Determination of Critical Buckling Loads for Variable Stiffness Euler Columns Using Homotopy Perturbation Method

2009 ◽  
Vol 10 (2) ◽  
Author(s):  
M. T. Atay
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Variable Stiffness ◽  
Buckling Loads ◽  
Homotopy Perturbation

scholarly journals ANALYSIS OF TILT‐BUCKLING OF EULER COLUMNS WITH VARYING FLEXURAL STIFFNESS USING HOMOTOPY PERTURBATION METHOD

2010 ◽  
Vol 15 (3) ◽  
pp. 275-286 ◽  
Author(s):  
Safa Bozkurt Coşkun
Keyword(s):  
Stability Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Elastic Stability ◽  
Efficient Technique ◽  
Mode Shapes ◽  
Flexural Stiffness ◽  
Buckling Loads ◽  
Homotopy Perturbation ◽  
Different Types

In this paper, the Homotopy Perturbation Method (HPM), is introduced for elastic stability analysis of tilt‐buckled columns with variable flexural stiffness. Buckling loads and corresponding mode shapes are determined considering different types of variations in flexural stiffness of columns. The proposed approach is an efficient technique for the elastic stability analysis of specified problems.

scholarly journals Free Vibration Analysis of an Euler Beam of Variable Width on the Winkler Foundation Using Homotopy Perturbation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Utkan Mutman
Keyword(s):  
Perturbation Method ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Homotopy Perturbation Method ◽  
Free Vibration Analysis ◽  
Nonlinear Problems ◽  
Variable Stiffness ◽  
Winkler Foundation ◽  
Euler Beam ◽  
Homotopy Perturbation

Homotopy Perturbation Method (HPM) is employed to investigate the vibration of an Euler beam resting on an elastic foundation. The beam is assumed to have variable stiffness along its length. HPM is an easy-to-use and very efficient technique for the solution of linear or nonlinear problems. HPM produces analytical approximate expression which is continuous in the solution domain. This work assures that HPM is a promising method for the vibration analysis of the variable stiffness Euler beams on elastic foundation. Different case problems have been solved by using the technique, and solutions have been compared with those available in the literature.

Homotopy Perturbation Method for General Form of Porous Medium Equation

2009 ◽  
Vol 12 (11) ◽  
pp. 1121-1127 ◽  
Author(s):  
Jafar Biazar ◽  
Zainab Ayati ◽  
Hamideh Ebrahimi
Keyword(s):  
Porous Medium ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Porous Medium Equation ◽  
Homotopy Perturbation ◽  
Medium Equation

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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