Abstract: A sequence of finite tandem queue is considered for
this study. Each one has a single server, which operates under the
egalitarian processor sharing discipline. External customers arrive at
each queue according to a renewal input process and having a general
service times distribution. Upon completing service, customers leave
the current queue and enter to the next. Under mild assumptions,
including critical data, we prove the existence and the uniqueness
of the fluid solution. For asymptotic behavior, we provide necessary
and sufficient conditions for the invariant state and the convergence
to this invariant state. In the end, we establish the convergence of a
correctly normalized state process to a fluid limit characterized by a
system of algebraic and integral equations.
Abstract: Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.
Abstract: The method of moments combined with the method
of symmetrical components is used for the analysis of interstitial
hyperthermia applicators. The basis and testing functions are both
piecewise sinusoids, qualifying our technique as a Galerkin one. The
dielectric coatings are modeled by equivalent volume polarization
currents, which are simply related to the conduction current
distribution, avoiding in that way the introduction of additional
unknowns or numerical integrations. The results of our method
for a four dipole circular array, are in agreement with those
already published in literature for a same hyperthermia configuration.
Apart from being accurate, our approach is more general, more
computationally efficient and takes into account the coupling between
the antennas.
Abstract: A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.
Abstract: A mathematical model and an effective numerical method for calculating the temperature field of the profile part of convection cooled blades have been developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli.The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations.The reliability of the developed methods is confirmed by the calculation-experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of a gas turbine.
Abstract: A new mathematical model for calculating the temperature field of the profile part of the cooled blades of gas turbines is developed. The theoretical substantiation of the method is based on the application of the method of potential theory (the method of boundary integral equations). The effectiveness of the implementation of the developed mathematical model is confirmed on the basis of a computational experiment.
Abstract: In contrast to existing methods which do not take into account
multiconnectivity in a broad sense of this term, we develop
mathematical models and highly effective combination (BIEM
and FDM) numerical methods of calculation of stationary and
quasi-stationary temperature field of a profile part of a blade
with convective cooling (from the point of view of realization
on PC). The theoretical substantiation of these methods is
proved by appropriate theorems. For it, converging quadrature
processes have been developed and the estimations of errors in
the terms of A.Ziqmound continuity modules have been
received. For visualization of profiles are used: the method of the least
squares with automatic conjecture, device spline, smooth
replenishment and neural nets. Boundary conditions of heat
exchange are determined from the solution of the
corresponding integral equations and empirical relationships.
The reliability of designed methods is proved by calculation
and experimental investigations heat and hydraulic
characteristics of the gas turbine first stage nozzle blade.
Abstract: In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.
Abstract: This paper studies a mathematical model based on the
integral equations for dynamic analyzes numerical investigations of a
non-uniform or multi-material composite beam. The beam is
subjected to a sub-tangential follower force and elastic foundation.
The boundary conditions are represented by generalized
parameterized fixations by the linear and rotary springs. A
mathematical formula based on Euler-Bernoulli beam theory is
presented for beams with variable cross-sections. The non-uniform
section introduces non-uniformity in the rigidity and inertia of beams
and consequently, more complicated equilibrium who governs the
equation. Using the boundary element method and radial basis
functions, the equation of motion is reduced to an algebro-differential
system related to internal and boundary unknowns. A generalized
formula for the deflection, the slope, the moment and the shear force
are presented. The free vibration of non-uniform loaded beams is
formulated in a compact matrix form and all needed matrices are
explicitly given. The dynamic stability analysis of slender beam is
illustrated numerically based on the coalescence criterion. A realistic
case related to an industrial chimney is investigated.
Abstract: Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.
Abstract: In this paper, numerical solution of system of
Fredholm and Volterra integral equations by means of the Spline
collocation method is considered. This approximation reduces the
system of integral equations to an explicit system of algebraic
equations. The solution is collocated by cubic B-spline and the
integrand is approximated by the Newton-Cotes formula. The error
analysis of proposed numerical method is studied theoretically. The
results are compared with the results obtained by other methods to
illustrate the accuracy and the implementation of our method.
Abstract: In this paper, we have proposed a numerical method
for solving fuzzy Fredholm integral equation of the second kind. In
this method a combination of orthonormal Bernstein and Block-Pulse
functions are used. In most cases, the proposed method leads to
the exact solution. The advantages of this method are shown by an
example and calculate the error analysis.
Abstract: In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.
Abstract: This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.
Abstract: By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.
Abstract: In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.
Abstract: In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.
Abstract: In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade.
Abstract: in this paper, we propose a numerical method
for the approximate solution of fuzzy Fredholm functional
integral equations of the second kind by using an iterative
interpolation. For this purpose, we convert the linear fuzzy
Fredholm integral equations to a crisp linear system of integral
equations. The proposed method is illustrated by some fuzzy
integral equations in numerical examples.
Abstract: A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.