Math. Comput. Appl., Volume 11, Issue 1 (April 2006) – 10 articles , Pages 1-90

A perturbation method, the Lindstedt-Poincare method, is used to obtain the asymptotic expansions of the solutions of a nonlinear differential equation arising in general relativity. The asymptotic solutions contain no secular term, which overcomes a defect in Khuri’s paper. A technique of numerical order verification is applied to demonstrate that the asymptotic solutions are uniformly valid for small parameter. Full article

This paper examines an economic production quantity (EPQ) model with rework and service level constraint. First, we prove that the expected overall costs for an imperfect EPQ model with backlogging permitted is less than or equal to that of the one without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whether the required service level is achievable. Then an equation for calculating the intangible backorder cost is proposed for situation when the required service level is not attainable. By including this intangible backorder cost in mathematical analysis, one can derive a new optimal lot-size policy that minimizes expected total costs as well as satisfies the maximal shortage level constraint for the EPQ model with rework. Numerical example is provided to demonstrate its practical usage. Full article

An infinitely wide lubricated slider bearing consisting of connected surfaces with thirtd grade fluid as lubricant is analyzed in the present study. Under the assumptions of the order of magnitudes of the variables, it is seen that only viscous and non-Newtonian terms have significant contributions, whereas inertia terms are negligible. Choosing non-Newtonian effects to be smaller than the viscous effects, analytical and numerical solutions are constructed. To illustrate the mathematical model, the set of equations is to used calculate the pressure for two special forms of the slider bearings, namely inclined and parabolic slider bearings. In these two cases, the variation of pressure, for a range of fluid and bearing parameters is presented. The results are presented both analytically and graphically. Full article

Determination of The Steady State Response of EFEF / VFVF Supported Rectangular Specially Orthotropic Plates is presented. EFEF and VFVF plates, these are rectangular plates with two opposite edges elastically or viscoelastically supported and remaining others free. Using the energy based finite difference method; the problem is modeled by a kind of finite difference element. Due to the significance of the fundamental frequency of the plate, its variation was investigated with respect to mechanical properties of plate material and translational spring coefficient of supports. The steady state response of viscoelastically supported plates was also investigated numerically for various damping coefficients. In the numerical examples, the natural frequency parameters and steady state responses to a sinusoidally varying force are assessed for the fundamental mode. Convergence studies are made. Many new results have been presented. Considered problems are solved within the frame work of Kirchhoff-Love hypothesis. Full article

In this study, time dependence of large-scale nuclear shell model calculations in a parallel cluster is investigated. Shell model calculations have been done for the light Sb isotopes by using serial and parallel versions of Drexel University Shell Model (DUSM) code and the time dependence of these calculations are obtained on the local Cyborg Parallel Cluster at Drexel University. Some analyses about what kind of parallel system we need to do the calculations have been done in order to do the nuclear shell model calculations for the other nuclei. Full article

The aim of this study was to investigate elasto-plastic thermal stresses in a thermoplastic composite disc that is reinforced by steel fibers, curvilinearly. Finite element method (FEM) was used to calculate the thermal stress distribution in the model of composite disc. The solution was performed by ANSYS software code. In order to evaluate the effects of uniform temperature, different values of it were carried out on the model of composite disc, uniformly. Radial and tangential stresses were calculated under a uniform temperature distribution which was selected from 60 C to 120 C. Because of the composite disc having different thermal expansions in radial and tangential directions, thermal stresses were produced in it by the applied uniform temperature values. The magnitude of the tangential stress component for elastic and elasto-plastic solutions was higher than the radial stress component. The radial stress components were obtained as compressive on the inner and outer surfaces. Besides the tangential stress components were calculated as compressive and tensile on the inner and outer surfaces, respectively. The absolute values of it were the highest on the inner surface both radial and tangential directions. The residual stress components also were calculated using elastic and elasto-plastic solution results. The obtained results showed that the positions of the improved thermal stresses and residual stresses were considerably affected increasing uniform temperature value. Full article

A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Scaling transformation is applied to the equations to determine the specific forms of these functions for which the equation admits such type of transformation. It is found that for arbitrary heat conduction function, scaling transformation exists for an inverse square heat transfer coefficient. Selecting also the conductivity as an exponential function, the partial differential equation is transferred to an ordinary differential equation via similarity transformations. The resulting equation is solved numerically and temperature distribution is determined for various heat conductivity parameters. Full article

In this study, a dual minimal curves of a dual unit sphere, and the minimal ruled surfaces corresponding it are defined, and represented that dual unit tangent, binormal and surface normal vectors, related to these, are dual isotropic lines. E.Study theorem is also given, for dual minimal curves, belonging to minimal curves and we give general solution of differential equation of this curves. Full article

The properties of a special function which is defined by an integral is presented. The numerical values of this function are tabulated correct to twenty decimal places. The curves of this function and its complementary are plotted. Some properties of this function are investigated. Full article

In this study, the in plane vibrations of cracked circular curved beams is investigated. The beam is an Euler-Bernoulli beam. Only bending and extension effects are included. The curvature is in a single plane. In plane vibrations is analyzed using FEM. In the analysis, elongation, bending and rotary inertia effects are included. Four degrees of freedom for in-plane vibrations is assumed. Natural frequencies of the beam with a crack in different locations and depths are calculated using FEM. Comparisons are made for different angles. Full article