Innovative theory for the compliance computation in rotors

Ranjbaran, Abdolrasoul; Ranjbaran, Mohammad

doi:10.24200/sci.2017.4269

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…For a change in a system (e.g., structure) the survived capacity and the fled capacity are important (Ranjbaran et al, 2008;Ranjbaran and Rousta, 2009;Ranjbaran, 2010;Ranjbaran et al, 2011;Ranjbaran, 2012;Ranjbaran and 237 Rousta, 2013a;Ranjbaran and Ranjbaran, 2014;Ranjbaran, 2015;Ranjbaran and Ranjbaran, 2016;2017a;2017b;2017c;Ranjbaran et al, 2020a-f;2021a;2021b). The capacity (kS), called system stiffness, is defined as a positive entity which has a finite specified value at the beginning of the lifetime (origin) and reduces to zero at the end of systems lifetime (destination).…”

Section: The Persian Curve Basicsmentioning

confidence: 99%

Persian Curve Versus Monte Carlo Method

Ranjbaran¹,

Ranjbaran²,

Ranjbaran³

2021

International Journal of Structural Glass and Advanced Material

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The Monte Carlo Simulation method is a powerful tool for solving problems including random variables. The basic idea to implement a Monte Carlo simulation is to first generate samples of random inputs from their assumed distribution functions and then perform a deterministic calculation on the generated random inputs, based on mathematical modeling of the system, to obtain output results. An early version of Monte Carlo simulation is the famous needle experiment. The idea of random experiment, have been used for solving many complex problems. Simulation based approaches have some disadvantages. Its implementation needs a massive use of computational resource and long calculation times. Moreover, providing linkage between input to the system and its output is difficult. Toward remedy, the phenomenon is considered as the change in the state of the system. Via logical reasoning, concise mathematics and using real world data, the output is related to the input via the Persian Curve. The Persian Curve provided a simple, cheap and exact solution to the problem. Consequently the Persian Curve is proposed as a replacement for the Monte Carlo Simulation. The validity of the work is verified via concise mathematics and comparison of the results with those of the others.

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Section: The Persian Curve Basicsmentioning

confidence: 99%

Persian Curve Versus Monte Carlo Method

Ranjbaran¹,

Ranjbaran²,

Ranjbaran³

2021

International Journal of Structural Glass and Advanced Material

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“…The strain energy release rate method is used to determine the compliance of cracked circular shaft. The ( SIF ) for circular cross section is not available (This argument was perhaps correct up to 10 years ago, but now that is not the case, interested reader may refer to Ranjbaran [54] and related references!) consequently the shaft is considered to be a sum of elementary independent rectangular strips which are used in calculation of the compliance by integrating along the crack tip.…”

Section: Introductionmentioning

confidence: 99%

A Reliable Fracture Mechanics

Ranjbaran

2020

IJRRS

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A branch of human knowledge, which treats the behavior of cracked structures, is called fracture mechanics. Since there is no intact structure in the world, then the paramount importance of fracture mechanics in human life is accentuated. The main parameter of fracture mechanics is called crack compliance, which is the amount of flexibility added to the flexibility of the intact structure due to the presence of a crack with specified size. The compliance, similar to flexibility, is the sole characteristics of the cracked structure. In this way for a given structure with a specified crack, there should be a single compliance. Unfortunately, in classical fracture mechanics that is not the case! The number of crack compliances for a clacked structure is equal to the number of researchers who treated the case! This diversity in the results stems from the presence of epistemic uncertainty in the mathematical basis of classical fracture mechanics. In view of the need for remedy, the Abdolrasoul Ranjbaran Team (ART), investigated the case and proposed a reliable fracture mechanics, which is based on sound logical reasoning. The proposed reliable fracture mechanics is described in the presented paper. The paper is managed via fourteen titles as, introduction, the mathematical basis of the classical fracture mechanics, birthplace of the state based philosophy, strong form of governing equation, analytical solution by Laplace transform, the weak form equation, the finite element equation, logical basis of the state based philosophy, state functions, Persian curves, reliable crack compliance, energy release rate, stress intensity factor, and weight function for the stress intensity factor in sections one to fourteen respectively. The paper concludes with a list of cited references.

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Persian Probability Function: An Alternative to Classical Probability Function

Ranjbaran

et al. 2022

NEDJR

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This paper presents the details of an analytical investigation which was carried out to propose Persian curve. The curve provides an alternative of probability functions to define the state of a system. The Persian curves are super functions of the state variable which includes state functions and two control parameters. The state variable is a scaled identification parameter of a system. The state functions are two specific functions of the state variable. The control parameters are determined from the real-world data. Since the Persian curve has the basic properties of the probability function, it is called the Persian probability function. It is concluded that all natural phenomena are certain and the lack of knowledge has led the humans to divide the phenomena into certain and stochastic categories. The proposed Persian curve was validated by analysing the probability data from different fields of study.

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Innovative theory for the compliance computation in rotors

Cited by 4 publications

References 24 publications

Persian Curve Versus Monte Carlo Method

Persian Curve Versus Monte Carlo Method

A Reliable Fracture Mechanics

Persian Probability Function: An Alternative to Classical Probability Function

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