Probability Density Function Of Strength Research Articles

Mathematic Model on Distribution Line Reliability Under Typhoon Weather

Distribution line reliability under typhoon weather is studied in the paper. Firstly, the probability density of wire and concrete pole bending strength is studied. Then, a distribution line reliability model with consideration of typhoon wind speed and wind direction is established. When wind speed and wind direction under typhoon weather are known, the load reliability of wire and pole is obtained according to wire tensile strength probability density function and pole bending strength probability density function. Line is equivalent to component series model for obtaining overhead distribution line reliability. The line load risk level is reflected.

Reliability assessment of structural systems with interval uncertainties under spectrum-compatible seismic excitations

The paper deals with reliability assessment of linear structures with interval parameters subjected to seismic excitations modeled as stationary spectrum-compatible Gaussian random processes. Under the Vanmarcke assumption that the up-crossings of a specified threshold occur in clumps, an efficient procedure for the evaluation of the bounds of the interval reliability function of the generic response process is presented. The key idea is to view the interval reliability function as depending on the first three interval spectral moments of the structural response rather than on the interval structural parameters. Then, the lower and upper bounds of the interval reliability function are obtained by properly combining the bounds of the interval spectral moments. Such bounds are evaluated in approximate form by applying an approach recently proposed by the authors. Finally, based on the knowledge of the interval reliability function, a method for evaluating the interval survival probability of a structural element with imprecise strength probability density function is developed.

The asymptotic stochastic strength of bundles of elements exhibiting general stress–strain laws

The fiber bundle model is widely used in probabilistic modeling of various phenomena across different engineering fields, from network analysis to earthquake statistics. In structural strength analysis, this model is an essential part of extreme value statistics that governs the left tail of the cumulative probability density function of strength. Based on previous nano-mechanical arguments, the cumulative probability distribution function of strength of each fiber constituting the bundle is assumed to exhibit a power-law left tail. Each fiber (or element) of the bundle is supposed to be subjected to the same relative displacement (parallel coupling). The constitutive equations describing various fibers are assumed to be related by a radial affinity while no restrictions are placed on their particular form. It is demonstrated that, even under these most general assumptions, the power-law left tail is preserved in the bundle and the tail exponent of the bundle is the sum of the exponents of the power-law tails of all the fibers. The results have significant implications for the statistical modeling of strength of quasibrittle structures.

Some stress-strength reliability models

This paper presents reliability expressions for five stress-strength models of parallel systems with non-identical units. Models are developed for the following systems: 1. (1) when system stress probability density function is exponentially distributed 2. (2) the stress probability density function follows gamma distribution 3. (3) system stresss probability density function can be described by beta distribution 4. (4) stress probability density function is given by a power series 5. (5) and finally, when system stress probability density function follows chi-square distribution. In these models, the unit strength probability density function is exponentially distributed with constant failure rate.