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

Ghaffarzadeh, Hosein; Nikkar, Ali

doi:10.1007/s12206-013-0866-4

Cited by 24 publications

(7 citation statements)

References 15 publications

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“…Deformation. There are many methods for describing a large deformation of a beam, for example, the Laplace-Padé coupling with NDHPM and HPM [10], VIM [11], and pseudolinear system [1]. In this section, we introduce the process of investigating semianalytical solution via LADM and some numerical results of pseudolinear system in [1].…”

Section: Fractional Order For Largementioning

confidence: 99%

Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

Theinchai

Chankan

Yukunthorn

2016

International Journal of Mathematics and Mathematical Sciences

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We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

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Section: Fractional Order For Largementioning

confidence: 99%

Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

Theinchai

Chankan

Yukunthorn

2016

International Journal of Mathematics and Mathematical Sciences

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“…The thickness of the specimen was designated as a variable, and there were five cases in which the thickness varied in increments of 10 mm from 25 mm to 65 mm. In the initial state, necking occurred in the DCB aluminum foam and thus, the thickness of the neck area was increased to mitigate this issue [18].…”

Section: Specimen and Materials Propertiesmentioning

confidence: 99%

Experimental and analytical verification of the characteristics of shear fatigue failure in the adhesive interface of porous foam materials

Cho

2015

J Mech Sci Technol

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In the past, many studies have been conducted to examine the effect of static load and fatigue load on the adhesive interface between two different materials or the same materials, but little research has been done on porous materials. Thus, this study was carried out to examine the effect of fatigue load on the adhesive interface formed by aluminum foam, which exhibits porous characteristics. For the experiment, five specimens were fabricated with the thicknesses varied in increments of 10 mm from 25 mm to 65 mm. The aluminum foam was bonded using the single-lap method, and MTS landmark was used to conduct the fatigue experiment. Based on the initial static experiment, the maximum reaction force at which total failure occurred in the adhesive interface was obtained, and fatigue load was applied on the lower load cell in the 10 Hz sine graph form. The results of the experiment showed that for all five of the specimens, the adhesive strength of the adhesive agent was maintained in the adhesive interface during the 5000 cycle of the fatigue load. Also, based on the correlation between displacement and repeated load cycles, it was discovered that the adhesive interface underwent total failure after a sharp displacement in the interface in all five cases when the load was repeated for more than 5000 cycles In addition, a numerical analysis was performed based on the experimental results, and the stress distribution was visualized. The numerical analysis results showed similar tendencies as the experimental results, which confirmed the reliability of the analysis results. Thus, it was deemed that it would be possible to analyze the fatigue failure behavior of actual, bonded structures made of a porous material based on the experimental and numerical analysis results obtained through this study.

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“…In the following section, to clarify the idea of the proposed method for solution of the nonlinear governing equation of a cantilever beam undergoing large deformation, the basic concept of variational iteration method-II [39,40] is firstly treated. A general nonlinear equation of th order is considered at the following form:…”

Section: Basic Concept Of Vim-iimentioning

confidence: 99%

“…Hence, after identifying the Lagrange multiplier , the variational iteration algorithm-II [39,40] is constructed as follows:…”

Section: Basic Concept Of Vim-iimentioning

confidence: 99%

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Assesment of New Analytical Method for Solving the Foam Drainage Equation

Nikkar

2014

Chinese Journal of Mathematics

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The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. In this study, a new reliable technique is used to handle the foam drainage equation. This new method resulted from VIM by a simple modification, that is, variational iteration method-II (VIM-II). It has been shown that the VIM-II is a powerful technique in obtaining accurate solutions that cannot be given otherwise by perturbation and other methods. The accuracy and convergence of the method are also investigated and compared with other methods. The results showed that there are good agreements between the results.

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

Cited by 24 publications

References 15 publications

Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

Experimental and analytical verification of the characteristics of shear fatigue failure in the adhesive interface of porous foam materials

Assesment of New Analytical Method for Solving the Foam Drainage Equation

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