Mehmet Tarık Atay

Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method

In this paper, variational iteration method (VIM) is applied to the problem of determination of critical buckling loads for Euler columns with constant and variable cross-sections. VIM is a powerful method for the solution of nonlinear ordinary and partial differential equations and integral equations. Hence it is a suitable approach for the analysis of engineering problems where an exact solution is difficult to obtain. This study presents the application of VIM to various buckling cases and results are produced for columns with different support conditions and with different variation of cross-sections. The results obtained are accurate which show that variational iteration method is a very efficient technique in the analysis of elastic stability problems.

Analysis of Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Using Variational Iteration Method with Comparison with Respect to Finite Element Analysis

In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM), the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM) and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems.

Elastic stability of Euler columns with a continuous elastic restraint using variational iteration method

In this paper, analysis of elastic stability for continuously restrained Euler columns is conducted by means of variational iteration method (VIM). A uniform homogeneous column is assumed to be restrained along its length. The restraint considered in this study is an elastic foundation model in engineering practice and it is of great interest to foundation engineers. Hence, the variation of the critical buckling loads with the stiffness of elastic restraint is investigated using VIM for the restrained columns with different end conditions. Obtaining analytical solutions for these types of problems is not a simple procedure since the equations of stability criteria are highly nonlinear. This study presents the application of VIM for obtaining exact solutions for continuously restrained Euler columns. The study proves that VIM is a very efficient and promising approach in the elastic stability analysis of specified problems.

Comparative Analysis of Power-Law Fin-Type Problems Using Variational Iteration Method and Finite Element Method

Variational iteration method is applied to examine the temperature distribution within a single fin with a one-dimensional steady-state nonlinear heat conduction equation. Variation of temperature due to different levels of nonlinearities is analyzed. The results obtained by means of variational iteration method are compared with the results obtained from finite element method. A fourth iteration variational iteration solution is used in all cases considered. An error analysis is also conducted to evaluate the performance of proposed solution technique. The results have shown that variational iteration method is a powerful solution technique in the analysis of power-law fin-type problems.

A novel hybrid method for better evaluation: Evaluating university instructors teaching performance by combining conventional content analysis with fuzzy rule based systems

Even though engineering and applied sciences deal with numerical data, they have successfully implemented fuzzy logic by using fuzzy rule based (FRB) systems by verbalizing data. On the other hand, social sciences such as sociology, education and physiology transform verbal type data into numerical values by using Likert type scale. Despite the fact that fuzzy set theory deals with verbal data very powerfully, social science fields in general have avoided to implement it to their verbal data up until now. One of the most active research areas in education field which generates verbal data is student evaluation of teaching (SET) questionnaires which are related to Total Quality Management applications in most of the competitive universities in the world. In this paper, we propose a novel hybrid method, which combines conventional content analysis (CCA) method and FRB systems and this new hybrid method is more suitable for the verbal data obtained from SET questionnaires. This novel CCA-FRB (conventional content analysis based fuzzy rule based systems) method uses a sample of 138 junior students from Gazi University in Turkey to implement the proposed method.

Effects of Nonlinearity on the Variational Iteration Solutions of Nonlinear Two-Point Boundary Value Problems with Comparison with Respect to Finite Element Analysis

Solution of a nonlinear two-point boundary value problem is studied using variational iteration method (VIM) considering its convergence behavior due to the changing nonlinearity effects in the equation. To achieve this, steady Burger equation is first solved by using finite element method (FEM) with a very fine mesh for the comparison of results obtained from VIM. Effect of the nonlinear term in the equation that is multiplied by a constant is taken into account for five different cases by changing the corresponding constant. Results have shown that VIM is a flexible, easy to apply, and promising method for the analysis of nonlinear two-point boundary value problems with the fact that the larger the effect of the nonlinear term of the equation, the slower the convergence rate when compared to FEM solutions.

The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

The Variational Iteration Method (VIM) and Modified Variational Iteration Method (MVIM) are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM) and the Modified Variational Iteration Method (MVIM) are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

Homotopy perturbation method for free vibration analysis of beams on elastic foundation

In this study, the homotopy perturbation method (HPM) is applied for free vibration analysis of beam on elastic foundation. This numerical method is applied on a previously available case study. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, Nr. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for the case considered in this study and the differential transform method (DTM) results available in the literature.

Numerical and Soft Computing Methods for Characteristic Value Problems of ODE and ODEs Systems

1 Department of Mathematics, Nigde University, Central Campus, 51100 Nigde, Turkey 2Department of Economical, Juridical and Social Studies, University of Sannio, 82100 Benevento, Italy 3 Department of Civil Engineering, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, Turkey 4A-26 Sivasakthi Nagar, 7th Cross, Chidambaram, Tamil Nadu 608001, India 5 Alanya Management Engineering Department, Akdeniz University, Kestel Campus, 07425 Alanya, Turkey 6 Faculty of Economics and Business Sciences, University of Sannio, Via Delle Puglie 82, 82100 Benevento, Italy