Abstract: In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Abstract: This work presents a numerical model developed to
simulate the dynamics and vibrations of a multistage tractor gearbox.
The effect of time varying mesh stiffness, time varying frictional
torque on the gear teeth, lateral and torsional flexibility of the shafts
and flexibility of the bearings were included in the model. The model
was developed by using the Lagrangian method, and it was applied to
study the effect of three design variables on the vibration and stress
levels on the gears. The first design variable, module, had little effect
on the vibration levels but a higher module resulted to higher bending
stress levels. The second design variable, pressure angle, had little
effect on the vibration levels, but had a strong effect on the stress
levels on the pinion of a high reduction ratio gear pair. A pressure
angle of 25o resulted to lower stress levels for a pinion with 14 teeth
than a pressure angle of 20o. The third design variable, contact ratio,
had a very strong effect on both the vibration levels and bending
stress levels. Increasing the contact ratio to 2.0 reduced both the
vibration levels and bending stress levels significantly. For the gear
train design used in this study, a module of 2.5 and contact ratio of
2.0 for the various meshes was found to yield the best combination
of low vibration levels and low bending stresses. The model can
therefore be used as a tool for obtaining the optimum gear design
parameters for a given multistage spur gear train.
Abstract: This paper mainly proposes an efficient modified
particle swarm optimization (MPSO) method, to identify a slidercrank
mechanism driven by a field-oriented PM synchronous motor.
In system identification, we adopt the MPSO method to find
parameters of the slider-crank mechanism. This new algorithm is
added with “distance" term in the traditional PSO-s fitness function to
avoid converging to a local optimum. It is found that the comparisons
of numerical simulations and experimental results prove that the
MPSO identification method for the slider-crank mechanism is
feasible.
Abstract: To achieve reliable solutions, today-s numerical and
experimental activities need developing more accurate methods and
utilizing expensive facilities, respectfully in microchannels. The analytical
study can be considered as an alternative approach to alleviate
the preceding difficulties. Among the analytical solutions, those with
high robustness and low complexities are certainly more attractive.
The perturbation theory has been used by many researchers to analyze
microflows. In present work, a compressible microflow with constant
heat flux boundary condition is analyzed. The flow is assumed to be
fully developed and steady. The Mach and Reynolds numbers are also
assumed to be very small. For this case, the creeping phenomenon
may have some effect on the velocity profile. To achieve robustness
solution it is assumed that the flow is quasi-isothermal. In this study,
the creeping term which appears in the slip boundary condition
is formulated by different mathematical formulas. The difference
between this work and the previous ones is that the creeping term
is taken into account and presented in non-dimensionalized form.
The results obtained from perturbation theory are presented based
on four non-dimensionalized parameters including the Reynolds,
Mach, Prandtl and Brinkman numbers. The axial velocity, normal
velocity and pressure profiles are obtained. Solutions for velocities
and pressure for two cases with different Br numbers are compared
with each other and the results show that the effect of creeping
phenomenon on the velocity profile becomes more important when
Br number is less than O(ε).
Abstract: New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.
Abstract: We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.
Abstract: The flow and heat transfer characteristics for natural
convection along an inclined plate in a saturated porous medium with
an applied magnetic field have been studied. The fluid viscosity has
been assumed to be an inverse function of temperature. Assuming
temperature vary as a power function of distance. The transformed
ordinary differential equations have solved by numerical integration
using Runge-Kutta method. The velocity and temperature profile
components on the plate are computed and discussed in detail for
various values of the variable viscosity parameter, inclination angle,
magnetic field parameter, and real constant (λ). The results have also
been interpreted with the aid of tables and graphs. The numerical
values of Nusselt number have been calculated for the mentioned
parameters.
Abstract: The hydrodynamic processes in bubbly liquid flowing
in tubes and nozzles are studied theoretically and numerically. The
principal regularities of non-stationary processes of boiling liquid
outflow are established under conditions of experiments when the
depressurization of a tube with high pressure inside occurs. The
steady-state solution of bubbly liquid flow in the nozzle of round
cross section with high pressure and temperature conditions inside
bubbles is studied accounting for phase transition and chemical
reactions.
Abstract: In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.
Abstract: The present work describes a computational study of
aerodynamic characteristics of GLC305 airfoil clean and with 16.7
min ice shape (rime 212) and 22.5 min ice shape (glaze 944).The
performance of turbulence models SA, Kε, Kω Std, and Kω SST
model are observed against experimental flow fields at different
Mach numbers 0.12, 0.21, 0.28 in a range of Reynolds numbers
3x106, 6x106, and 10.5x106 on clean and iced aircraft airfoil
GLC305. Numerical predictions include lift, drag and pitching
moment coefficients at different Mach numbers and at different angle
of attacks were done. Accuracy of solutions with respect to the
effects of turbulence models, variation of Mach number, initial
conditions, grid resolution and grid spacing near the wall made the
study much sensitive. Navier Stokes equation based computational
technique is used. Results are very close to the experimental results.
It has seen that SA and SST models are more efficient than Kε and
Kω standard in under study problem.
Abstract: The paper addresses a problem of optimal staffing in
open shop environment. The problem is to determine the optimal
number of operators serving a given number of machines to fulfill the
number of independent operations while minimizing staff idle. Using
a Gantt chart presentation of the problem it is modeled as twodimensional
cutting stock problem. A mixed-integer programming
model is used to get minimal job processing time (makespan) for
fixed number of machines' operators. An algorithm for optimal openshop
staffing is developed based on iterative solving of the
formulated optimization task. The execution of the developed
algorithm provides optimal number of machines' operators in the
sense of minimum staff idle and optimal makespan for that number of
operators. The proposed algorithm is tested numerically for a real life
staffing problem. The testing results show the practical applicability
for similar open shop staffing problems.
Abstract: Clustering is one of an interesting data mining topics
that can be applied in many fields. Recently, the problem of cluster
analysis is formulated as a problem of nonsmooth, nonconvex optimization,
and an algorithm for solving the cluster analysis problem
based on nonsmooth optimization techniques is developed. This
optimization problem has a number of characteristics that make it
challenging: it has many local minimum, the optimization variables
can be either continuous or categorical, and there are no exact
analytical derivatives. In this study we show how to apply a particular
class of optimization methods known as pattern search methods
to address these challenges. These methods do not explicitly use
derivatives, an important feature that has not been addressed in
previous studies. Results of numerical experiments are presented
which demonstrate the effectiveness of the proposed method.
Abstract: Capacity and efficiency of any refrigerating system
diminish rapidly as the difference between the evaporating and
condensing temperature is increased by reduction in the evaporator
temperature. The single stage vapour compression refrigeration
system is limited to an evaporator temperature of -40 0C. Below
temperature of -40 0C the either cascade refrigeration system or multi
stage vapour compression system is employed. Present work
describes thermal design of main three heat exchangers namely
condenser (HTS), cascade condenser and evaporator (LTS) of
R404A-R508B and R410A-R23 cascade refrigeration system. Heat
transfer area of condenser (HTS), cascade condenser and evaporator
(LTS) for both systems have been compared and the effect of
condensing and evaporating temperature on heat-transfer area for
both systems have been studied under same operating condition. The
results shows that the required heat-transfer area of condenser and
cascade condenser for R410A-R23 cascade system is lower than the
R404A-R508B cascade system but heat transfer area of evaporator is
similar for both the system. The heat transfer area of condenser and
cascade condenser decreases with increase in condensing temperature
(Tc), whereas the heat transfer area of cascade condenser and
evaporator increases with increase in evaporating temperature (Te).
Abstract: The methodology of numerical simulation and calculation of aerodynamic characteristics of aircraft taking into account impact of wake on it has been developed. The results of numerical experiment in comparison with the data obtained in the wind tunnel are presented. Efficiency of methodology of calculation and the reliability of the results is shown.
Abstract: Categorical data based on description of the
agricultural landscape imposed some mathematical and analytical
limitations. This problem however can be overcome by data
transformation through coding scheme and the use of non-parametric
multivariate approach. The present study describes data
transformation from qualitative to numerical descriptors. In a
collection of 103 random soil samples over a 60 hectare field,
categorical data were obtained from the following variables: levels of
nitrogen, phosphorus, potassium, pH, hue, chroma, value and data on
topography, vegetation type, and the presence of rocks. Categorical
data were coded, and Spearman-s rho correlation was then calculated
using PAST software ver. 1.78 in which Principal Component
Analysis was based. Results revealed successful data transformation,
generating 1030 quantitative descriptors. Visualization based on the
new set of descriptors showed clear differences among sites, and
amount of variation was successfully measured. Possible applications
of data transformation are discussed.
Abstract: Transient Stability is an important issue in power systems planning, operation and extension. The objective of transient stability analysis problem is not satisfied with mere transient instability detection or evaluation and it is most important to complement it by defining fast and efficient control measures in order to ensure system security. This paper presents a new Fuzzy Support Vector Machines (FSVM) to investigate the stability status of power systems and a modified generation rescheduling scheme to bring back the identified unstable cases to a more economical and stable operating point. FSVM improves the traditional SVM (Support Vector Machines) by adding fuzzy membership to each training sample to indicate the degree of membership of this sample to different classes. The preventive control based on economic generator rescheduling avoids the instability of the power systems with minimum change in operating cost under disturbed conditions. Numerical results on the New England 39 bus test system show the effectiveness of the proposed method.
Abstract: Supply chain consists of all stages involved, directly
or indirectly, includes all functions involved in fulfilling a customer
demand. In two stage transportation supply chain problem,
transportation costs are of a significant proportion of final product
costs. It is often crucial for successful decisions making approaches
in two stage supply chain to explicit account for non-linear
transportation costs. In this paper, deterministic demand and finite
supply of products was considered. The optimized distribution level
and the routing structure from the manufacturing plants to the
distribution centres and to the end customers is determined using
developed mathematical model and solved by proposed particle
swarm optimization based genetic algorithm. Numerical analysis of
the case study is carried out to validate the model.
Abstract: The rheological properties of light crude oil and its mixture with water were investigated experimentally. These rheological properties include steady flow behavior, yield stress, transient flow behavior, and viscoelastic behavior. A RheoStress RS600 rheometer was employed in all of the rheological examination tests. The light crude oil exhibits a Newtonian and for emulsion exhibits a non-Newtonian shear thinning behavior over the examined shear rate range of 0.1–120 s-1. In first time, a series of samples of crude oil from the Algerian Sahara has been tested and the results expressed in terms of τ=f(γ) have demonstrated their Newtonian character for the temperature included in [20°C, 70°C]. In second time and at T=20°C, the oil-water emulsions (30%, 50% and 70%) by volume of water), thermodynamically stable, have demonstrated a non-Newtonian rheological behavior that is to say, Herschel-Bulkley and Bingham types. For each type of crude oil-water emulsion, the rheological parameters are calculated by numerical treatment of results.
Abstract: Two-dimensional finite element model was created in this work to investigate the stresses distribution within rock-like samples with offset open non-persistent joints under biaxial loading. The results of this study have explained the fracture mechanisms observed in tests on rock-like material with open non-persistent offset joints [1]. Finite element code SAP2000 was used to study the stresses distribution within the specimens. Four-nodded isoperimetric plain strain element with two degree of freedom per node, and the three-nodded constant strain triangular element with two degree of freedom per node were used in the present study.The results of the present study explained the formation of wing cracks at the tip of the joints for low confining stress as well as the formation of wing cracks at the middle of the joint for the higher confining stress. High shear stresses found in the numerical study at the tip of the joints explained the formation of secondary cracks at the tip of the joints in the experimental study. The study results coincide with the experimental observations which showed that for bridge inclination of 0o, the coalescence occurred due to shear failure and for bridge inclination of 90o the coalescence occurred due to tensile failure while for the other bridge inclinations coalescence occurred due to mixed tensile and shear failure.
Abstract: In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.