Search results for: closed form solution.

Authors: Danesh Nourzadeh, Sepideh Khorshid, Shiro Takada, Khosrow Bargi

Abstract:

In this paper, transversal vibration of buried pipelines during loading induced by underground explosions is analyzed. The pipeline is modeled as an infinite beam on an elastic foundation, so that soil-structure interaction is considered by means of transverse linear springs along the pipeline. The pipeline behavior is assumed to be ideal elasto-plastic which an ultimate strain value limits the plastic behavior. The blast loading is considered as a point load, considering the affected length at some point of the pipeline, in which the magnitude decreases exponentially with time. A closed-form solution for the quasi-static problem is carried out for both elastic and elasticperfect plastic behaviors of pipe materials. At the end, a comparative study on steel and polyethylene pipes with different sizes buried in various soil conditions, affected by a predefined underground explosion is conducted, in which effect of each parameter is discussed.

Keywords: Beam on elastic foundation, Buried pipelines, External explosion, Non-linear quasi-static solution.

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Authors: Gorazd Karer

Abstract:

When performing a diagnostic procedure or surgery in general anesthesia (GA), a proper introduction and dosing of anesthetic agents is one of the main tasks of the anesthesiologist. That being said, depth of anesthesia (DoA) also seems to be a suitable process for closed-loop control implementation. To implement such a system, one must be able to acquire the relevant signals online and in real-time, as well as stream the calculated control signal to the infusion pump. However, during a procedure, patient monitors and infusion pumps are purposely unable to connect to an external (possibly medically unapproved) device for safety reasons, thus preventing closed-loop control. This paper proposes a conceptual solution to the aforementioned problem. First, it presents some important aspects of contemporary clinical practice. Next, it introduces the closed-loop-control-system structure and the relevant information flow. Focusing on transferring the data from the patient to the computer, it presents a non-invasive image-based system for signal acquisition from a patient monitor for online depth-of-anesthesia assessment. Furthermore, it introduces a User-Datagram-Protocol-based (UDP-based) communication method that can be used for transmitting the calculated anesthetic inflow to the infusion pump. The proposed system is independent of medical-device manufacturer and is implemented in MATLAB-Simulink, which can be conveniently used for DoA control implementation. The proposed scheme has been tested in a simulated GA setting and is ready to be evaluated in an operating theatre. However, the proposed system is only a step towards a proper closed-loop control system for DoA, which could routinely be used in clinical practice.

Keywords: Closed-loop control, Depth of Anesthesia, DoA, optical signal acquisition, Patient State index, PSi, UDP communication protocol.

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

Abstract:

A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: Analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction.

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Authors: M. Chumburidze, D. Lekveishvili

Abstract:

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: The couple-stress thermo-elasticity, boundary value problems.

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Authors: M. Karami Khorramabadi, P. Khazaeinejad

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The static stability analysis of stiffened functionally graded cylindrical shells by isotropic rings and stringers subjected to axial compression is presented in this paper. The Young's modulus of the shell is taken to be function of the thickness coordinate. The fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical axial loads. The effects of material properties, geometric size and different material coefficient on the critical axial loads are examined. The analytical results are compared and validated using the finite element model.

Keywords: Functionally graded material, Stability, Stiffened cylindrical shell, Finite element analysis

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Authors: Arnaud Nougues

Abstract:

This paper describes a two-stage methodology derived from IMC (Internal Model Control) for tuning a PID (Proportional-Integral-Derivative) controller for levels or other integrating processes in an industrial environment. Focus is ease of use and implementation speed which are critical for an industrial application. Tuning can be done with minimum effort and without the need of time-consuming open-loop step tests on the plant. The first stage of the method applies to levels only: the vessel residence time is calculated from equipment dimensions and used to derive a set of preliminary PI (Proportional-Integral) settings with IMC. The second stage, re-tuning in closed-loop, applies to levels as well as other integrating processes: a tuning correction mechanism has been developed based on a series of closed-loop simulations with model errors. The tuning correction is done from a simple closed-loop step test and application of a generic correlation between observed overshoot and integral time correction. A spin-off of the method is that an estimate of the vessel residence time (levels) or open-loop process gain (other integrating process) is obtained from the closed-loop data.

Keywords: closed-loop model identification, IMC-PID tuning method, integrating process control, on-line PID tuning adaptation

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Authors: Anat Thapinta

Abstract:

This research aimed to study on the efficiency of wastewater treatment by comparing the different aeration times of surface aerators in Suan Sunandha Rajabhat University. In doing so, the operation of surface aerators was divided into 2 groups which included the groups of 8 hours (8-0/opened-closed) and 4 hours (2-2/opened-closed) of aeration time per day. As a result of the study, it was found that the efficiency of wastewater treatment in the forms of DO, BOD, turbidity and NO₂^- by 8 hours (8-0/opened-closed) and 4 hours (2-2/opened-closed) of aeration time per day of surface aerators was not statistically different [Sig. = .644, .488, .716 and .054 > α (.05)] while the efficiency in the forms of NO₃^- and P was significantly different at the statistical level of .01 [Sig. = .001 and .000 < α (.01)].

Keywords: Aeration time, Surface aerator, Wastewater treatment.

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Authors: Reza Abazari, Rasool Abazari

Abstract:

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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Authors: Fares Senouci, Bachir Imine

Abstract:

This document provides numerical and experimental optimization of the aerodynamic performance of a drone equipped with three types of horizontal stabilizer. To build this optimal configuration, an experimental and numerical study was conducted on three parameters: the geometry of the stabilizer (horizontal form or reverse V form), the position of the horizontal stabilizer (up or down), and the landing gear position (closed or open). The results show that up-stabilizer position with respect to the horizontal plane of the fuselage provides better aerodynamic performance, and that the landing gear increases the lift in the zone of stability, that is to say where the flow is not separated.

Keywords: Aerodynamics, wind tunnel, turbulence model, lift, drag.

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

Abstract:

The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: Control, limits cycle, robot, stability.

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Authors: Ahmed Hossam_ ElDin, Ahmed Farag, Ibrahim Madi., Hanaa Karawia

Abstract:

In our modern society electricity is vital to our health, safety, comfort and well-being. While our daily use of electricity is often taken for granted, public concern has arisen about potential adverse health effects from electric and magnetic – electromagnetic – fields (EMFs) produced by our use of electricity. This paper aims to compare between the measured magnetic field values and the simulated models for the indoor medium to low voltage (MV/LV) distribution substations. To calculate the magnetic flux density in the substations, interactive software SUBCALC is used which is based on closed form solution of the Biot-Savart law with 3D conductor model. The comparison between the measured values and the simulated models was acceptable. However there were some discrepancies, as expected, may be due to the current variation during measurements.

Keywords: Distribution substation, magnetic field, measurement, simulation.

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Authors: U. Schmidt, D. Dannehl, I. Schuch, J. Suhl, T. Rocksch, R. Salazar-Moreno, E. Fitz-Rodrigues, A. Rojano Aquilar, I. Lopez Cruz, G. Navas Gomez, R. A. Abraham, L. C. Irineo, N. G. Gilberto

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The integration of agricultural production systems into urban areas is a challenge for the coming decades. Because of increasing greenhouse gas emission and rising resource consumption as well as costs in animal husbandry, the dietary habits of people in the 21st century have to focus on herbal foods. Intensive plant cultivation systems in large cities and megacities require a smart coupling of information, material and energy flow with the urban infrastructure in terms of Horticulture 4.0. In recent years, many puzzle pieces have been developed for these closed processes at the Humboldt University. To compile these for an urban plant production, it has to be optimized and networked with urban infrastructure systems. In the field of heat energy production, it was shown that with closed greenhouse technology and patented heat exchange and storage technology energy can be provided for heating and domestic hot water supply in the city. Closed water circuits can be drastically reducing the water requirements of plant production in urban areas. Ion sensitive sensors and new disinfection methods can help keep circulating nutrient solutions in the system for a longer time in urban plant production greenhouses.

Keywords: Semi closed, greenhouses, urban farming, solar heat collector, closed water cycles, aquaponics.

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Authors: Niti Kammuang-lue, Kritsada On-ai, Phrut Sakulchangsatjatai, Pradit Terdtoon

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The objectives of this paper are to investigate effects of dimensionless numbers on thermal performance of the vertical closed-loop pulsating heat pipe (VCLPHP) and to establish a correlation to predict the thermal performance of the VCLPHP. The CLPHPs were made of long copper capillary tubes with inner diameters of 1.50, 1.78, and 2.16mm and bent into 26 turns. Then, both ends were connected together to form a loop. The evaporator, adiabatic, and condenser sections length were equal to 50 and 150 mm. R123, R141b, acetone, ethanol, and water were chosen as variable working fluids with constant filling ratio of 50% by total volume. Inlet temperature of heating medium and adiabatic section temperature was constantly controlled at 80 and 50^oC, respectively. Thermal performance was represented in a term of Kutateladze number (Ku). It can be concluded that when Prandtl number of liquid working fluid (Pr_l), and Karman number (Ka) increases, thermal performance increases. On contrary, when Bond number (Bo), Jacob number (Ja), and Aspect ratio (L_e/D_i) increases, thermal performance decreases. Moreover, the correlation to predict more precise thermal performance has been successfully established by analyzing on all dimensionless numbers that have effect on the thermal performance of the VCLPHP.

Keywords: Vertical closed-loop pulsating heat pipe, working fluid, thermal performance, dimensionless parameter.

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Authors: R. Parimelazhagan, N. Nagaveni

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In this paper we introduce a new class of mg-continuous mapping and studied some of its basic properties.We obtain some characterizations of such functions. Moreover we define sub minimal structure and further study certain properties of mg-closed sets.

Keywords: M-structure, mg-continuous mapping, minimal structure, mg T2 space, sub minimal structure, T12 space, mg-compact set.

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Authors: Kang-Le Guan, Seung-Jae Lee, Myeon-Song Choi

Abstract:

The protection issues in distribution systems with open and closed-loop are studied, and a generalized protection setting scheme based on the traditional over current protection theories is proposed to meet the new requirements. The setting method is expected to be easier realized using computer program, so that the on-line adaptive setting for coordination in distribution system can be implemented. An automatic setting program is created and several cases are taken into practice. The setting results are verified by the coordination curves of the protective devices which are plotted using MATLAB.

Keywords: protection setting, on-line system analysis, over current protection, closed-loop distribution system

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Authors: Wen Po Cheng, Chi Hua Fu, Ping Hung Chen, Ruey Fang Yu

Abstract:

Aluminum salt that is generally presents as a solid phase in the water purification sludge (WPS) can be dissolved, recovering a liquid phase, by adding strong acid to the sludge solution. According to the reaction kinetics, when reactant is in the form of small particles with a large specific surface area, or when the reaction temperature is high, the quantity of dissolved aluminum salt or reaction rate, respectively are high. Therefore, in this investigation, water purification sludge (WPS) solution was treated with ultrasonic waves to break down the sludge, and different acids (1 N HCl and 1 N H2SO4) were used to acidify it. Acid dosages that yielded the solution pH of less than two were used. The results thus obtained indicate that the quantity of dissolved aluminum in H2SO4-acidified solution exceeded that in HCl-acidified solution. Additionally, ultrasonic treatment increased the rate of dissolution of aluminum and the amount dissolved. The quantity of aluminum dissolved at 60℃ was 1.5 to 2.0 times higher than that at 25℃.

Keywords: Coagulant, Aluminum, Ultrasonic, Acidification, Temperature, Sludge.

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Authors: Jochen Edmund Kerschenbauer, Roman Salinger, Daniel Strametz

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Insufficient informal communication systems can lead to the first crisis (‘Crisis of Leadership’) for start-ups. Management Control Systems (MCS) are one way for high-technology start-ups to successfully overcome these problems. So far the literature has investigated the incubation of a start-up, but focused less on the post-incubation stage. This paper focuses on the use of MCS in post-incubation and, if failed start-ups agree, on how MCS are used. We conducted 14 semi-structured interviews for this purpose, to obtain our results. The overall conclusion is that the majority of the companies were closed down due to a combination of strategic, operative and financial reasons.

Keywords: Closed down, high-technology, incubation, Levers of Control, management control systems, post-incubation, start-ups.

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Authors: Ionel Stanculeanu, Theodor Borangiu

Abstract:

This paper presents a new approach in the identification of the quadrotor dynamic model using a black-box system for identification. Also the paper considers the problems which appear during the identification in the closed-loop and offers a technical solution for overcoming the correlation between the input noise present in the output

Keywords: System identification, UAV, prediction error method, quadrotor.

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Authors: Andras Szekrenyes

Abstract:

This work presents the mixed-mode II/III prestressed split-cantilever beam specimen for the fracture testing of composite materials. In accordance with the concept of prestressed composite beams one of the two fracture modes is provided by the prestressed state of the specimen, and the other one is increased up to fracture initiation by using a testing machine. The novel beam-like specimen is able to provide any combination of the mode-II and mode-III energy release rates. A simple closed-form solution is developed using beam theory as a data reduction scheme and for the calculation of the energy release rates in the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode beam specimen can be used to obtain the fracture criterion of transparent composite materials in the GII - GIII plane in a relatively simple way.

Keywords: Composite, fracture mechanics, toughness testing, mixed-mode II/III fracture.

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Authors: Yuan-Jye Tseng, Yi-Shiuan Chen

Abstract:

In this paper, a new concept of closed-loop design for a product is presented. The closed-loop design model is developed by integrating forward design and reverse design. Based on this new concept, a closed-loop design model for sustainable manufacturing by integrated evaluation of forward design, reverse design, and green manufacturing using a fuzzy analytic network process is developed. In the design stage of a product, with a given product requirement and objective, there can be different ways to design the detailed components and specifications. Therefore, there can be different design cases to achieve the same product requirement and objective. Subsequently, in the design evaluation stage, it is required to analyze and evaluate the different design cases. The purpose of this research is to develop a model for evaluating the design cases by integrated evaluating the criteria in forward design, reverse design, and green manufacturing. A fuzzy analytic network process method is presented for integrated evaluation of the criteria in the three models. The comparison matrices for evaluating the criteria in the three groups are established. The total relational values among the three groups represent the total relational effects. In applications, a super matrix model is created and the total relational values can be used to evaluate the design cases for decision-making to select the final design case. An example product is demonstrated in this presentation. It shows that the model is useful for integrated evaluation of forward design, reverse design, and green manufacturing to achieve a closed-loop design for sustainable manufacturing objective.

Keywords: Design evaluation, forward design, reverse design, closed-loop design, supply chain management, closed-loop supply chain, fuzzy analytic network process.

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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Authors: D. B. Gohil

Abstract:

Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: Experimentation, forging, process modeling, strain distribution.

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Authors: George Yungchih Wang

Abstract:

This paper argues that increased uncertainty, in certain situations, may actually encourage investment. Since earlier studies mostly base their arguments on the assumption of geometric Brownian motion, the study extends the assumption to alternative stochastic processes, such as mixed diffusion-jump, mean-reverting process, and jump amplitude process. A general approach of Monte Carlo simulation is developed to derive optimal investment trigger for the situation that the closed-form solution could not be readily obtained under the assumption of alternative process. The main finding is that the overall effect of uncertainty on investment is interpreted by the probability of investing, and the relationship appears to be an invested U-shaped curve between uncertainty and investment. The implication is that uncertainty does not always discourage investment even under several sources of uncertainty. Furthermore, high-risk projects are not always dominated by low-risk projects because the high-risk projects may have a positive realization effect on encouraging investment.

Keywords: real options, geometric Brownian motion, mixeddiffusion-jump process, mean- reverting process, jump amplitudeprocess

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Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVP­s­) in ordinary differential equations (ODE­s­) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, First Order Ordinary Differential Equations, Hybrid, Self starting.

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Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

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Authors: A. Kurşun, M. Tunay Çetin, E. Çetin, H. Aykul

Abstract:

In this investigation an elastic stress analysis is carried out a woven steel fiber reinforced thermoplastic cantilever beam loaded uniformly at the upper surface. The composite beam material consists of low density polyethylene as a thermoplastic (LDFE, f.2.12) and woven steel fibers. Granules of the polyethylene are put into the moulds and they are heated up to 160°C by using electrical resistance. Subsequently, the material is held for 5min under 2.5 MPa at this temperature. The temperature is decreased to 30°C under 15 MPa pressure in 3min. Closed form solution is found satisfying both the governing differential equation and boundary conditions. We investigated orientation angle effect on stress distribution of composite cantilever beams. The results show that orientation angle play an important role in determining the responses of a woven steel fiber reinforced thermoplastic cantilever beams and an optimal design of these structures.

Keywords: Cantilever beam, elastic stress analysis, orientation angle, thermoplastic.

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Authors: O.M. Mohamed vall, M. Radhi

Abstract:

This work presents a recursive identification algorithm. This algorithm relates to the identification of closed loop system with Variable Structure Controller. The approach suggested includes two stages. In the first stage a genetic algorithm is used to obtain the parameters of switching function which gives a control signal rich in commutations (i.e. a control signal whose spectral characteristics are closest possible to those of a white noise signal). The second stage consists in the identification of the system parameters by the instrumental variable method and using the optimal switching function parameters obtained with the genetic algorithm. In order to test the validity of this algorithm a simulation example is presented.

Keywords: Closed loop identification, variable structure controller, pseud-random binary sequence, genetic algorithms.

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Authors: Abdu Masanawa Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: B. Chetti, W. A. Crosby

Abstract:

The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: Two-lobe bearing, thermal effect, static and dynamic characteristics.

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Authors: Yuan-Jye Tseng, Yi-Shiuan Chen

Abstract:

The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.

Keywords: Closed-loop design, closed-loop supply chain, design evaluation, mathematical model, supply chain management, sustainable design model.

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