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**Elastic stability of Euler columns with a continuous elastic restraint using variational iteration method.**
*(English)*
Zbl 1189.65158

Summary: An 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.

### MSC:

65L99 | Numerical methods for ordinary differential equations |

34A45 | Theoretical approximation of solutions to ordinary differential equations |

74H55 | Stability of dynamical problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

### Keywords:

variational iteration method; buckling; continuous restraint; Euler column; elastic stability
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\textit{M. T. Atay} and \textit{S. B. Coşkun}, Comput. Math. Appl. 58, No. 11--12, 2528--2534 (2009; Zbl 1189.65158)

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