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.

Improved Secant Matrices for the Postbuckling Analysis of Thin Composite Plates

2003 ◽  
Vol 03 (03) ◽  
pp. 355-375 ◽  
Author(s):  
S. Arul Jayachandran ◽  
S. Gopalakrishnan ◽  
R. Narayanan
Keyword(s):  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Initial Imperfection ◽  
Composite Plates ◽  
Shear Stiffness ◽  
Laminated Composite Plates ◽  
Postbuckling Behavior ◽  
Initial Imperfections ◽  
First Order ◽  
Total Displacement

To study the postbuckling behavior of imperfect laminated composite plates, improved incremental or secant matrices are presented in this paper using what is called additional displacement formulation (ADF). These secant matrices are derived using the Marguerre's shell theory and they can be used in combination with any thin plate finite element. The advantage of the present formulation is that it involves no numerical approximation in forming the initial imperfection matrices as opposed to earlier secant matrices published in the literature using total displacement formulation. With the addition of shear stiffness matrix and little modification, the present incremental matrices could be extended to model postbuckling behavior of plates using the first-order shear deformation theory. The secant matrices presented in this study are shown to be very accurate in tracing the postbuckling behavior of thin isotropic and laminated composite plates with general initial imperfections.

Who Did the Audit? Audit Quality and Disclosures of Other Audit Participants in PCAOB Filings

2014 ◽  
Vol 90 (5) ◽  
pp. 1939-1967 ◽  
Author(s):  
Carol Callaway Dee ◽  
Ayalew Lulseged ◽  
Tianming Zhang
Keyword(s):  
Audit Quality ◽  
Market Reaction ◽  
Audit Fees ◽  
Discretionary Accruals ◽  
Multivariate Model ◽  
Significant Decline ◽  
Earnings Response Coefficients ◽  
Absolute Value ◽  
Earnings Response ◽  
First Time

ABSTRACT We empirically test whether audit quality is affected when part of an SEC issuer's audit is outsourced to auditors other than the principal auditor (“participating auditors”). We find a significantly negative market reaction and a significant decline in earnings response coefficients (ERCs) for experimental issuers disclosed for the first time as having participating auditors involved in their audits. However, we find no market reaction and no decline in ERCs for a matching sample of issuers that are not disclosed as using participating auditors, nor for issuers disclosed for the second or third time as using participating auditors. We also find actual audit quality as measured by absolute value of performance-matched discretionary accruals is lower for the experimental issuers, although we find no difference in audit fees paid by the experimental and matching issuers in a multivariate model. Our findings suggest that the PCAOB's proposed rule requiring disclosure of the use of other auditors in addition to the principal auditor would provide information useful to investors in assessing audit quality for SEC issuers.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

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.

The central limit problem for trimmed sums

1987 ◽  
Vol 102 (2) ◽  
pp. 329-349 ◽  
Author(s):  
Philip S. Griffin ◽  
William E. Pruitt
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Random Variable ◽  
Limit Problem ◽  
Absolute Value ◽  
Trimmed Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Central Limit Problem ◽  
Trimmed Sum

Let X, X1, X2,… be a sequence of non-degenerate i.i.d. random variables with common distribution function F. For 1 ≤ j ≤ n, let mn(j) be the number of Xi satisfying either |Xi| > |Xj|, 1 ≤ i ≤ n, or |Xi| = |Xj|, 1 ≤ i ≤ j, and let (r)Xn = Xj if mn(j) = r. Thus (r)Xn is the rth largest random variable in absolute value from amongst X1, …, Xn with ties being broken according to the order in which the random variables occur. Set (r)Sn = (r+1)Xn + … + (n)Xn and write Sn for (0)Sn. We will refer to (r)Sn as a trimmed sum.

A population birth-and-mutation process, I: explicit distributions for the number of mutants in an old culture of bacteria

1974 ◽  
Vol 11 (03) ◽  
pp. 437-444 ◽  
Author(s):  
Benoit Mandelbrot
Keyword(s):  
Growth Rate ◽  
Mutation Rate ◽  
Growth Rates ◽  
Random Variable ◽  
Mutation Process ◽  
Limit Condition ◽  
Rate Of Growth ◽  
Mathematical Techniques ◽  
First Time

Luria and Delbrück (1943) have observed that, in old cultures of bacteria that have mutated at random, the distribution of the number of mutants is extremely long-tailed. In this note, this distribution will be derived (for the first time) exactly and explicitly. The rates of mutation will be allowed to be either positive or infinitesimal, and the rate of growth for mutants will be allowed to be either equal, greater or smaller than for non-mutants. Under the realistic limit condition of a very low mutation rate, the number of mutants is shown to be a stable-Lévy (sometimes called “Pareto Lévy”) random variable, of maximum skewness ß, whose exponent α is essentially the ratio of the growth rates of non-mutants and of mutants. Thus, the probability of the number of mutants exceeding the very large value m is proportional to m –α–1 (a behavior sometimes referred to as “asymptotically Paretian” or “hyperbolic”). The unequal growth rate cases α ≠ 1 are solved for the first time. In the α = 1 case, a result of Lea and Coulson is rederived, interpreted, and generalized. Various paradoxes involving divergent moments that were encountered in earlier approaches are either absent or fully explainable. The mathematical techniques used being standard, they will not be described in detail, so this note will be primarily a collection of results. However, the justification for deriving them lies in their use in biology, and the mathematically unexperienced biologists may be unfamiliar with the tools used. They may wish for more details of calculations, more explanations and Figures. To satisfy their needs, a report available from the author upon request has been prepared. It will be referred to as Part II.

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.

Asynchronous trilobite extinctions at the early to middle Cambrian transition

Geology ◽  
2020 ◽  
Vol 48 (5) ◽  
pp. 441-445 ◽  
Author(s):  
F.A. Sundberg ◽  
K.E. Karlstrom ◽  
G. Geyer ◽  
J.R. Foster ◽  
J.W. Hagadorn ◽  
...  
Keyword(s):  
Critical Time ◽  
Data Sets ◽  
Early Cambrian ◽  
Earth System ◽  
Middle Cambrian ◽  
West Gondwana ◽  
Paleoclimatic Data ◽  
First Time ◽  
Age Constraints ◽  
Prior Models

Abstract Trilobites appeared and diversified rapidly in the Cambrian, but it is debated as to whether their radiations and extinctions were globally synchronous or geographically restricted and diachronous. The end of the early Cambrian is a classic example—it has traditionally been defined by the extinction of olenellid and redlichiid trilobites and the appearance of paradoxidid trilobites. Here we integrate the global biostratigraphy of these three trilobite groups with high-precision tuff and tandem detrital zircon U-Pb age constraints to falsify prior models for global synchronicity of these events. For the first time, we demonstrate that olenellid trilobites in Laurentia went extinct at least 3 Ma after the first appearance of paradoxidids in Avalonia and West Gondwana (ca. 509 Ma). They also disappeared before the extinction of redlichiids and prior to the base of the Miaolingian at ca. 506 Ma in South China. This indicates that these three trilobite groups (paradoxidids, olenellids, and redlichiids) and their associated biotas overlapped in time for nearly 40% of Cambrian Epoch 2, Age 4. Implications of this chronological overlap are: (1) trilobite transitions were progressive and geographically mediated rather than globally synchronous; and (2) paleontological databases underestimate the diversity of the early Cambrian. This ∼3 Ma diachroneity, at a critical time in the early evolution of animals, also impacts chemostratigraphic and paleoclimatic data sets that are tied to trilobite biostratigraphy and that collectively underpin our understanding of the Cambrian Earth system.

Castaing’s Electron Microprobe and Its Impact on Materials Science

2001 ◽  
Vol 7 (2) ◽  
pp. 178-192 ◽  
Author(s):  
Dale E. Newbury
Keyword(s):  
Electron Microprobe ◽  
Materials Science ◽  
Critical Time ◽  
Materials Engineering ◽  
Macro Scale ◽  
Materials Science And Engineering ◽  
Basic Infrastructure ◽  
The Impact ◽  
First Time

Abstract The development of the electron microprobe by Raymond Castaing provided a great stimulus to materials science at a critical time in its history. For the first time, accurate elemental analysis could be performed with a spatial resolution of 1 µm, well within the dimensions of many microstructural features. The impact of the microprobe occurred across the entire spectrum of materials science and engineering. Contributions to the basic infrastructure of materials science included more accurate and efficient determination of phase diagrams and diffusion coefficients. The study of the microstructure of alloys was greatly enhanced by electron microprobe characterization of major, minor, and trace phases, including contamination. Finally, the electron microprobe has proven to be a critical tool for materials engineering, particularly to study failures, which often begin on a micro-scale and then propagate to the macro-scale with catastrophic results.

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.

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