Math. Comput. Appl., Volume 16, Issue 3 (December 2011) – 23 articles , Pages 556-783

In this study, free vibration of an Euler-Bernoulli beam resting on a variable Winkler foundation is considered. Structures which are supported along their length such as beams or pipelines resting on elastic soil are very commonly modeled with a Winkler foundation. In this problem, the elastic coefficient of the foundation is variable along the beam major axis. Constant, linear and parabolic variations are considered. The problem is handled for three different boundary conditions: simply supported-simply supported, clamped-clamped and cantilever (clamped-free) beams. The governing differential equations of the beam are solved by using Differential Transform Method (DTM). DTM is an easy transformation technique based on Taylor expansion series, providing high accuracy. Full article

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is based on the differential transform method (DTM), Laplace transform and Padé approximants. The results to get the differential transformation method (DTM) are applied Padé approximants. The reliability of this method is investigated by comparison with the classical fourth-order Runge–Kutta (RK4) method and Cos-AT and Sine-AT method. Our the presented method showed results to analytical solutions of nonlinear ordinary differential equation. Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods. Full article

This paper investigates optimal replenishment lot size and optimal number of shipments for economic production quantity (EPQ) model with rework process using an algebraic approach. The classic EPQ model assumes a perfect quality production for all items produced and a continuous issuing policy for satisfying customer‟s demand. However, in a real life vendor-buyer integrated-production-inventory system, a multi- delivery policy is commonly used in lieu of a continuous issuing policy and generation of defective items during a production run seems to be inevitable. A recent published work examined such an identical problem using mathematical modeling and differential calculus to derive the optimal replenishment lot size and optimal number of deliveries that minimizes overall production-inventory-shipment costs. This paper proposes a straightforward algebraic approach to replace the use of calculus on the cost function for determining optimal production-shipment policies. It also presents a simpler form for calculating the long-run average cost for such an imperfect EPQ problem. Full article

The scattering process of waves by a wedge with phase conjugate faces is investigated with the aid of the modified diffraction theory of Kirchhoff. The scattering integral is evaluated asymptotically. The uniform diffracted waves and geometrical optics fields are plotted and examined numerically. Full article

A direct full-wave solution via the Analytical Regularization Method (ARM) is proposed for the diffraction problem concerning knife edges under TM wave excitation. This problem is reduced to solving an infinite linear algebraic equation system of the second kind which, in principle, can be solved with arbitrary predetermined accuracy via a truncation procedure. Full article

An appropriate design of a drip irrigation system in order to increase the uniformity of water distribution with a high efficiency is of importance. The first step for the design is the determination of suitable length of laterals. In order to do this, the emitter characteristics and the friction losses of new designed laterals on which the emitters are placed must be known by laboratory experiments. On the other hand, mathematical models developed can also be used for the determination of friction losses in drip irrigation laterals. In this study, a software in Visual Basic 6.0 programming language was developed and it helps analyzing the data from a new designed emitter in order to find out the main characteristics and friction losses and to obtain the optimum lateral length of the lateral in the shortest time with an acceptable accuracy in. The software included several options for the selection of in-line or on-line emitter type, pressure compensating or non-pressure compensating emitters. The software calculates the optimum lateral length based on the measurement and model equations and utilizes the step by step procedure. Optimum lateral length criterias in the software such as Cu and qvar for non-pressure compensating emitter and lateral end pressure for compensating emitter were used. The comparison of optimum lateral lengths indicated a very good agreement between the experimentally obtained results and the results from the use of mathematical models for different criteria and different slope conditions. The differences in optimum lateral lengths between the experimental and calculated values obtained from the mathematical models ranged between -0.4 and 0.7%. Full article

Since goal programming was introduced by Charnes, Cooper and Ferguson (1955), goal programming has been widely studied and applied in various areas. Parameter estimation is quite important in many areas. Recently, many researches have been studied in fuzzy estimation. In this study, fuzzy goal programming was proposed by Hannan (1981) adapted to estimation of randomized complete block design parameters. Suggested fuzzy goal programming is used for estimation of randomized complete block design parameters. Two numerical examples are used to illustrate the applicability of the suggested method. Then, the results obtained from classical method and suggested methods have been compared. Full article

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some existing techniques in literature. It is observed that FDTM can be utilized as an alternative tool for the solution of this type of problems. Full article

A new methodology for simulating the flow field inside an arteriovenous (AV) graft to vein anastomoses by the adaptive neuro fuzzy inference system (ANFIS) is presented in this study. For determining the optimal AV graft angle, an ANFIS-based model of neuro fuzzy-graft-vein (NF-GVEIN) is proposed. Therefore engineering design of the graft can be supported. The advantage of this neuro-fuzzy hybrid model is that it does not require the model structure to be known a priori, in contrast to most of the modeling techniques. A case study with real experimental data was carried out. NFGVEIN was optimized by means of selection of the algorithm among 34 ANFIS algorithms by terms of minimal error. The optimal neural network structure was determined. The optimal AV graft angle causing the least turbulence was obtained. The simulation results showed that this model is feasible for forecasting of finding the optimal AV graft angle inside AV graft to vein anastomoses with different flow rates. Full article

An assumed stress 8-node hybrid finite element is presented for buckling analysis. The formulation is based on Hellinger-Reissner variational principle. The element has 24 membrane degrees of freedom and 24 bending degrees of freedom. The stress stiffness matrix is derived by using the Green-Lagrange strains. The element performance is assessed by comparison with numerical examples. Full article

Dual numbers and dual vectors are widely used in spatial kinematics [3,5- 15,18]. Plücker line coordinates of a straight line can be represented by a dual unit vector located at the dual unit sphere (DUS). By this way, the trajectory of the screw axis of a rigid body in 3 R (the real three space) corresponds to a dual curve on the DUS. This correspondence is done through Study Mapping [8,9]. Conversely a dual curve on DUS obtained from the rotations of the DUS represents a rigid body motion in 3 R [8]. The dual Euler parameters are used in defining the screw transformation in 3 R [8], but originally in this paper these parameters are constructed from the Rodrigues and the dual Rodrigues parameters [15]. Full article

In this paper, the use of Data Envelopment Analysis (DEA) as a tool for Multiple Criteria Decision Making (MCDM) is investigated for assessing various irrigation management strategies in terms of economic, environmental and social criteria. To carry out this task, an irrigation management research project report is used for the comparison of various MCDM and DEA rankings as well as providing the required data. The DEA methods called Charnes-Cooper-Rhodes (CCR), Banker- Charnes-Cooper (BCC) and Reduced-CCR (RCCR) are employed by the integration of criteria weights through the addition of assurance regions to improve discriminating power of the analysis, and to reach the ranking of strategies. The results indicate that DEA constitutes a valuable approach to be used alternatively or in addition to MCDM, and incorporating managerial preferences into the DEA methods provide correlated results with MCDM techniques. Full article

A wide range-infrared free electron laser (IR-FEL) is being constructed for science and industrial applications in the Accelerator Technologies Institute, Ankara University. In the facility, in order to obtain electron beam with energy 40 MeV, 4.5 cell RF cavities are considered. IR-FEL system covers 2.5-250 µm wavelength range that based on 15-40 MeV e-linac and two undulators to generate up to 250 μm coherent infrared radiations. In this study, IR-FEL Resonator System parameters, mirror parameters, undulator parameters besides mirror diffraction losses are calculated and optimized with analytically and by using Optical Propagation Code and GENESIS 1.3. These Codes are also used to simulate beam behavior inside the resonator and along the undulator while GLAD Code is used for mirror diffraction losses. Full article

Lateral rigidity is a great issue in the view of structural analysis in civil engineering applications such as production of buildings, bridges, dams and roads. Furthermore, the connection properties have a remarkable role on the lateral rigidity and the tendency of structures under service loads. In fact, there aren’t any structures with perfectly rigid connections between beams and columns. Therefore, all connections performed by construction process can be defined as semi-rigid as, especially connections in steel structures. The effect of connection type on the lateral rigidity values of structures can be determined by reducing coefficients decreasing lateral rigidity with a certain extent. In the scope of this study, connection flexibility is modeled by linear elastic rotational springs for semi-rigid frames. The reducing coefficients are determined by using a computer program. Results are compared to the values predicted by artificial neural network (ANN) analyses. A strong relationship was established between calculated and predicted values. Full article

The interaction between regular water waves and the oscillating water column (OWC) geometry is presented in this work. The OWC has a vertical cylindrical geometry, with walls of negligible thickness. Water waves are generated in a numerical wave tank, with the commercial CFD code Fluent, where the dynamic mesh feature and the VOF Model is used for wave generation and the water-air interaction, respectively. The flow is assumed to be viscous, unsteady and incompressible for the numerical model. To focus on the flow inside, 3D, single phase modelling of the OWC device itself is handled by adopting a piston-like pumping flow, using the free surface elevation data found in the former model as an input. To validate the results, a simplified theoretical model of a wave energy converter, namely the Japanese multi- OWC barge Kaimei is used. The theoretical model is based on the theory of a compressible air flow where the free surface elevation is assumed to be one dimensional.
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In this paper, we have developed a new method called Generalized Taylor collocation method (GTCM), which is based on the Taylor collocation method, to give approximate solution of linear fractional differential equations with variable coefficients. Using the collocation points, this method transforms fractional differential equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Generalized Taylor coefficients. Generally, the method is based on computing the Generalized Taylor coefficients by means of the collocation points. This method does not require any intensive computation. Moreover, It is easy to write computer codes in any symbolic language. Hence, the proposed method can be used as effective alternative method for obtaining analytic and approximate solutions for fractional differential equations. The effectiveness of the proposed method is illustrated with some examples. The results show that the method is very effective and convenient in predicting the solutions of such problems. Full article

Chapter 7 of the 2007 Turkish Earthquake Code (TEC) entitled “Assessment and Strengthening of Existing Buildings” sets standards for assessment and rehabilitation of existing buildings. Linear elastic and non-linear evaluation procedures of 2007 TEC are applied to reinforced concrete buildings. 2007 TEC gives two methods for assessment and rehabilitation of existing buildings. Linear elastic and non-linear static evaluation procedures are proposed for structural evaluation. A performance-based evaluation methodology is used under three levels of earthquake ground motion intensities with different return periods. The performance acceptance criteria are based on demand to capacity ratios at critical sections for the linear evaluation procedures (equivalent seismic load method and mode superposition method) and material strains for the non-linear evaluation procedures (the non-linear static pushover analysis). Member performance limits are described for three damage levels, considering the anticipated failure mode and ductility capacity of each member. Structural performance is then calculated by accounting for the distribution of member damages over the building.. Consistency between the results of the methods used for seismic evaluation of existing buildings is of prime importance. For this purpose, an irregular structure of in plane (A3 type) and 3 story is considered. The target performance level of the building is obtained by applying the linear and the non-linear evaluation procedures. The results are given comparatively on the target performance level of the building. Furthermore non-linear procedure results are compared between 2007TEC and FEMA-440 Capacity-Spectrum Method (CSM) and Displacement- Coefficient Method (DCM). Full article

In this study, thermal stresses analysis of ZrO2 insulation coatings on Cr-Ni substrate during the cooling process was investigated. A transient thermal analysis was performed using finite element method (FEM) via ANSYS software. The temperature versus the time curve obtained from FEM solution was controlled with the temperaturetime diagram measured by a thermocouple. The results obtained from the numerical calculations were improved by the experimental measurement. Additionally, residual stresses were calculated by FEM solutions and they were compared in different points. The compressive and tensile stresses occurred in ZrO2 coating and Cr-Ni substrate owing to the different thermal expansion coefficients in each material, respectively. Full article

In the present paper, the researchers discuss the problem of weighted interval approximation of fuzzy numbers. This interval can be used as a crisp set approximation with respect to a fuzzy quantity. Then, by using this, the researchers propose a novel approach to ranking fuzzy numbers. This method can effectively rank various fuzzy numbers, their images and overcome the shortcomings of the previous techniques. Full article

In this study, an investigation of buckling analysis which includes geometric and material effects on critical load of thermoplastic-matrix composite plates with square hole is carried out by using finite element method (FEM). A finite element computer program is developed for finding critical loads. The composite plates ([0⁰/ 0⁰]₂) under transverse loading are formed by stacking four composite layers bonded symmetrically or antisymmetrically. Each layer with constant thickness is meshed into 48 elements and 228 nodes.The first-order shear deformation theory is employed in mathematical formulation. the effects on critical load by ply lamination geometry, plate thickness ratio, loading types, hole size, and material modulus ratio have been investigated. Numerical solutions are given in graphical forms. Full article

The objective of this study was to examine load-deformation characteristics at different fill layers of a high fill and to determine typical modeling parameters by using plate loading tests in a real construction site. The average value of the modulus of elasticity Eplaxis was found to be 53 MN/m2 and Poisson’s ratio was found to be 0.2 for the dense sand soil of the construction site. With proper compaction, load-deformation characteristics were found to be almost identical in different layers of the fill and very close to that of the natural soil. Full article

The power generated by wind turbines depends on several factors. Two of them are the wind speed and the tower height of wind turbine. In this study, the annual average wind speed based on the tower height is predicted using Artificial Neural Networks (ANN) and comparisons made with conventional model approach. The backpropagation multi layer ANNs were used to estimate annual average wind speed for three locations in Turkey. The Model has been developed with the help of neural network methodology. It involves four input variables-wind speed of measured location, desired height on measured location, height above ground level of measured location and Hellmann coefficient and one output variables-annual average wind speed. The model accuracy is evaluated by comparing the conventional model results with the actual measured and calculated values. Full article