Coşkun Güler

Dynamical (harmonic) interface stress field in the half-plane covered by the prestretched layer under a strip load

Within the framework of the piecewise homogeneous body model, by employing the three-dimensional linearized theory of elastic waves in initially stressed bodies the dynamical problem of the stress distribution in a half-plane covered with a prestretched layer is investigated. It is assumed that the free face plane of the covered layer is subjected to a uniformly distributed harmonic load acting on a strip extending to infinity in the x3 direction, which is perpendicular to the x1-x2 plane and is of width 2a in the x1 direction. The plane-strain state in the x1-x2 plane is analysed. The corresponding boundary-value problems are investigated by employing the exponential Fourier integral transformation. The numerical results regarding the interface normal stress distribution are presented. The influences of the problem parameters and pre-stretching of the covered layer on this distribution are analysed. Practical engineering application fields of the results are suggested.

Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments

Laguerre collocation method is applied for solving a class of the Fredholm integro-differential equations with functional arguments. This method transforms the considered problem to a matrix equation which corresponds to a system of linear algebraic equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. Also, the approximate solutions are corrected by using the residual correction method.

Dynamic (Harmonic) Interfacial Stress Field in a Half-Plane Covered with a Prestretched Soft Layer

A half-plane covered with a prestretched layer is considered under the action of a periodic dynamic (harmonic) lineal load applied to the free surface of the layer. Within the framework of a piecewise homegeneous body model, with the use of equations of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the problem of stress state is formulated. It is assumed that the materials of the layer and half-plane are linearly elastic, homogeneous, and isotropic, and a plane strain state is considered. The corresponding boundary-value problems are solved analyticaly by employing the exponential Fourier transformations. Numerical results are obtained in the case where the elastic modulus of the half-plane material is greater than that of the layer material. It is established that, because of softening of the layer material, the stresses on the interplane increase mainly in the vicinity of the acting force and this increase has a local character. Moreover, it is established that the prestretching of the cover layer decreases the absolute values of these stresses.

A solution proposal to the transportation problem with the linear fractional objective function

This paper deals with the transportation problem of minimizing the ratio of two linear functions subject to a set of linear equations and non-negativity conditions on the variables (or constraints of the classical transportation problem). In this paper, we extend the transportation problem with the linear objective function to the transportation problem with the linear fractional objective function and we propose a new algorithm in order to obtain an initial solution for this problem which is similar to Vogel approximation method in the classical transportation problem and then we construct the optimality conditions for the transportation problem with the linear fractional objective functions.[5]

A new numerical algorithm for the Abel equation of the second kind

An algorithm based on the Taylor matrix method is proposed and applied to the non-linear Abel equation of the second kind. A Padé approximation of the problem is also obtained. The results are compared and tabulated.An algorithm based on the Taylor matrix method is proposed and applied to the non-linear Abel equation of the second kind. A Pade approximation of the problem is also obtained. The results are compared and tabulated.

The fractional transportation problem with interval demand, supply and costs

The data of real world applications generally cannot be expressed strictly. An efficient way of handling this situation is expressing the data as intervals. Thus this paper focuses on the Interval Fractional Transportation Problem (IFTP) in which all the parameters i.e. cost and preference coefficients of the objective function, supply and demand quantities are expressed as intervals. A Taylor series approach is presented for IFTP by means of the expression of intervals with its left and right limits. Also a numerical example is executed for the linear case to illustrate the procedure.

Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation

An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations (ODEs) to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written in Maple and Matlab.

Bernstein Collocation Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations in the Most General Form

A collocation method based on the Bernstein polynomials defined on the interval is developed for approximate solutions of the Fredholm-Volterra integrodifferential equation (FVIDE) in the most general form. This method is reduced to linear FVIDE via the collocation points and quasilinearization technique. Some numerical examples are also given to demonstrate the applicability, accuracy, and efficiency of the proposed method.

A Numerical Approach Based on Taylor Polynomials for Solving a Class of Nonlinear Differential Equations

In this study, a matrix method based on Taylor polynomials and collocation points is presented for the approximate solution of a class of nonlinear differential equations, which have many applications in mathematics, physics and engineering. By means of matrix forms of the Taylor polynomials and their derivatives, the technique we have used reduces the solution of the nonlinear equation with mixed conditions to the solution of a matrix equation which corresponds to a system of nonlinear algebraic equations with the unknown Taylor coefficients. On the other hand, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing results in literature.