanical system subject to unstable symmetrical buckling, Burtterfly-type bifurcation, using a discrete degree of freedom model. Uncertainties in the order of 10% will be considered in its deterministic parameters, to obtain lower and reliable limits for the project. The proposed uncertainty in the spring stiffness parameters does not change the type of bifurcation and the value of the critical load, only the value of the minimum post-critical of the bifurcation diagrams. The results showed the erosion of the attraction basin and the decrease of the factors of integrity, local and global, for the trivial solutions with the increase of the static load, for the investigated bifurcation.

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.

Initial Postbuckling Behavior of Imperfect, Antisymmetric Cross-Ply Cylindrical Shells Under Torsion

1987 ◽  
Vol 54 (1) ◽  
pp. 174-180 ◽  
Author(s):  
David Hui ◽  
I. H. Y. Du
Keyword(s):  
Cylindrical Shells ◽  
Elastic Stability ◽  
Buckling Load ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Torsional Buckling ◽  
Buckling Mode ◽  
Young’S Moduli ◽  
Coupling Behavior ◽  
Parameter Variations

This paper deals with the initial postbuckling of antisymmetric cross-ply closed cylindrical shells under torsion. Under the assumptions employed in Koiter’s theory of elastic stability, the structure is imperfection-sensitive in certain intermediate ranges of the reduced-Batdorf parameter (approx. 4 ≤ ZH ≤ 20.0). Due to different material bending-stretching coupling behavior, the (0 deg inside, 90 deg outside) two-layer clamped cylinder is less imperfection sensitive than the (90 deg inside, 0 deg outside) configuration. The increase in torsional buckling load due to a higher value of Young’s moduli ratio is not necessarily accompanied by a higher degree of imperfection-sensitivity. The paper is the first to consider imperfection shape to be identical to the torsional buckling mode and presents concise parameter variations involving the reduced-Batdorf paramter and Young’s moduli ratio.

Dynamic Buckling of 1-DOF Autonomous Potential Systems Under Tilted Cusp Catastrophe

2001 ◽  
Author(s):  
Anthony N. Kounadis
Keyword(s):  
Autonomous Systems ◽  
Total Potential Energy ◽  
Dynamic Buckling ◽  
Local Analysis ◽  
Cusp Catastrophe ◽  
Imperfection Sensitivity ◽  
Buckling Loads ◽  
Total Potential ◽  
Constant Direction ◽  
Step Loading

Abstract Nonlinear dynamic buckling of one-degree-of freedom (1-DOF) undamped systems under step loading (autonomous systems) of constant direction and infinite duration is discussed in detail using Catastrophe Theory. Attention is focused on the relation of static cuspoind catastrophes to the corresponding dynamic catastrophes for 1-DOF autonomous undamped systems by determining properly the dynamic singularity and bifurcational sets for such systems. Using local analysis one has to classify first the total potential energy (TPE) function of the system into one of the elementary Thom’s catastrophes by defining the corresponding control (unfolding) parameters. Subsequently, using global analyses one can readily obtain exact results for the dynamic buckling loads (DBLs) and their imperfection sensitivity of systems subjected to dynamic dual cusp and tilted cusp catastrophes. It was found that the maximum DBL of the dynamic tilted cusp catastrophe corresponds to a limit point lying in the vicinity of the hysteresis point (related to the static tilted cusp catastrophe). Numerical examples illustrate the methodology proposed herein.

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).

Elastic Postbuckling Behavior of Stiffened and Barreled Cylindrical Shells

1969 ◽  
Vol 36 (4) ◽  
pp. 784-790 ◽  
Author(s):  
J. W. Hutchinson ◽  
J. C. Frauenthal
Keyword(s):  
General Theory ◽  
Boundary Conditions ◽  
Type Theory ◽  
Cylindrical Shells ◽  
Buckling Load ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Different Boundary Conditions ◽  
Stiffened Cylindrical Shells

The initial postbuckling behavior of axially stiffened cylindrical shells is studied with a view to ascertaining the extent to which various effects such as stringer eccentricity, load eccentricity, and barreling influence the imperfection-sensitivity of these structures to buckling. In most cases, when these effects result in an increase in the buckling load of the perfect structure, they increase its imperfection-sensitivity as well. In some instances, however, barreling can significantly raise the buckling load of the shell while reducing its imperfection-sensitivity. The analysis, which is based on Koiter’s general theory of postbuckling behavior and is made within the context of Ka´rma´n-Donnell-type theory, takes into account nonlinear prebuckling deformations and different boundary conditions.

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.

EFFECTS OF IMPACT VELOCITY AND SLENDERNESS RATIO ON DYNAMIC BUCKLING LOAD FOR LONG COLUMNS

2008 ◽  
Vol 22 (31n32) ◽  
pp. 5596-5602 ◽  
Author(s):  
K. MIMURA ◽  
T. UMEDA ◽  
M. YU ◽  
Y. UCHIDA ◽  
H. YAKA
Keyword(s):  
Impact Velocity ◽  
Dynamic Load ◽  
Slenderness Ratio ◽  
Testing Machine ◽  
Dynamic Buckling ◽  
Impact Testing ◽  
Buckling Load ◽  
Square Function ◽  
Buckling Loads ◽  
The Impact

In this research, the buckling behavior of long columns under dynamic load was investigated both experimentally and numerically, and an effective buckling criterion for dynamic load was derived from the results in terms of the impact velocity and the slenderness ratio. In the experiments, a free fall drop-weight type impact testing machine was employed. The dynamic buckling loads were measured by the load sensing block, and the displacements were measured by a high speed magnetic-resistance device. In the numerical analyses, dynamic FEM code 'MSC-Dytran' was used to simulate the typical experimental results, and the validity and the accuracy of the simulations were checked. The dynamic buckling loads at various impact velocities were then systematically investigated. From both experimental and simulated results, it was found that the dynamic to static buckling load ratios can be successfully described as a square function of the slenderness ratio of the columns, while they can be also described by a power law of the applied impact velocity.

Remarks on the Static and Dynamic Imperfection-Sensitivity of Nonsymmetric Structures

1980 ◽  
Vol 47 (1) ◽  
pp. 111-115 ◽  
Author(s):  
Isaac Elishakoff
Keyword(s):  
Dynamic Buckling ◽  
Buckling Load ◽  
Imperfection Sensitivity ◽  
Nonlinear Spring ◽  
Asymmetric Structures ◽  
Rod System ◽  
Rigid Rod

The simple static and dynamic buckling model (the three-hinge rigid-rod system, constrained laterally by a nonlinear spring) originally proposed by Budiansky and Hutchinson, is modified so that the force of the spring includes both quadratic and cubic terms. Expressions are given for the buckling load of the imperfect structure as function of the imperfection. These formulas generalize the classical expressions for the static buckling load (due to Koiter), and for the dynamic buckling load (due to Budiansky and Hutchinson) for symmetric or asymmetric structures, to nonsymmetric ones.

Experimental Evaluation of Dynamic Buckling Load of GFRP Rod for Gas Circuit Breaker

2014 ◽  
Vol 566 ◽  
pp. 593-598 ◽  
Author(s):  
H. Hashimoto ◽  
H. Yaka ◽  
I Riku ◽  
T. Umeda ◽  
K. Mimura
Keyword(s):  
Slenderness Ratio ◽  
Circuit Breaker ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Elastic Buckling ◽  
Time Duration ◽  
Buckling Loads ◽  
Compression Load ◽  
Power Substation ◽  
The Impact

Dynamic elastic buckling behaviors of GFRP and Aluminum rods were experimentally investigated. In a gas circuit breaker of an electric power substation, an operating rod consisting of insulating materials is connected to an interrupter. The rod securely insulate between the interrupter and an operating mechanism. The rod is configured with a slender rod made of Glass Fiber Reinforced Plastics (GFRP). When the gas circuit breaker ends the opening operation, impulsive compression load acts on the GFRP rod. To develop a smaller and lighter GFRP rod, dynamic buckling loads of the rod must be studied. In this study, dynamic elastic buckling loads for slender GFRP and aluminum rods were investigated by an experimental method. The drop weight impact tests of the GFRP rods and aluminum rods were employed. In the testing device, a special load cell called the “Load Sensing Block” was used to measure the dynamic load of long time duration. Slender GFRP rods with various lengths were axially loaded at the impact velocities ranging from 0.75m/s to 4.5m/s. From the experimental results, an empirical criterion for the dynamic buckling load of the GFRP rod was proposed in terms of the impact velocity and the slenderness ratio. Furthermore, results showed the proposed criterion could successfully describe the buckling behavior of not only the GFRP rod but also the aluminum rod.

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