Safa Bozkurt Coşkun

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.

Buckling of Euler Columns with a Continuous Elastic Restraint via Homotopy Analysis Method

Homotopy Analysis Method (HAM) is applied to find the critical buckling load of the Euler columns with continuous elastic restraints. HAM has been successfully applied to many linear and nonlinear, ordinary and partial, differential equations, integral equations, and difference equations. In this study, we presented the application of HAM to the critical buckling loads for Euler columns with five different support cases continuous elastic restraints. The results are compared with the analytic solutions.

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.

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.

Analytical Solution for Free Vibration Analysis of Beam on Elastic Foundation with Different Support Conditions

Analytical solutions for free vibration analyses of a beam on elastic foundation are obtained for different support conditions. The analytical solutions are applied on three different axially loaded cases, namely; (1) one end clamped, the other end simply supported; (2) both ends clamped, and (3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load, , acting on the beam to Euler buckling load, . The analytical solutions give results which are in excellent agreement with the variational iteration method (VIM) and homotopy perturbation method (HPM) results available in the literature for the particular problem considering all the cases provided in this study and the differential transform method (DTM) results available in the literature for the clamped-pinned case.

Transient dynamic analysis of dam‐reservoir interaction by coupling DRBEM and FEM

In this paper, time domain dynamic analysis of dam‐reservoir interaction is presented by coupling the dual reciprocity boundary element method in the infinite fluid domain and the finite element method in the solid domain. An efficient coupling procedure is formulated by using sub‐structuring method. Sommerfelds boundary condition for far end of the infinite domain is implemented. To verify the proposed scheme, numerical examples are carried out to compare with the available exact solutions and results of the finite‐finite element coupling.

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

Elastic Stability Analysis of Euler Columns Using Analytical Approximate Techniques

In most of the real world engineering applications, stability analysis of compressed members is very crucial. There have been many researches dedicated to the buckling behavior of axially compressed members. On the other hand, obtaining analytical solutions for the buckling behavior of columns with variable cross-section subjected to complicated load configurations are almost impossible in most of the cases. Some of the works related to obtaining analytical or analytical approximate solutions for the column buckling problem are provided below.