Non-Probabilistic Models of Uncertainty in the Nonlinear Buckling of Shells With General Imperfections: Theoretical Estimates of the Knockdown Factor

1989 ◽  
Vol 56 (2) ◽  
pp. 403-410 ◽  
Author(s):  
Yakov Ben-Haim ◽  
Isaac Elishakoff
Keyword(s):  
Probabilistic Models ◽  
Theoretical Estimate ◽  
Initial Imperfection ◽  
Theoretical Models ◽  
Buckling Load ◽  
Dimensional Euclidean Space ◽  
Theoretical Treatment ◽  
Nonlinear Buckling ◽  
Initial Imperfections ◽  
Geometrical Imperfections

A non-probabilistic, set-theoretical treatment of the buckling of shells with uncertain initial geometrical imperfections is presented. The minimum buckling load is determined as a function of the parameters which describe the (generally infinite) range of possible initial imperfection profiles of the shell. The central finding of this paper is a theoretical estimate of the knockdown factor as a function of the characteristics of the uncertainty in the initial imperfections. Two classes of set-theoretical models are employed. The first class represents the range of variation of the most significant N Fourier coefficients by an ellipsoidal set in N-dimensional Euclidean space. The minimum buckling load is then explicitly evaluated in terms of the shape of the ellipsoid. In the second class of models, the uncertainty in the initial imperfection profile is expressed by an envelope of functions. The bounding functions of this envelope can be viewed as a radial tolerance on the shape. It is demonstrated that a non-probabilistic model of uncertainty in the initial imperfections of shells is successful in determining the minimum attainable buckling load of an ensemble of shells and that such an approach is computationally feasible.

Comparisons of Probabilistic and Two Nonprobabilistic Methods for Uncertain Imperfection Sensitivity of a Column on a Nonlinear Mixed Quadratic-Cubic Foundation

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Xiaojun Wang ◽  
Isaac Elishakoff ◽  
Zhiping Qiu ◽  
Lihong Ma
Keyword(s):  
Elastic Foundation ◽  
Probabilistic Method ◽  
Initial Imperfection ◽  
Theoretical Models ◽  
Buckling Load ◽  
Dimensional Euclidean Space ◽  
Limited Information ◽  
Imperfection Sensitivity ◽  
Sensitive Structure ◽  
Range Of Variation

Two nonprobabilistic set-theoretical treatments of the initial imperfection sensitive structure—a finite column on a nonlinear mixed quadratic-cubic elastic foundation—are presented. The minimum buckling load is determined as a function of the parameters, which describe the range of possible initial imperfection profiles of the column. The two set-theoretical models are “interval analysis” and “convex modeling.” The first model represents the range of variation of the most significant N Fourier coefficients by a hypercuboid set. In the second model, the uncertainty in the initial imperfection profile is expressed by an ellipsoidal set in N-dimensional Euclidean space. The minimum buckling load is then evaluated in both the hypercuboid and the ellipsoid. A comparison between these methods and the probabilistic method are performed, where the probabilistic results at different reliability levels are taken as the benchmarks of accuracy for judgment. It is demonstrated that a nonprobabilistic model of uncertainty may be an alternative method for buckling analysis of a column on a nonlinear mixed quadratic-cubic elastic foundation under limited information on initial imperfection.

Elastic Buckling Analysis of Rigidly Jointed Single Layer Reticulated Domes with Random Initial Imperfection

1992 ◽  
Vol 7 (4) ◽  
pp. 265-273 ◽  
Author(s):  
Toshiro Suzuki ◽  
Toshiyuki Ogawa ◽  
Kikuo Ikarashi
Keyword(s):  
Single Layer ◽  
Initial Imperfection ◽  
Random Variable ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Mode Shapes ◽  
Elastic Buckling ◽  
Nonlinear Buckling ◽  
Reticulated Domes ◽  
Nonlinear Buckling Analysis

In the present paper, the effect of imperfection on the elastic buckling load and mode shapes of externally-loaded single layer reticulated domes is investigated. The types of buckling concerned here are the general buckling, the local (dimple) buckling and the buckling of a member. As to the geometric parameter of a dome, the slenderness factor S is adopted which represents the openness and slenderness of the dome. The maximum value of the imperfection is assumed to be the normal random variable. The buckling loads are computed by the linear and the nonlinear buckling analysis using the finite element method. The statistical values are calculated by the three-points estimates method. The main points of interest are the influence of the shape and the extent of an imperfection on the buckling load.

Nonlinear Buckling Analysis of Wind Turbine Towers

2011 ◽  
Vol 383-390 ◽  
pp. 6469-6475
Author(s):  
Qing Cao ◽  
Yang Li ◽  
Hao Zhang
Keyword(s):  
Wind Turbine ◽  
Buckling Load ◽  
Plastic Buckling ◽  
Nonlinear Buckling ◽  
Integration Algorithm ◽  
Critical Buckling Load ◽  
Initial Imperfections ◽  
Elastic Plastic ◽  
Post Buckling ◽  
Wind Turbine Towers

Wind turbine towers are belonging to towering cylinder shell structures, which are easy to appear buckling instability under wind or other complicated loads, and on which integral elastic-plastic buckling analyses have great theoretical and practical significances. This paper used large deflection nonlinear pre-buckling and Koiter initial post-buckling theories, and adopted the finite element scheme of updated integration algorithm and LDC nonlinear solution method, then analyzed the linear buckling, elastic-plastic static buckling, and post-buckling response of the towers with initial imperfections in different location and size. It has obtained that: 1) the critical load of towers with elastic-plastic buckling is much smaller than it with elastic buckling; 2) gravity has certain influence on the critical buckling load; 3) the critical buckling load is insensitive to initial imperfections, meanwhile the imperfections which located on the top or the bottom of the tower are inferior for the stability of tower.

The Influence of Stochastic Imperfection Field on the Bearing Capacity of Hyperbolic Cooling Towers

2011 ◽  
Vol 374-377 ◽  
pp. 2297-2300
Author(s):  
Hai Zhao ◽  
Ya Zhou Xu ◽  
Guo Liang Bai
Keyword(s):  
Bearing Capacity ◽  
Large Scale ◽  
Initial Imperfection ◽  
Orthogonal Basis ◽  
Imperfection Sensitivity ◽  
Stochastic Field ◽  
Buckling Mode ◽  
Material Inhomogeneity ◽  
Initial Imperfections ◽  
Distribution Form

The uncontrollable factors such as construction errors, material inhomogeneity, etc. will inevitably lead to a certain initial imperfections. It is generally known that the stochastic initial imperfection of the structure is an important factor for affecting structural stability and bearing capacity. Since these imperfections are random in nature, this paper proposes the method mainly based on the standard orthogonal basis to expand the stochastic field, taking into account the decomposition of the stochastic initial imperfections related to structures, which is projected in the buckling mode orthogonal basis. In the end, the article by the stability analysis example shows that this method can use less random variables effectively describing the original stochastic imperfection field, and efficiently search for the most unfavorable initial imperfection distribution form in order to ensure the imperfection sensitivity structures have a higher reliability, so it can be applied to large-scale engineering structure stochastic imperfection analysis.

scholarly journals Experimental and Numerical Investigations of Ultimate Strength of Imperfect Stiffened Plates of Different Slenderness

2020 ◽  
Vol 27 (4) ◽  
pp. 120-129
Author(s):  
Krzysztof Woloszyk ◽  
Yordan Garbatov ◽  
Jakub Kowalski ◽  
Leszek Samson
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Ultimate Strength ◽  
Compressive Force ◽  
Initial Imperfection ◽  
Element Model ◽  
Stiffened Plates ◽  
Structural Behaviour ◽  
Middle Cross Section ◽  
Geometrical Imperfections

AbstractThe objective of this study is to analyse the behaviour of compressed stiffened plates of different slenderness using experimental and numerical methods. The presented results are part of a long-term project to investigate the ultimate strength of geometrically imperfect structures subjected to different degradation phenomena, including corrosion degradation and locked cracks. Several specimens were subjected to a uniaxial compressive force, and the most important quantities related to the structural behaviour were captured and analysed. A finite element model, accounting for material and geometrical nonlinearities and initial geometrical imperfections, was developed using the commercial software ANSYS. The residual welding-induced stresses were measured in the middle cross-section for two specimens. The initial imperfection was identified by employing a close-range photogrammetry approach. It was concluded that the numerical analyses, based on the finite element model, predict the ultimate strength of stiffened plates accurately, although some deviations were also observed. The detailed analysis with the indication of possible uncertainty is presented, and several conclusions are derived.

PHOTOGRAMMETRY MEASUREMENTS OF INITIAL IMPERFECTIONS FOR THE ULTIMATE STRENGTH ASSESSMENT OF PLATES

2021 ◽  
Vol 156 (A4) ◽  
Author(s):  
A Cubells ◽  
Y Garbatov ◽  
C Guedes Soares
Keyword(s):  
Finite Element ◽  
Ultimate Strength ◽  
Compressive Load ◽  
Initial Imperfection ◽  
Maximum Load ◽  
Surface Shape ◽  
Element Analysis ◽  
Strength Assessment ◽  
Load Carrying ◽  
Geometrical Imperfections

The objective of the present study is to develop a new approach to model the initial geometrical imperfections of ship plates by using Photogrammetry. Based on images, Photogrammetry is able to take measurements of the distortions of plates and to catch the dominant surface shape, including the deformations of the edges. Having this data, it is possible to generate faithful models of plate surface based on third order polynomial functions. Finally, the maximum load- carrying capacity of the plates is analysed by performing a nonlinear finite element analysis using a commercial finite element code. Three un-stiffened and four stiffened plates have been modelled and analysed. For each plate, two initial imperfection models have been generated one, based on photogrammetric measurements and the other, based on the trigonometric Fourier functions. Both models are subjected to the same uniaxial compressive load and boundary conditions in order to study the ultimate strength.

scholarly journals Fracture and its Role in Determining Ice Forces on Offshore Structures

1983 ◽  
Vol 4 ◽  
pp. 216-221 ◽  
Author(s):  
A.C. Palmer ◽  
D. J. Goodman ◽  
M. F. Ashby ◽  
A. G. Evans ◽  
J.W. Hutchinson ◽  
...  
Keyword(s):  
Deformation Mode ◽  
Theoretical Models ◽  
Offshore Structures ◽  
The Arctic ◽  
Theoretical Treatment ◽  
Strain Rates ◽  
Natural Processes ◽  
Design Loads ◽  
Ice Forces ◽  
Fracture Processes

One of the most conspicuous phenomena in the Arctic Is the fracture of sea ice. It is scarcely possible to travel far without seeing a variety of fracture forms, produced both by natural processes and by human activity.At strain-rates below about 10−4s−1, deformation is dominated by creep, but at higher strain-rates fracture is much more important. One of the reasons for this is the very low fracture toughness of ice. The movements of ice in contact with offshore structures often induce strain-rates well beyond the level at which fracture begins, and so offshore structures will often operate in the fracture regime, and it is fracture processes which will determine the design loads. We consider the different modes of repeated fracture that will occur, and classify them into distinct mechanisms of crushing, spalling, and radial and circumferential cracking. Experimental and field observations are plotted on a deformation mode map. A theoretical treatment of radial cracking confirms that very low loads can propagate cracks to long distances; these loads are small by comparison with those calculated from theoretical models that treat ice as a plastically-deforming continuum.

Analytical Study for Lateral Buckling of Imperfect Pipelines With Distributed Buoyancy Section

2019 ◽  
Author(s):  
Zhenkui Wang ◽  
G. H. M. van der Heijden ◽  
Yougang Tang
Keyword(s):  
Compressive Stress ◽  
Analytical Study ◽  
Lateral Displacement ◽  
Initial Imperfection ◽  
Lateral Buckling ◽  
Maximum Compressive Stress ◽  
Initial Imperfections ◽  
Post Buckling ◽  
Subsea Pipelines ◽  
Sway Motion

Abstract Distributed buoyancy method is one of the buckle initiation techniques used to trigger controlled lateral buckling at planned locations for subsea pipelines operating under high temperature and high pressure (HT/HP) conditions. Deviations from a straight profile for pipelines may be introduced by the pipe-laying vessel’s sway motion during the installation process. In this study, analytical solutions of lateral buckling are deduced for imperfect unburied subsea pipelines with a distributed buoyancy section. The effect of initial imperfections on buckled configurations and typical post-buckling behaviours is illustrated and analysed. The results show that, compared to the case without initial imperfection, lateral displacement amplitude becomes larger when initial imperfection exists. Maximum compressive stress increases when wavelength of initial imperfection is smaller than buckled length of pipeline. However, maximum compressive stress decreases when wavelength of initial imperfection is larger than buckled length of pipeline. So it’s better to introduce longer wavelength of initial imperfection.

Buckling Analysis of Wind Power Tower Considering the Effect of Nonlinearity

2012 ◽  
Vol 256-259 ◽  
pp. 792-795
Author(s):  
Bo Song ◽  
Shuai Huang ◽  
Wen Shan He ◽  
Wei Wei
Keyword(s):  
Wind Power ◽  
Geometric Nonlinearity ◽  
Local Buckling ◽  
Element Model ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Nonlinear Buckling ◽  
Buckling Behavior ◽  
Geometry Nonlinearity ◽  
Material And Geometric Nonlinearity

Based on the 3D finite element model of the wind power tower, buckling behavior of the wind power tower in different wind directions is analyzed, and the effect considering geometry nonlinearity and considering the material and geometry nonlinearity to the buckling analysis is studied. The results show when the ratio of the radius of the tower drum and the length of the element is 18.75, the calculated precision can reach 95%. Local buckling of the wind power tower first appears, and buckling load and displacement considering the material and geometric nonlinearity reduce 52% and 58% compared with that only considering geometry nonlinearity. The linear and nonlinear buckling load of the wind power tower which is 90° sidewind are 1.8 and 1.2 times than those facing the wind direction.

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