Explicit solution to the large deformation of a cantilever beam under point load at the free tip using the variational iteration method-II

2013 ◽  
Vol 27 (11) ◽  
pp. 3433-3438 ◽  
Author(s):  
Hosein Ghaffarzadeh ◽  
Ali Nikkar
Keyword(s):  
Large Deformation ◽  
Cantilever Beam ◽  
Iteration Method ◽  
Explicit Solution ◽  
Variational Iteration Method ◽  
Point Load ◽  
Variational Iteration

An Explicit Solution to Continuum Compliant Cantilever Beam Problem with Various Variational Iteration Algorithms

2019 ◽  
Vol 32 ◽  
pp. 1-13
Author(s):  
Theddeus T. Akano
Keyword(s):  
Large Deformation ◽  
Cantilever Beam ◽  
Nonlinear Problems ◽  
Point Load ◽  
Research Topic ◽  
Experimental Result ◽  
Variational Iteration ◽  
Vertical Displacements ◽  
The Difference ◽  
The Continuum

The geometric nonlinearity resulting from large deformation of compliant members has continued to be an interesting research topic in nonlinear mechanics. In this study, two standard variational iteration algorithms, VIM-I and VIM-III are employed to investigate the large deformation of the continuum compliant beam under point load. The VIM is an efficient technique that bypasses the linearization process and proffers solutions to nonlinear problems. The horizontal and vertical displacements of the continuum compliant cantilever beam free end are expressed in explicit analytical forms. Numerical experiment and simulations were carried out to validate the efficacy and applicability of the semi-analytical method. The VIM-I was split into two; VIM-I(A) and VIM-I(B), with the difference being the initial approximations. The results from the VIM-I(A), VIM-I(B) and VIM-III algorithms were compared with the experimental and exact solution. The outcomes reveal that both algorithms correlated well with the analytical solution and experimental result.

scholarly journals Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

2010 ◽  
Vol 65 (5) ◽  
pp. 418-430 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

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