AN APPROXIMATE METHOD TO PRESENT THE BUCKLING STRENGTH OF A GRILLAGE IN A PROBABILISTIC FORM

An approximate method for calculation in probabilistic terms of the buckling strength of a grillage under unidirectional in-plane compression is proposed. The geometric properties of longitudinals and transverses and the mechanical properties (yield stress and modulus of elasticity) of the material they are built from are treated as random parameters that may change over ship’s service life. The cumulative distribution function of the grillage’s critical buckling strength is calculated by using an analytical formula for multitude sets of input parameters while all of them having the same level of certainty. The assumption is that the critical buckling strength has the same (or very similar) level of certainty as that of the input parameters. The accuracy of the proposed approximate method is relatively high (the maximal error is around 2%). It is recommended for use when specialized computer programs for application of Monte Carlo simulation method are not available. The method does not require a complicated specialized computer program and can be run on EXCEL computer program.

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An Approximate Method to Present the Buckling Strength of A Grillage in A Probabilistic Form – Technical Note

10.3940/rina.ijme.2013.a4.266tn ◽

2013 ◽

Vol 155 (A4) ◽

Keyword(s):

Computer Program ◽

Approximate Method ◽

Cumulative Distribution Function ◽

Analytical Formula ◽

Simulation Method ◽

Technical Note ◽

Cumulative Distribution ◽

Buckling Strength ◽

Input Parameters ◽

Plane Compression

An approximate method for calculation in probabilistic terms of the buckling strength of a grillage under unidirectional in-plane compression is proposed. The geometric properties of longitudinals and transverses and the mechanical properties (yield stress and modulus of elasticity) of the material they are built from are treated as random parameters that may change over ship's service life. The cumulative distribution function of the grillage's critical buckling strength is calculated by using an analytical formula for multitude sets of input parameters while all of them having the same level of certainty. The assumption is that the critical buckling strength has the same (or very similar) level of certainty as that of the input parameters. The accuracy of the proposed approximate method is relatively high (the maximal error is around 2%). It is recommended for use when specialized computer programs for application of Monte Carlo simulation method are not available. The method does not require a complicated specialized computer program and can be run on EXCEL computer program.

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Cumulative distribution function solutions of advection–reaction equations with uncertain parameters

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2014.0189 ◽

2014 ◽

Vol 470 (2166) ◽

pp. 20140189 ◽

Cited By ~ 16

Author(s):

F. Boso ◽

S. V. Broyda ◽

D. M. Tartakovsky

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Hyperbolic Conservation Laws ◽

Computational Cost ◽

Cumulative Distribution ◽

State Variables ◽

Correlation Lengths ◽

Advective Flux ◽

Wide Range ◽

Input Parameters

We derive deterministic cumulative distribution function (CDF) equations that govern the evolution of CDFs of state variables whose dynamics are described by the first-order hyperbolic conservation laws with uncertain coefficients that parametrize the advective flux and reactive terms. The CDF equations are subjected to uniquely specified boundary conditions in the phase space, thus obviating one of the major challenges encountered by more commonly used probability density function equations. The computational burden of solving CDF equations is insensitive to the magnitude of the correlation lengths of random input parameters. This is in contrast to both Monte Carlo simulations (MCSs) and direct numerical algorithms, whose computational cost increases as correlation lengths of the input parameters decrease. The CDF equations are, however, not exact because they require a closure approximation. To verify the accuracy and robustness of the large-eddy-diffusivity closure, we conduct a set of numerical experiments which compare the CDFs computed with the CDF equations with those obtained via MCSs. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties of the two input parameters, such as their correlation lengths and variance of the coefficient that parametrizes the advective flux.

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Gradient based empirical cumulative distribution function approximation for robust aerodynamic design

Aerospace Science and Technology ◽

10.1016/j.ast.2021.106630 ◽

2021 ◽

pp. 106630

Author(s):

Elisa Morales ◽

Andrea Bornaccioni ◽

Domenico Quagliarella ◽

Renato Tognaccini

Keyword(s):

Distribution Function ◽

Function Approximation ◽

Cumulative Distribution Function ◽

Cumulative Distribution ◽

Aerodynamic Design ◽

Empirical Cumulative Distribution Function ◽

Gradient Based

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Determinants of the Strategic Mortgage Default Cumulative Distribution Function

Journal of Real Estate Literature ◽

10.1080/10835547.2016.12090420 ◽

2016 ◽

Vol 24 (1) ◽

pp. 183-199

Author(s):

Michael J. Seiler

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Cumulative Distribution ◽

Mortgage Default

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DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488501000594 ◽

2001 ◽

Vol 09 (01) ◽

pp. 39-53 ◽

Cited By ~ 2

Author(s):

RONALD R. YAGER

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Probability Distributions ◽

Random Variables ◽

Cumulative Distribution ◽

General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

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