Probability Distribution of Peaks for Nonlinear Combination of Vector Gaussian Loads

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Sayan Gupta ◽  
P. H. A. J. M. van Gelder
Keyword(s):  
Probability Distribution ◽  
Gaussian Process ◽  
Joint Probability ◽  
Random Processes ◽  
Von Mises Stress ◽  
Analytical Approximations ◽  
Multidimensional Integration ◽  
Reliability Method ◽  
Non Gaussian ◽  
Von Mises

The problem of approximating the probability distribution of peaks, associated with a special class of non-Gaussian random processes, is considered. The non-Gaussian processes are obtained as nonlinear combinations of a vector of mutually correlated, stationary, Gaussian random processes. The Von Mises stress in a linear vibrating structure under stationary Gaussian loadings is a typical example for such processes. The crux of the formulation lies in developing analytical approximations for the joint probability density function of the non-Gaussian process and its instantaneous first and second time derivatives. Depending on the nature of the problem, this requires the evaluation of a multidimensional integration across a possibly irregular and disjointed domain. A numerical algorithm, based on first order reliability method, is developed to evaluate these integrals. The approximations for the peak distributions have applications in predicting the expected fatigue damage due to combination of stress resultants in a randomly vibrating structure. The proposed method is illustrated through two numerical examples and its accuracy is examined with respect to estimates from full scale Monte Carlo simulations of the non-Gaussian process.

scholarly journals Probability distribution of von Mises stress in the presence of pre-load.

2013 ◽  
Author(s):  
Daniel Joseph Segalman ◽  
Field, Richard V., ◽  
Garth M. Reese
Keyword(s):  
Probability Distribution ◽  
Von Mises Stress ◽  
Von Mises

Estimating the Probability Distribution of von Mises Stress for Structures Undergoing Random Excitation

1999 ◽  
Vol 122 (1) ◽  
pp. 42-48 ◽  
Author(s):  
Dan Segalman ◽  
Garth Reese ◽  
Richard Field, ◽  
Clay Fulcher
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Asymptotic Properties ◽  
Monte Carlo Sampling ◽  
Random Excitation ◽  
Von Mises Stress ◽  
Second Order Statistics ◽  
Analytic Expressions ◽  
Numerical Precision ◽  
Von Mises

The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. For deterministic loads, both static and dynamic, the calculation of von Mises stress is straightforward, as is the resulting calculation of reliability. For loads modeled as random processes, the task is different; the response to such loads is itself a random process and its properties must be determined in terms of those of both the loads and the system. This has been done in the past by Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the problem. Here, we present a method that provides analytic expressions for the probability distributions of von Mises stress which can be evaluated efficiently and with good numerical precision. Further, this new approach has the important advantage of providing the asymptotic properties of the probability distribution. [S0739-3717(00)00801-1]

Influence of Roughness Parameters Skewness and Kurtosis on Fatigue Life Under Mixed Elastohydrodynamic Lubrication Point Contacts

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Xiao-Liang Yan ◽  
Xiao-Li Wang ◽  
Yu-Yan Zhang
Keyword(s):  
Fatigue Life ◽  
Elastohydrodynamic Lubrication ◽  
Von Mises Stress ◽  
Maximum Pressure ◽  
Point Contacts ◽  
Roughness Parameters ◽  
Numerical Studies ◽  
Non Gaussian ◽  
Von Mises ◽  
Skewness And Kurtosis

The numerical studies on the influences of surface parameters skewness and kurtosis on tribological characteristics under mixed elastohydrodynamic lubrication (mixed EHL) conditions are extended to fatigue life. Non-Gaussian rough surfaces are generated numerically with given autocorrelation function, skewness, and kurtosis. The results show that the maximum pressure increases as the skewness increases, however its variation with kurtosis is closely related to skewness. Similar trends to that of the maximum pressure are observed for the maximum von Mises stress. The fatigue life decreases as the skewness increases, however it undergoes apparent fluctuations with the increase of kurtosis. As the kurtosis increases, the influence of skewness on fatigue life becomes more significant, and vice versa.

Generalization of Rayleigh Probability Distribution and its Application

1978 ◽  
Vol 22 (04) ◽  
pp. 259-265
Author(s):  
Michel K. Ochi
Keyword(s):  
Probability Distribution ◽  
Surface Effect ◽  
Ocean Waves ◽  
Random Processes ◽  
Rayleigh Distribution ◽  
Nonlinear Damping ◽  
Statistical Prediction ◽  
Rolling Motion ◽  
Surface Effect Ship ◽  
Non Gaussian

The Rayleigh probability distribution has been used extensively for statistical prediction of ocean waves, responses of ships, and marine structures in a seaway. However, the Rayleigh distribution cannot be used for statistical prediction of non-Gaussian random processes, a typical example of which is ship rolling motion with nonlinear characteristics. To evaluate the statistical properties of the maxima (peak values) of non-Gaussian random processes, this paper discusses generalization of the Rayleigh distribution and its application to practical problems. As examples of application, the problems associated with rolling motion of a vessel stabilized by rudders, responses of a surface effect ship in a seaway, and rolling motion of a ship with nonlinear damping are presented.

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