Elastic stability of Euler columns with a continuous elastic restraint using variational iteration method

Analysis of Tilt‐buckling of Euler Columns With Varying Flexural Stiffness Using Homotopy Perturbation Method

“…In previous works [3,4,6,7], an initial approximation was chosen as the solution of the elastic stability problems of Euler columns. In the variational iteration method an initial approximation is chosen as the solution of the linear part of governing equation, i.e., solution of Lw = 0.…”

“…Hence, a third order polynomial which is the solution of Lw = 0 for Eq. (3.7), was previously used in variational iteration analysis of buckling of Euler columns [7,4]. The same initial approximation was also used in previous works employing HPM [3,6] and is given as follows:…”

“…Atanackovic [2] examined the stability problems and equilibrium states of elastic rods in detail with Euler energy and dynamical methods for a number of problems. Coşkun and Atay [7] and Atay and Coşkun [4] studied column buckling problems for the columns with variable flexural stiffness and for the columns on elastic foundation by using variational iteration method.…”

Elastic Stability Analysis of Euler Columns Using Analytical Approximate Techniques

“…A cubic polynomial with four unknown coefficients can be chosen as an initial guess which was shown previously to be an effective one in problems related to Euler beams and columns [23][24][25][26][27][28][29].…”

“…Later on, analytical approximate techniques were used for the stability analysis of elastic columns. Coşkun and Atay [23] and Atay and Coşkun [24] studied column buckling problems for the columns with variable flexural stiffness and for the columns with continuous elastic restraints by using the variational iteration method which produces analytical approximations. Coşkun [25,26] used the homotopy perturbation method for buckling of Euler columns on elastic foundations and tilt-buckling of variable stiffness columns.…”