Vibration of Nonlinear Nonlocal Elastic Column with Initial Imperfection

2021 ◽  
pp. 93-98
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu ◽  
Bogdan Marinca
Keyword(s):  
Initial Imperfection ◽  
Elastic Column

Hoff’s Problem in a Probabilistic Setting

1980 ◽  
Vol 47 (2) ◽  
pp. 403-408 ◽  
Author(s):  
Isaac Elishakoff
Keyword(s):  
Monte Carlo ◽  
Compression Test ◽  
Nonlinear Differential Equations ◽  
Initial Imperfection ◽  
Maximum Load ◽  
Reliability Function ◽  
Gaussian Random Fields ◽  
Autocorrelation Functions ◽  
Probabilistic Setting ◽  
Elastic Column

Hoff’s problem—that of investigation of the maximum load supported by an elastic column in a compression test—is considered in a probabilistic setting. 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. The Fourier coefficients of the expansion for the initial imperfection function are simulated numerically; for each realization of the initial imperfection function, the maximum load supported by an elastic column in a compression test is found by the solution of a set of coupled nonlinear differential equations. For slightly imperfect columns, the closed solution is given in terms of Bessel and Lommel functions and turns out to compare well with the result of numerical integration. Results of the Monte Carlo solution are used in constructing the reliability function at a specified load. Reliability functions for different manufacturing processes (represented by different autocorrelation functions with equal variance) are calculated; design requirement suggests then that, other conditions being equal, the preference should be given to the manufacturing process resulting higher reliability.

scholarly journals Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
S. P. Xu ◽  
M. R. Xu ◽  
C. M. Wang
Keyword(s):  
Size Effect ◽  
Homotopy Perturbation Method ◽  
Large Deflection ◽  
Initial Imperfection ◽  
Nonlocal Elasticity Theory ◽  
Equilibrium Path ◽  
Postbuckling Behavior ◽  
Homotopy Perturbation ◽  
Parametric Studies ◽  
Elastic Column

Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.

Determination of collapse moment of different angled pipe bends with initial geometric imperfection subjected to in-plane bending moments

2021 ◽  
pp. 095440622199640
Author(s):  
Manish Kumar ◽  
Pronab Roy ◽  
Kallol Khan
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Initial Imperfection ◽  
Bend Angle ◽  
Bending Moments ◽  
Element Analysis ◽  
Geometric Imperfection ◽  
Initial Geometric Imperfection

From the recent literature, it is revealed that pipe bend geometry deviates from the circular cross-section due to pipe bending process for any bend angle, and this deviation in the cross-section is defined as the initial geometric imperfection. This paper focuses on the determination of collapse moment of different angled pipe bends incorporated with initial geometric imperfection subjected to in-plane closing and opening bending moments. The three-dimensional finite element analysis is accounted for geometric as well as material nonlinearities. Python scripting is implemented for modeling the pipe bends with initial geometry imperfection. The twice-elastic-slope method is adopted to determine the collapse moments. From the results, it is observed that initial imperfection has significant impact on the collapse moment of pipe bends. It can be concluded that the effect of initial imperfection decreases with the decrease in bend angle from 150∘ to 45∘. Based on the finite element results, a simple collapse moment equation is proposed to predict the collapse moment for more accurate cross-section of the different angled pipe bends.

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.

Stayed Column with Initial Imperfection

1982 ◽  
Vol 108 (7) ◽  
pp. 1623-1640 ◽  
Author(s):  
Kevin C. Wong ◽  
Murray C. Temple
Keyword(s):  
Initial Imperfection

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.

Buckling of an elastic column containing a fatigue crack

1972 ◽  
Vol 12 (8) ◽  
pp. 368-371 ◽  
Author(s):  
A. Berkovits ◽  
A. Golod
Keyword(s):  
Fatigue Crack ◽  
Elastic Column

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.

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