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Hashemi G.,Aryan Institute of Science and Technology | Ahmadi M.,Aryan Institute of Science and Technology | Aghajari S.,Iran University of Science and Technology
Asian Journal of Civil Engineering | Year: 2015

An analytical technique is used to solve the radius of curvature beam equation called the variational iteration method (VIM). VIM leads to high exactness of the solutions with only one repetition. It has been found that VIM is very prolific, rapid, functional, and do not demand small perturbation and is also sufficiently accurate to both linear and nonlinear problems in engineering. The obtained consequences show that the approximate solution is uniformly legitimate on the whole solution field in comparison with the numerical solution. VIM could simply be enlarged to other powerfully nonlinear problems and it could be found widely feasible in engineering and science. The results of this method (VIM) are compared with the obtained results of numerical solution that shows the results of the present method are in excellent agreement with numerical solution.


Ahmadi M.,Aryan Institute of Science and Technology | Hashemi G.,Aryan Institute of Science and Technology | Asghari A.,Semnan University
Latin American Journal of Solids and Structures | Year: 2014

This paper is devoted to the new classes of analytical techniques called the Iteration Perturbation Method (IPM) and Hamiltonian Approach (HA) for solving the equation of motion governing the nonlinear vibration of Euler-Bernoulli beams subjected to the axial loads. It has been found that the IPM and HA are very prolific, rapid, functional and do not demand small perturbation and are also sufficiently accurate to both linear and nonlinear problems in engineering. Comparison of the results of these methods with together and with the results of numerical solution reveals that the IPM and HA are very effective and convenient, and can be easily extended to other nonlinear systems so that can be found widely applicable in engineering and other sciences.

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