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.

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.

Buckling of a Stochastically Imperfect Finite Column on a Nonlinear Elastic Foundation: A Reliability Study

1979 ◽  
Vol 46 (2) ◽  
pp. 411-416 ◽  
Author(s):  
Isaac Elishakoff
Keyword(s):  
Elastic Foundation ◽  
Initial Imperfection ◽  
Relative Number ◽  
Reliability Function ◽  
Gaussian Random Fields ◽  
Imperfection Sensitivity ◽  
Initial Imperfections ◽  
Nonlinear Elastic Foundation ◽  
The Monte Carlo Method ◽  
Nonlinear Elastic

The paper is concerned with the problem of buckling of finite columns with initial imperfections, resting on a “softening” nonlinear elastic foundation. The approach is probabilistic. The initial imperfections are assumed to be Gaussian random fields with given mean and autocorrelation functions, and the problem is solved by the Monte Carlo Method. For each realization of the initial imperfection function, the buckling load was found through transformation of the two-point nonlinear boundary-value problem into an initial-value problem and results were used in constructing the empirical reliability function at the specified load (relative number of columns with buckling loads exceeding this specified load). Numerous results are presented with regard to the influence of the parameters of the columns on their imperfection sensitivity.

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.

Buckling Load Estimation of Two-way Grid Domes Stiffened by Diagonal Braces Under Vertical Load

2021 ◽  
Vol 62 (1) ◽  
pp. 7-23
Author(s):  
Shiro Kato ◽  
Shoji Nakazawa ◽  
Yoichi Mukaiyama ◽  
Takayuki Iwamoto
Keyword(s):  
Slenderness Ratio ◽  
Fem Analysis ◽  
Buckling Load ◽  
Vertical Load ◽  
Imperfection Sensitivity ◽  
Plastic Buckling ◽  
Elastic Plastic ◽  
Alternative Formula ◽  
Efficient Scheme ◽  
Estimation Scheme

The present study proposes an efficient scheme to estimate elastic-plastic buckling load of a shallow grid dome stiffened by diagonal braces. The dome is circular in plan. It is assumed to be subject to a uniform vertical load and to be supported by a substructure composed of columns and anti-earthquake braces. Based on FEM parametric studies considering various configurations and degrees of local imperfections, a set of formulations are presented to estimate the elastic-plastic buckling load. In the scheme, the linear buckling load, elastic buckling load, and imperfection sensitivity are first presented in terms of related parameters, and the elasticplastic buckling load is then estimated by a semi-empirical formula in terms of generalized slenderness ratio using a corresponding plastic load. For the plastic load, the present scheme adopts a procedure that it is calculated by a linear elastic FEM analysis, while an alternative formula for the plastic load is also proposed based on a shell membrane theory. The validity of the estimation scheme is finally confirmed through comparison with the results based on FEM nonlinear analysis. The formulations are so efficient and simple that the estimation may be conducted for preliminary design purposes almost with a calculator. .

Buckling analysis of functionally graded annular sector plates resting on elastic foundations

2010 ◽  
Vol 225 (2) ◽  
pp. 312-325 ◽  
Author(s):  
A Naderi ◽  
A R Saidi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.

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.

Imperfection Sensitivity Analysis of Double Domes Free Form Space Structures

2015 ◽  
Vol 15 (04) ◽  
pp. 1450067 ◽  
Author(s):  
Mehdi Abbasi Mousavi ◽  
Karim Abedi ◽  
Mohamadreza Chenaghlou
Keyword(s):  
Finite Element ◽  
Limit Equilibrium ◽  
Single Layer ◽  
Initial Imperfection ◽  
Free Form ◽  
Space Structures ◽  
Equilibrium Path ◽  
Imperfection Sensitivity ◽  
Step Method ◽  
Buckling Modes

This paper investigates the effects of applying different buckling modes obtained by linearized eigenvalue buckling analysis as the initial imperfection for double domes free form space structures. Nonlinear elastic–plastic analysis of rigidly jointed single layer double domes are carried out using the finite element method. Having verified the finite element modeling, several different collapse analyses have been undertaken in order to examine the stability behavior of these structures. By using the approximate-perturbed method, the results of the analyses show that in free form double domes, the lowest buckling modes could not be considered as the effective modes to change the bifurcation equilibrium path into the limit equilibrium one. Therefore, the generalized conformable imperfection mode method has been suggested in the present study in order to apply geometric imperfections in free form double domes. Also, one step method has been suggested in order to eliminate 60% of buckling modes, which are nonsensitive, before applying the approximate-perturbed method.

scholarly journals Dynamic Buckling of a Clamped Finite Column Resting on a Non – linear Elastic Foundation

2019 ◽  
pp. 1-47
Author(s):  
E. Julius, Bassey ◽  
M. Anthony, Ette ◽  
U. Joy, Chukwuchekwa ◽  
C. Atulegwu, Osuji
Keyword(s):  
Elastic Foundation ◽  
Governing Equation ◽  
Asymptotic Expansions ◽  
Perturbation Technique ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Linear Elastic ◽  
Non Linear ◽  
Relevant Variables ◽  
Independent Parameters

The analysis of the dynamic buckling of a clamped finite imperfect viscously damped column lying on a quadratic-cubic elastic foundation using the methods of asymptotic and perturbation technique is presented. The proposed governing equation contains two small independent parameters (δ and ϵ) which are used in asymptotic expansions of the relevant variables. The results of the analysis show that the dynamic buckling load of column decreases with its imperfections as well as with the increase in damping. The results obtained are strictly asymptotic and therefore valid as the parameters δ and ϵ become increasingly small relative to unity.

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.

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