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Article
Publication date: 25 February 2014

Olufikayo Aderinlewo and Gabriel Ayodele Alade

The behaviours of four indeterminate frame-support combinations namely Type I (with fixed supports), Type II (with pinned supports), Type III (with fixed-pinned supports) and Type…

Abstract

Purpose

The behaviours of four indeterminate frame-support combinations namely Type I (with fixed supports), Type II (with pinned supports), Type III (with fixed-pinned supports) and Type IV (with fixed-roller supports) frames under the exposure conditions and loads as existing on site were simulated. Two categories of these combinations (I and II) were studied namely single storey-single bay and multiple storey-single bay frames, as illustrated in the case studies treated. A procedure for determining the probability of failure at different sections along the frame types, the range between the probability of failure bounds and the reliability ratings of the frame types were developed based on the kinetic method of plastic moment analysis, minimum weight design method, piecewise method of moment analysis and first order-second moment (FOSM) methods. The analysis results of the Category I frames showed that the Type I frame was most reliable (with the lowest probability of failure range of 0.3269), while the Type II frame was least reliable (with the highest probability of failure range of 0.4918). These results were consistent with those of the Category II frames. The paper aims to discuss these issues.

Design/methodology/approach

Collapse mechanisms were generated for four frame-support types and the corresponding plastic moments were determined using both the kinematic plastic analyses and minimum weight design methods. The members were designed and the plastic moments were distributed at sections of constant interval along the frame length to generate corresponding envelopes. A similar process was carried out to determine the elastic moment variables due to the loads. The reliability index and the corresponding probability of failure at each frame section were determined. Then, the probabilities of failure bounds for the frames were then compared to determine the most reliable.

Findings

It was observed that there existed a wide margin between the elastic and plastic moments indicating that design of steel structures at the elastic limit does not take full advantage of its strength. Hence, the design can be carried out beyond the elastic limit and within the safety margin given in equation (3). However, the safety of the entire frame is assessed on the basis of range of values between the highest and the lowest probability of failure bounds. The lower this range is (not exceeding 0.5 or 50 per cent), the more reliable the frame is.

Research limitations/implications

The equations developed in this study can only be directly applied to multi storey-single bay frames. However, the reliability-based analysis and design procedure developed can be extended to other types of frames.

Practical implications

A practical approach for analysing steel frames with different supports with the overall goal of producing safe and economical designs has been developed and presented in this paper.

Originality/value

The procedure adopted is very original and can be backed up by existing literature. The piecewise method for analysing moments at various sections along a frame is also innovative. The whole concept can be adopted to determine the reliability of other types of frames such as multiple bay-multistorey frames with different support types.

Details

Journal of Engineering, Design and Technology, vol. 12 no. 1
Type: Research Article
ISSN: 1726-0531

Keywords

Article
Publication date: 5 January 2015

Yuan Fangyang and Chen Zhongli

The purpose of this paper is to develop new types of direct expansion method of moments (DEMM) by using the n/3th moments for simulating nanoparticle Brownian coagulation in the…

Abstract

Purpose

The purpose of this paper is to develop new types of direct expansion method of moments (DEMM) by using the n/3th moments for simulating nanoparticle Brownian coagulation in the free molecule regime. The feasibilities of new proposed DEMMs with n/3th moments are investigated to describe the evolution of aerosol size distribution, and some of the models will be applied to further simulation of physical processes.

Design/methodology/approach

The accuracy and efficiency of some kinds of methods of moments are mainly compared including the quadrature method of moments (QMOM), Taylor-expansion method of moments (TEMOM), the log-normal preserving method of moments proposed by Lee (LMM) and the derived DEMM in this paper. QMOM with 12 quadrature approximation points is taken as a reference to evaluate other methods.

Findings

The newly derived models, namely DEMM(4/3,4) and DEMM(2,6), as well as the previous DEMM(2,4), are considered to be qualified models due to their high accuracy and efficiency. They are confirmed to be valid and alternative models to describe the evolution of aerosol size distribution for particle dynamical process involving the n/3th moments.

Originality/value

The n/3th moments, which have clear physical interpretations when n stands for first several integers, are first introduced in the DEMM method for simulating nanoparticle Brownian coagulation in the free molecule regime.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 April 1948

D.A.C. Nicholls

THE method which is to be outlined is not a new way of approaching continuous beam problems, it was first introduced in America by Professor Hardy Cross, and appears to be little…

Abstract

THE method which is to be outlined is not a new way of approaching continuous beam problems, it was first introduced in America by Professor Hardy Cross, and appears to be little known in this country. It is felt that the method is much easier to handle than the normal approach to such problems by the Theorem of Three Moments. Engineers dealing with structural design will find it particularly useful, as a very good approximation to the bending moments at the supports can be obtained during the early stages of the work. The method will be helpful to the engineering student, in removing any doubts he may have in determining the directions of bending moments at the supports.

Details

Aircraft Engineering and Aerospace Technology, vol. 20 no. 4
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 25 January 2011

Tirthankar Ghosh and Dilip Roy

The main purpose of this paper is to consider the role of discretization of random variables in analyzing statistical tolerancing, and to propose a new discretizing method along…

Abstract

Purpose

The main purpose of this paper is to consider the role of discretization of random variables in analyzing statistical tolerancing, and to propose a new discretizing method along with a study on its usefulness.

Design/methodology/approach

The approach for discretization of a continuous distribution is based on the concept of moment equalization with the original random variable, conditionally given a set of points of realization. For the purpose of demonstration the normal distribution has been discretized into seven points. Application of the discretization method in approximating the distribution/survival function of a complex system has also been studied. Numerical analysis on two important engineering items has been undertaken and the closeness between the values of the distribution/survival functions obtained by simulation and the proposed method has been examined to indicate the advantage of the proposed approach.

Findings

A comparative study with the earlier reported discretizing methods indicates that the proposed method, which is easy to implement, provides better results for most of the cases studied in this work.

Research limitations/implications

Using the proposed approach one can approximate the probability distribution of a complex system with random component values, which cannot be analytically expressed.

Practical implications

This paper is able to provide a new direction in reliability management research, because it can be used for product design of many important engineering items such as solid‐shaft, hollow cylinder, torsion bar, I‐beam etc.

Originality/value

This research gives a new linear method of discretization. It gives better results than the existing discretization methods of Experimental design, Moment equalization, and Discrete Concentration for reliability (survival probability) determination of solid‐shaft and power resistor.

Details

International Journal of Quality & Reliability Management, vol. 28 no. 2
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 1 November 1942

Leslie P. Dudley

PROBLEMS relating to built‐in or rigid‐end members under transverse loading are frequently encountered by the aircraft engineer. In the following paper discussion of relevant…

Abstract

PROBLEMS relating to built‐in or rigid‐end members under transverse loading are frequently encountered by the aircraft engineer. In the following paper discussion of relevant theorems leads to the development of Clapeyron's Theorem of Three Moments. The latter is particularly valuable in, for example, estimating the crankshaft bearing loads in a non‐radial engine. Attention is also drawn to Wilson's method of solving continuous beam problems. This simple method produces results identical with those given by the Theorem of Three Moments and deserves wider recognition.

Details

Aircraft Engineering and Aerospace Technology, vol. 14 no. 11
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 18 December 2007

Antonio Lanzotti and Amalia Vanacore

In this work, an efficient and easy statistical method to find an equivalent discrete distribution for a continuous random variable (r.v.) is proposed. The proposed method is…

Abstract

In this work, an efficient and easy statistical method to find an equivalent discrete distribution for a continuous random variable (r.v.) is proposed. The proposed method is illustrated by applying it to the treatment of the anthropometrical noise factors in the context of Robust Ergonomic Design (RED; Lanzotti 2006; Barone S. and Lanzotti A., 2007).

Details

Asian Journal on Quality, vol. 8 no. 3
Type: Research Article
ISSN: 1598-2688

Keywords

Article
Publication date: 12 July 2023

Jing Liu, Yuchen An, Wanli Fancheng, Changke Tang and Lixin Xu

Bearing friction moments are important factors that affect the vibrations of rotor systems. The bearing friction moments are related to the dimension parameters, lubrication…

Abstract

Purpose

Bearing friction moments are important factors that affect the vibrations of rotor systems. The bearing friction moments are related to the dimension parameters, lubrication conditions and manufacturing errors of support bearings. This work studies the effects of the bearing friction moments on the vibrations of rotor systems.

Design/methodology/approach

The rotor is separated into several shaft elements for formulating a flexible rotor. The time-varying friction moment (TFM) is affected by the time-varying contact loads. The vibrations of FRS from the TFM and Palmgren's friction moment (PFM) calculation methods are compared. Moreover, the effects of the rotor offset and radial clearance on the frequency-amplitude characteristics of FRS are studied.

Findings

The TFM method is more consistent with the actual operation mechanisms. The rotor offset and radial clearance can significantly affect the nonlinear vibrations of FRS. This work provides a new reference and research method for the vibration analysis of rotor systems considering the friction effects.

Originality/value

The elastohydrodynamic lubrication (EHL), elastic hysteresis and differential sliding are considered. A flexible rotor system (FRS) dynamic model considering the TFM is proposed. The vibrations of FRS from the TFM calculation method and empirical calculation formula are compared. The effects of the rotor offset and radial clearance on the frequency–amplitude characteristics of FRS are studied.

Details

Engineering Computations, vol. 40 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Open Access
Article
Publication date: 14 July 2021

Jihane Abdelli and Brahim Brahimi

In this paper, the authors applied the empirical likelihood method, which was originally proposed by Owen, to the copula moment based estimation methods to take advantage of its…

Abstract

Purpose

In this paper, the authors applied the empirical likelihood method, which was originally proposed by Owen, to the copula moment based estimation methods to take advantage of its properties, effectiveness, flexibility and reliability of the nonparametric methods, which have limiting chi-square distributions and may be used to obtain tests or confidence intervals. The authors derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.

Design/methodology/approach

In this paper we applied the empirical likelihood method which originally proposed by Owen, to the copula moment based estimation methods.

Findings

We derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.

Originality/value

In this paper we applied the empirical likelihood method which originally proposed by Owen 1988, to the copula moment based estimation methods given by Brahimi and Necir 2012. We derive an new estimator of copula parameters and the asymptotic normality of the empirical likelihood based on copula moment estimation methods.

Details

Arab Journal of Mathematical Sciences, vol. 28 no. 2
Type: Research Article
ISSN: 1319-5166

Keywords

Article
Publication date: 13 February 2023

Oguz Kose and Tugrul Oktay

The purpose of this paper is to optimize the simultaneous flight performance of a hexarotor unmanned aerial vehicle (UAV) by using simultaneous perturbation stochastic…

Abstract

Purpose

The purpose of this paper is to optimize the simultaneous flight performance of a hexarotor unmanned aerial vehicle (UAV) by using simultaneous perturbation stochastic approximation (i.e. SPSA), deep neural network and proportional integral derivative (i.e. PID) according to varying arm length (i.e. morphing).

Design/methodology/approach

In this paper, proper PID gain coefficients and morphing ratio were obtained using the stochastic optimization method, also known as SPSA to maximize flight efficiency. Because it is difficult to establish an analytical connection between the morphing ratio and hexarotor moments of inertia, the deep neural network was used to obtain the moments of inertia according to the morphing ratio. By using SPSA and deep neural network, the best performance indexes were obtained and both longitudinal and lateral flight simulations were performed with the obtained data.

Findings

With SPSA, the best PID coefficients and morphing ratio are obtained for both longitudinal and lateral flight. Because the hexarotor solid body model changes according to the morphing ratio, the moment of inertia values used in the simulations also change. According to the morphing ratio, the moment of inertia values was obtained with the deep neural network over a created data set.

Research limitations/implications

It takes a long time to obtain the morphing ratio suitable for the hexarotor model and the PID gain coefficients suitable for this morphing ratio. However, this situation can be overcome with the proposed SPSA. In addition, it takes a long time to obtain the appropriate moments of inertia according to the morphing ratio. However, in this case, it was overcome using the deep neural network.

Practical implications

Determining the morphing ratio and PID gain coefficients using the optimization method, as well as determining the moments of inertia using the deep neural network, is very useful as it can increase the efficiency of hexarotor flight and flight efficiently with different arm lengths. With the proposed method, the hexarotor design performance criteria (i.e. rise time, settling time and overshoot) values were significantly improved compared to similar studies.

Social implications

Determining the hexarotor flight parameters using SPSA and deep neural network provides advantages in terms of time, cost and applicability.

Originality/value

The hexarotor flight efficiency is improved with the proposed SPSA and deep neural network approaches. In addition, the desired flight parameters can be obtained more quickly and reliably with the proposed approaches. The design performance criteria were also improved, enabling the hexarotor UAV to follow the given trajectory in the best way and providing convenience for end users. SPSA was preferred because it converged faster than other methods. While other methods perform 2n operations per iteration, SPSA only performs two operations. To obtain the moment of inertia, many physical parameter values of the UAV are required in the existing methods. In the proposed method, by creating a date set, only arm length and moment of inertia were estimated without the need to obtain physical parameters with the deep neural network structure.

Details

Aircraft Engineering and Aerospace Technology, vol. 95 no. 6
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 29 September 2022

Fei Wang and Tat Leung Chan

The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population…

Abstract

Purpose

The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency.

Design/methodology/approach

In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme.

Findings

The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost.

Originality/value

The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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