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.

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.

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.

The Effect of Transverse Shear on the Postbuckling and Growth Characteristics of Delaminations in Composites

1999 ◽  
Vol 121 (4) ◽  
pp. 406-412 ◽  
Author(s):  
Catherine H. Ferrie ◽  
Izhak Sheinman ◽  
George A. Kardomateas
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Shear Deformation ◽  
Release Rate ◽  
Transverse Shear ◽  
Coupling Effect ◽  
Nonlinear Differential Equations ◽  
Kinematic Model ◽  
Initial Imperfection ◽  
Plate Length

A geometrically nonlinear formulation for the behavior of composite delaminated beams of arbitrary stacking sequence, and with the effects of transverse shear deformation included, is presented. The formulation is based on a first-order shear deformation kinematic model, which incorporates the bending-stretching coupling effect and also assumes an arbitrary initial imperfection. The nonlinear differential equations are solved by Newton’s method using a finite-difference scheme. The growth of the delamination is also studied by applying the J-integral in order to derive a formula for the energy release rate, which includes transverse shear. Results are presented which illustrate the shear effect, especially with respect to the ratio of the in-plane extensional over shear modulus and with respect to the ratio of plate length over thickness. It is seen that transverse shear can affect largely the displacement profiles, rendering the structure more compliant, and can promote growth by increasing the energy release rate, but this latter effect is moderate and mainly noticable only at the later stages in the postbuckling regime.

Compression after Impact Performance of Composite Stiffened Panels

2011 ◽  
Vol 415-417 ◽  
pp. 2231-2235 ◽  
Author(s):  
Zhe Sun ◽  
Fei Xu ◽  
Wei Xie ◽  
Bo Wang
Keyword(s):  
Structural Damage ◽  
Initial Imperfection ◽  
Maximum Load ◽  
Experimental Results ◽  
Low Velocity Impact ◽  
Thickness Direction ◽  
Low Velocity ◽  
Stiffened Panels ◽  
Velocity Impact ◽  
Compression After Impact

Composite stiffened panels are widely used in the modern aircraft structure with the advantages of light weight, structural efficiency and good crack performance. But the stiffened panels have poor performance at thickness direction, especially for low-velocity impact. First of all, compressive tests were investigated and analyzed for two types of composite stiffened panels, which are integrated specimens and post-impact specimens. And the effect of low-velocity impact to the supporting capacity of composite stiffened panels was researched. Secondly，the finite element model was established to simulate the CAI (Compression After Impact)strength with the equivalent hole method. It is found that the analyze results match the experimental results well. According to the experimental results, structural damage and the maximum load caused by impact energy are scattering. Then the imperfect factors were introduced to reflect the initial imperfection, namely the initial deflection at thickness direction. The effect of different imperfect factors to the maximum load was discussed.

Post-Buckling Behavior of Z-Shaped Columns under Variables of Lengths and Initial Imperfections

2013 ◽  
Vol 437 ◽  
pp. 62-65
Author(s):  
Ji Nao Zhang
Keyword(s):  
Failure Modes ◽  
Control Method ◽  
Three Dimensional ◽  
Initial Imperfection ◽  
Maximum Load ◽  
Element Analysis ◽  
Initial Imperfections ◽  
Solution Methods ◽  
Post Buckling ◽  
Displacement Control Method

This paper conducts three-dimensional, nonlinear finite element analysis to investigate the results of using different solution methods and the influence of initial imperfections and material plasticity on failure modes and maximum load of various Z-shaped column lengths; it also compares the column buckling responses between various lengths, each with different initial imperfections. Further analyses include investigating the element suitability and computational costs. Results showed that both displacement control method and Riks method are fully capable of receiving promising results from this analysis. In terms of the effects of initial imperfection and material plasticity on the maximum load that column could carry, the imperfection is the major contributing factor when the column is long whereas the plasticity is the major contributing factor when the column is short.

Axial Impact Buckling of a Column With Random Initial Imperfections

1978 ◽  
Vol 45 (2) ◽  
pp. 361-365 ◽  
Author(s):  
I. Elishakoff
Keyword(s):  
Critical Time ◽  
Initial Imperfection ◽  
Random Variable ◽  
Axial Impact ◽  
Absolute Value ◽  
Initial Imperfections ◽  
Total Displacement ◽  
Probabilistic Setting ◽  
Probabilistic Nature ◽  
First Time

Axial impact buckling of perfectly elastic bars with initial imperfections is considered in a probabilistic setting. It is assumed that the initial imperfection function involved a single parameter, which in turn is a continuous random variable with given probability distribution function. The structure is said to buckle if the absolute value of the total displacement exceeds a prescribed value. The probabilistic nature of the random, critical time when such a failure occurs for the first time, is studied.

POST-BUCKLING OF AN ELASTIC COLUMN WITH VARIOUS ROTATIONAL END RESTRAINTS

2005 ◽  
Vol 05 (01) ◽  
pp. 113-123 ◽  
Author(s):  
B. PHUNGPAINGAM ◽  
S. CHUCHEEPSAKUL
Keyword(s):  
Shooting Method ◽  
Nonlinear Differential Equations ◽  
Compressive Force ◽  
Limit Load ◽  
Technical Note ◽  
Buckling Behavior ◽  
End Conditions ◽  
Post Buckling ◽  
Secondary Bifurcation ◽  
Elastic Column

In this technical note, the post-buckling behavior of a simply supported elastic column with various rotational end conditions of the supports is investigated. The compressive force is applied at the tip of the column. The characteristic equation for solving the critical loads is obtained from the boundary value problem of linear systems. In the post-buckling state, a set of nonlinear differential equations with boundary conditions is established and numerically solved by the shooting method. The interesting features associated with this problem such as the limit load point, snap-through phenomenon and the secondary bifurcation point will be highlighted herein.

EFFECTIVENESS OF THE COMPARATIVE RELIABILITY ASSESSMENT TECHNIQUES EVALUATING QUALITY & RELIABILITY IN ENGINEERING DESIGN

1995 ◽  
Vol 02 (03) ◽  
pp. 309-326 ◽  
Author(s):  
GEORGE A. BOHORIS
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Engineering Design ◽  
Reliability Assessment ◽  
Reliability Function ◽  
Wilcoxon Test ◽  
Weight Functions ◽  
Engineering Designs ◽  
Assessment Techniques ◽  
Kolmogorov Smirnov

In this paper a new generalization of the Wilcoxon test is proposed for the comparative reliability evaluation of alternative engineering designs. Using Monte Carlo simulations the performance of the new test is assessed against the results provided by four other two-sample tests for censored reliability data, i.e., the Gehan-Wilcoxon, Peto-Prentice, Logrank and modified Kolmogorov-Smirnov tests. The results of the simulations suggest that the Wilcoxon alternatives based on weight functions that are reliability function estimates, such as the Peto-Prentice and the Bohoris-Wilcoxon, are the most preferable for routine use.

Research note: Avian gut passage reduces seed exit costs in Sorbus aucuparia (Rosaceae) as measured by a diametral compression test

2006 ◽  
Vol 33 (4) ◽  
pp. 401 ◽  
Author(s):  
Torbjørn R. Paulsen ◽  
Ommund Lindtjørn ◽  
Nils Roar Gjerdet ◽  
Göran Högstedt
Keyword(s):  
Compression Test ◽  
Seed Coat ◽  
Seed Weight ◽  
Seedling Emergence ◽  
Maximum Load ◽  
Sorbus Aucuparia ◽  
Diametral Compression ◽  
Gut Passage ◽  
Exit Costs ◽  
Diametral Compression Test

Reduced seed exit costs have been suggested to explain advanced seedling emergence and increased seedling growth in Sorbus aucuparia L. (Rosaceae; rowan) following Turdus spp. (Turdidae; thrush) gut passage. In the present study, seed coat tension strength of Turdus merula L. (Turdidae; blackbird) gut-passed and non-ingested control seeds were tested with a diametral compression test. Both maximum load (N) and work (mJ) required for opening the seeds were reduced in gut-passed seeds, although scanning electron microscopy showed no visible differences in seed coat surface structure between treatments. In addition, gut passage increased dry seed weight by 0.64 mg (22%), weight of hydrated seeds by 0.62 mg (16%) and width of hydrated seeds by 0.1 mm (9%). Absorption causing the seed coat to yield more easily to the germinating seedling is proposed as an explanation for the reduction in seed exit costs. For the emerging seedling, the time and force needed to open the seed coat was reduced, thus lowering dispersal and germination costs of S. aucuparia.

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